PREDICTIONS

Pre-registering the framework's claims before the data arrives

Version 11.9  |  May 31, 2026

"If we can't say how we're wrong, we can't say we're right."

THE CENTRAL CLAIM (v11.8 reframe)

TSO's central claim is that reality has three phases — Wave (quantum), Solid (classical), and Dust (below floor) — and that the Wave-to-Solid transition is an observable physical phase change at a specific coupling.

Everything else in the framework — the seven paths, the Fano plane structure, the percolation threshold pc = 0.3116, the Lindblad analogue, the Pip catalog, the constants like ν and λ — is supporting machinery. Useful, sometimes striking, but downstream of the phase structure. The framework's truth or falsity hinges on whether the phase transition exists at the predicted location with the predicted floor, not on whether any particular critical exponent comes out at any particular value.

The decisive test of this central claim is Prediction 1: a tunable Rydberg sweep through Γnet = −pc. The supporting predictions (ν, δW, peak structure, sigmoid edge, etc.) constrain which universality class governs the transition and how the supporting machinery aligns, but they do not test the central claim — only the existence of the phase transition does. Read Prediction 1's three pre-registered outcome scenarios (A, B, C) for the honest interpretation of each result.

What a successful Rydberg test would and would not prove. A positive result would establish that the Wave-to-Solid boundary is a real physical phenomenon with the predicted structure. It would not prove that TSO's seven-path explanation, Fano geometry, or Pip catalog are correct — those remain underdetermined by any single experiment. The framework can survive in modified form even if Scenario B (non-standard universality class) emerges. Only Scenario C (no transition at all) falsifies the central claim.

WHAT THIS PAGE IS

This page is the canonical list of every falsifiable claim TSO makes. It exists to solve a specific problem: predictions generated across many working sessions have been getting lost between sessions, and without a single reference document it becomes easy to unconsciously adjust claims after the data arrives. This page is the commitment. If an experiment comes back and the result does not match what is written here, the correct response is to retire the prediction rather than reinterpret it.

Each entry is flagged as either a prediction (stated before the relevant data was examined), a retrodiction (matched against data that already existed), or pre-empirical (no relevant data exists yet). Honest labeling matters because most of what frameworks call "predictions" are actually retrodictions, and this distinction affects how much evidential weight a match carries.

How to read this page. The summary table below lists every entry with its status tag. The detailed sections that follow give the specific claim, test method, falsification condition, and current evidence for each. The final section documents predictions that have been retired from the framework, with the reason for each retirement — because the track record of killing one's own claims is part of the case for taking the remaining ones seriously. The computational notebooks behind each prediction are indexed on the notebooks page.

EMPIRICAL SCOPE FINDING (v11.7, May 24, 2026)

Four pre-registered hardware tests have produced a consistent pattern: TSO's structural predictions (sign patterns, ordering relations, combinatorial structure on Fano lines) have replicated. TSO's specific-magnitude predictions on quantum hardware have not.

The four tests in this cluster:

  • Fix 4 (April 2026, lepton √mass scale): sign of the Fano-Tetrahedron prediction matches Koide mean; magnitude off by 14σ from the measured value under PDG uncertainty. The bare-vs-pole reframe is structurally interesting but the explicit QED magnitude correction has not been derived to land at the observed offset. Status: CANDIDATE, magnitude-pending.
  • P40 (May 24, 2026, Fano fidelity lock on IBM ibm_marrakesh): 6 pre-registered runs across calibration cycles. FANO infidelity 0.0895, predicted σ = 0.18058. Pre-registered criterion (a) FAILED at exactly σ/2 (ratio 0.495 ± 0.043). Sign ordering (NULL < FANO < RANDOM) preserved. Status: FALSIFIED on magnitude, signs replicated.
  • P41 (May 24, 2026, three-FANO + matched random on IBM ibm_kingston): structural sign matches across three independent Fano subgraphs (criterion A1 PASS); within-Fano coefficient of variation 30%+ (criterion A2 FAIL); FANO/RANDOM and FANO/NULL ratios below May 14 thresholds (criteria B1, B2 FAIL). Status: structural signs replicated, magnitude separation not.
  • P42 (May 24, 2026, hexagon-with-∅-at-center + path roles on IBM ibm_marrakesh): queued at IBM free-tier allowance exhaustion. Will run when next-month allowance resets or via paid plan. Pre-registered structural criteria documented; magnitude criteria deliberately omitted following the P40/P41 pattern.

The pattern is consistent enough to register as an empirical scope finding. The framework's TSO-specific content lives in the structural relations between paths (signs, orderings, three-body correlations on Fano lines), not in the specific numerical magnitudes those relations produce on a given hardware platform. Magnitude predictions remain part of the framework where they are theoretically well-derived (e.g. σ on a Rydberg array sweep through p_c) but should not be tested on platforms that are engineered to stay on one side of the percolation transition.

The platform constraint. IBM superconducting QPUs are engineered to stay above p_c (kept classical); Quandela photonic QPUs are engineered to stay below p_c (kept coherent). Neither chip is allowed to cross the transition because crossing it would mean the chip isn't functioning. The decisive TSO sigmoid prediction (Prediction 1) therefore requires a platform whose physical regime is tunable across p_c — a Rydberg neutral-atom array is the natural candidate. Until Rydberg lab access is established, all quantum-hardware-based TSO testing should be considered structural rather than quantitative.

What this is not. This is not a retirement of magnitude predictions in general. It is a narrowing of where they can legitimately be tested. The Rydberg sigmoid test (Prediction 1), the cosmic Ω_m match (Prediction 10), the syn3.0 minimal genome match (Prediction 14), and the Goldilocks kT ≈ δW band (Prediction 15) all remain quantitatively testable on their native domains — those domains are not engineered to stay on one side of p_c. What is narrowed is specifically: "test the σ magnitude on a quantum computer." That test, by the physics of how quantum computers are built, cannot succeed regardless of TSO's correctness.

What this is. An honest empirical update to what the framework claims to predict, on what platform, at what level of specificity. Four pre-registered tests is enough data to call the pattern. The framework should describe itself accurately, which means saying: on quantum hardware, TSO predicts the structure of Fano correlations, not the specific magnitudes of friction.

NOTATION UPDATE (v11.8, May 30, 2026)

Previous versions of the framework used κ for two distinct mathematical objects. This created confusion across math.html, predictions.html, and several Colab notebooks — the same symbol was doing the work of a rate constant in one formula and a critical exponent in another. v11.8 separates them into three named quantities with clean roles.

Previous symbolNew symbolRoleAsserted value
αα (unchanged)Effective branching factorαmax/(1 + λρc), αmax = 7
κ1 (in α formula)λ (lambda)Constraint screening rate constante ≈ 2.71828
κ2 (in sigmoid formula)ν (nu)Correlation-length critical exponent of percolation≈ 0.88 (3D, corrected from previously asserted 4/3)

Why the rename. α (the branching factor) is a derived quantity from S7 geometry, not a critical exponent — it kept its name because there was no confusion to clean up. λ replaces the old κ1 because it's a rate constant, not an exponent; using λ aligns the framework's notation with how rate constants are written everywhere else in physics. ν replaces the old κ2 because it is a correlation-length critical exponent in the standard sense, and using the standard symbol from Stauffer & Aharony unifies TSO's notation with the percolation literature for free.

What changed beyond names. The previous claim ν = 4/3 from 2D percolation universality was based on a "d_eff ≈ 2.18 rounds down to 2D" argument that the framework itself questioned in April 2026. v11.8 retires that claim and replaces it with ν ≈ 0.88 from 3D percolation universality, which is what direct Monte Carlo simulation of the Fano-bond model on a Z = 7 lattice actually produces. See Predictions 2 (retired) and 40 (the new ν claim) below.

The single source of truth. Notebook 1 (the reference notebook) is the canonical definition of all renamed constants. See the notebooks page for the link. Any inconsistency between this page and Notebook 1 should be reported as a bug; the notebook wins.

STATUS LEGEND

FIRM Follows directly from core axioms with no assumptions; a single decisive experiment exists or is planned.

EMPIRICALLY FIRM Numerical match to data is strong (typically < 1σ); theoretical derivation is open or incomplete. The claim is supported by what the data says, not by what the axioms force.

TESTABLE Sharp claim, specific falsification condition, data path identified.

CONDITIONAL Testability depends on another result being established first.

CANDIDATE Recently proposed result with strong numerical match; pending derivation work before promotion to FIRM.

CORRECTED Replaces a previous claim that turned out to be overstated or wrong. The original claim is kept visible in the retired section.

SUGGESTIVE Consistent with existing data but not decisive; could be coincidence or weak evidence.

SPECULATIVE Roof-level extension; probably wrong but falsifiable in principle.

RETIRED Was claimed in an earlier version; no longer part of the framework.

THE FALSIFIABILITY BOUNDARY

The 7-path lattice is not an ontological claim about the total number of dimensions in nature. It is the minimum connectivity required to recover classical three-dimensional reality, the Standard Model charge spectrum, and the Born rule from percolation geometry alone. This makes Z = 7 the falsifiability boundary of the framework: every TSO prediction that operates at Z = 7 is in principle testable against experiment.

Structure above Z = 7 may exist — the framework does not forbid it — but it lies beyond the falsifiability horizon by construction. Claims about Z > 7 are not part of TSO unless a specific falsification test is proposed alongside them. Additional paths above 7 contribute nothing measurable to classical reality or quantum statistics as currently observable; they may be real, but they are silent. TSO is defined by where its claims can be killed. Where the predictions end, the speculation begins. This page marks that line.

SUMMARY TABLE

  1. Phase transition between Wave and Solid at Γ_net = −p_c (the central TSO claim)   FIRM
  2. Critical exponent κ = 4/3 from path-rotation projection   RETIRED   (see #40 for replacement)
  3. No fermion outside charge set {0, ±1/3, ±2/3, ±1}   TESTABLE
  4. No colored leptons   TESTABLE
  5. Neutrinos are Majorana (self-conjugate Sector B class)   TESTABLE
  6. Dark matter halos are cored (inner slope 0.8–1.2), not cuspy   FIRM
  7. DM halos are spherical even for disk galaxies   FIRM
  8. DM self-interaction cross section σ/m < 1 cm²/g   SUGGESTIVE
  9. DM has no classical moment of inertia   FIRM
  10. Cosmic matter fraction Ω_m ≈ p_c = 0.3116; dark energy Ω_Λ ≈ 1−p_c = 0.6884   SUGGESTIVE
  11. Baryon asymmetry η within 19% via Walton-Chalmers/Avrami math   SUGGESTIVE
  12. CMB birefringence β ≠ 0 from cosmic chirality bias   SUGGESTIVE
  13. DESI confirms dynamical dark energy (Avrami-consistent)   SUGGESTIVE
  14. Minimal genome ≈ 473 genes with 31.5% unknowns (p_c)   SUGGESTIVE
  15. Life clusters in kBT ≈ δW band (room-temperature)   SUGGESTIVE
  16. syn3.0 unknown genes remain >70% connectivity/maintenance   TESTABLE
  17. JWST findings consistent with cosmic percolation   SUGGESTIVE
  18. J/Pip universal across hardware platforms   CONDITIONAL
  19. IBM gate-depth sweep as independent sigmoid test   TESTABLE
  20. No spontaneous coherence revival in isolated systems   FIRM
  21. Casimir-assisted coherence anomaly near 1 μm   SPECULATIVE
  22. DM diffraction around kpc-scale structures   SPECULATIVE
  23. Quantized vortex structures in DM halos   SPECULATIVE
  24. Wave-wave gravitational coupling (open question)   SPECULATIVE
  25. 25. LRD number density follows sigmoid on decline side (sublimation test)   TESTABLE
  26. 26. LEL cascade as crystallization trigger — updated S-field equation   CONDITIONAL
  27. 27. Percolation-critical metamaterial with anomalous inertial and EM properties   SPECULATIVE
  28. 28. Space Roar as Larmor radiation from W-space bobbing   SUGGESTIVE
  29. 29. Sigmoid decoherence transition width = dW = p_c − 2/7   TESTABLE
  30. 30. Peak decoherence rate dV/dΓ occurs at Γ_c, not before it   TESTABLE
  31. 31. THz spectral feature in Johnson noise of quantum-critical materials   SPECULATIVE
  32. 32. Scattering anisotropy near decoherence threshold   SPECULATIVE
  33. 33. Cosmic web cluster statistics match percolation universality class   TESTABLE
  34. 34. 3D volumetric fractal interference (separable-circuit version falsified)   NARROWED
  35. 35. Induced EMF in conductor loop spanning gravity gradient (TSO ≠ GR+Maxwell)   SPECULATIVE
  36. 36. Coupling constants run as power law at extreme scales   SPECULATIVE
  37. 37. Position uncertainty grows linearly with Lorentz factor above γ_crit   SPECULATIVE
  38. 38. Lepton √mass scale A = √E_Pip × (Z/V_tet)² (Fano-Tetrahedron candidate)   CANDIDATE
  39. 39. p_q = (1+p_c)/2 = 0.6558 — sigmoid saturation edge in extended Rydberg sweep   TESTABLE
  40. 40. Correlation exponent ν ≈ 0.88 from 3D percolation universality (replaces retired κ = 4/3)   CORRECTED
  41. 41. Rate constant λ = e in α formula (MIPT fit 0.12σ from e)   EMPIRICALLY FIRM
  42. 42. Dark matter is epi-matter: protected percolation regions (no direct detection, ever; Euclid DR1 predictions for halo profiles, axis ratios, cosmic web universality)   MECHANISM FIRM RATIO OPEN

CORE DECOHERENCE PREDICTIONS

1. Phase transition between Wave and Solid at Γ_net = −p_c FIRM

The central claim of TSO is that reality has three phases — Wave (quantum), Solid (classical), and Dust (below floor) — and that the Wave-to-Solid transition is an observable physical phase change at a specific coupling. A tunable Rydberg array is the cleanest available platform to test this because its interaction strength can actually cross the predicted threshold (unlike fixed-coupling QPUs that sit on one side). When total environmental coupling on a Rydberg array is swept through the critical value where Γ_net = −p_c, TSO predicts a discontinuous-in-character collapse of coherence (sigmoid, not pure exponential) with W bottoming out at the predicted floor W_floor = 2/7 ≈ 0.286. The shape change versus a pure exponential is approximately 35% at the transition region. This is the decisive TSO test; the framework's other quantities are downstream of the phase structure.

Type
PRE-EMPIRICAL — no dedicated experiment has been performed
Source
Direct consequence of the percolation axiom in foundation.html. The decisive TSO prediction. The central claim being tested is the existence of the phase transition, not the value of any specific critical exponent.
What this experiment actually tests (v11.8 reframe)

Earlier framings (v10–v11.7) treated this prediction as "find a sigmoid with κ = 4/3" — a single tight discriminator. v11.8 reframes the test around the phase-transition existence claim itself, with multiple supporting observables ordered by what's load-bearing for the central claim versus what's informational about the universality class.

Why the reframe. The numerical value of the correlation-length critical exponent ν is, from TSO's perspective, of undetermined origin. Standard 3D site percolation gives ν ≈ 0.88. The previously-asserted 2D-universality value ν = 4/3 has been retired (see Prediction 2 retired). The framework is fairly agnostic about which value will emerge — both are consistent with the phase transition existing. Measuring ν informs the universality class identification; it does not test the central TSO claim. The signatures below are reordered accordingly.

Experimental protocol (Rydberg physicist language)

System: Neutral-atom tweezer array, Rydberg dressing. Principal quantum number n* = 50–100 (strong van der Waals regime, C₆ ~ n*¹¹). Array spacing a tunable from R_b/2 to 2R_b where R_b = (C₆/ℏΩ)^(1/6) is the blockade radius. N ≥ 400 atoms (20×20 minimum for percolation statistics).

Independent definition of the control parameter:
Γ_net = (Ω_R / Γ_dephase) − 1
where Ω_R = Rabi coupling frequency (laser parameter), and Γ_dephase = single-atom dephasing rate measured independently by a single-atom Ramsey sequence with no drive. This is on the instrument before the sweep starts — no curve-fitting required.

Sweep: Ω_R from 0.1×Γ_dephase to 3×Γ_dephase in 15 steps (dense near Γ_net = 0). At each Ω_R: (1) prepare |+⟩ = (|g⟩+|r⟩)/√2, (2) evolve for times t ∈ {0, T/10, …, T} where T = 5/Γ_dephase, (3) apply π/2 pulse and measure. Record C(t) = Ramsey contrast at each t. 100–1000 repetitions per (Ω_R, t) point.

Analysis: At each Ω_R, fit C(t) to exponential and sigmoid models. Compare using ΔAIC. A ΔAIC > 10 constitutes strong evidence for one shape. TSO predicts the exponential wins below Γ_net ≈ 0 and the sigmoid wins at Γ_net ≈ 0. Also extract W_∞ (long-time limit) at each Ω_R and check whether it converges to W_floor = 2/7 ≈ 0.286 in the strong-coupling regime.

Signatures ordered by what's load-bearing

Tier 1 — Existence of the phase transition (the central TSO claim; decisive):

  • 1A. Does the coherence collapse occur at the predicted location Γ_net ≈ −p_c? (TSO p_c = 0.3116; the 3D site percolation threshold by independent reference.)
  • 1B. Is the collapse discontinuous-in-character (sigmoid) rather than continuous (pure exponential)? ΔAIC > 10 in favor of sigmoid at Γ_net ≈ 0.
  • 1C. Does W bottom out at the predicted floor W_floor = 2/7 ≈ 0.286 in the strong-coupling limit?

These three together establish "there is a phase transition at the predicted location with the predicted floor." That is what the experiment is for. A clean positive on all three is strong support for the central phase-structure claim regardless of what ν turns out to be.

Tier 2 — Universality class identification (informative, not load-bearing):

  • 2A. What value of ν does the sigmoid steepness give? Standard 3D percolation: 0.88. Standard 2D: 4/3 = 1.333. Other: indicates a non-standard universality class.
  • 2B. How does the universality class depend on system size (finite-size scaling)? Run at N = 100, 225, 400.
  • 2C. Does the transition width δW match 0.026? (Prediction 29.) Falsified if width > 5.2% or < 1.3%.

These constrain the theoretical interpretation but do not test the central phase-structure claim. ν = 0.88 says "3D class, the framework's lattice geometry is on track." ν = 4/3 says "non-standard class — both Belenos and Rydberg are seeing something the simple Fano-bond model misses, framework needs theoretical work." Either is informative; neither is decisive on TSO's central claim.

Tier 3 — TSO-specific multi-observable signatures (strongest support if confirmed; bonus):

  • 3A. Simultaneous sigmoid in coherence envelope AND in Wigner negativity at the same Γ_net with the same ν (the linked-sigmoid prediction in math).
  • 3B. Peak decoherence rate |dC/dt| maximal at t = t_c > 0 (the inflection point), not at t ≈ 0. (Prediction 30.) Falsified if peak at t < 0.1 t_c.
  • 3C. Convergence of measured W_floor to 2/7 across different system sizes.

These would be the harder-to-explain-by-coincidence signatures. They are not required for Tier 1 success, but they would distinguish TSO from "any 3D percolation system."

Three pre-registered outcome scenarios

To avoid post-hoc rationalization, the framework pre-registers its interpretation of three possible Rydberg outcomes before the experiment is run.

Scenario A — Phase transition observed at predicted location, sigmoid shape, ν ≈ 0.88. Strong support for the central TSO claim. 3D percolation universality consistent with the framework's lattice geometry. Belenos QPU's 1.325 measurement becomes a QPU-calibration question rather than a framework question.

Scenario B — Phase transition observed at predicted location, sigmoid shape, ν significantly different from 0.88 (e.g., 1.2–1.4 range, matching Belenos). Strong support for the central TSO claim. Non-standard universality class — both Belenos and Rydberg are seeing something the simple Fano-bond MC misses. Framework needs theoretical work to identify the actual universality class (candidates: protected percolation variants, hypergraph percolation, partial-projection done properly). The central phase-transition claim is supported; the supporting machinery needs revision.

Scenario C — No phase transition; pure exponential decay at all Γ_net. TSO's central claim — that there is a phase transition between Wave and Solid — is falsified. The framework retires. The seven-path structure, Fano geometry, Pip catalog, and percolation analogies become a coincidence pattern with no underlying physical phase boundary.

All three scenarios are honestly committed to in advance. A and B both support the central claim; only C falsifies it.

Falsification conditions (any of these falsifies the central claim)
F1: Pure exponential at all Ω_R — no shape change across the full sweep (Scenario C above).
F2: Coherence collapse occurs but NOT at Γ_net ≈ −p_c (significantly different location).
F3: W_∞ in the strong-coupling limit does NOT converge to W_floor = 2/7 (different floor or no floor).
F4: No systematic sharpening of the transition with array size N (run at N = 100, 225, 400) — would indicate the apparent transition is a finite-size artifact, not a real phase boundary.
Note: ν not matching 0.88 is NOT a falsification of the central claim — only of the specific universality class identification. See Scenario B above.
What a successful Rydberg test would and would not prove

This needs to be said clearly. The Rydberg sweep is the cleanest available test of TSO's phase-structure claim. If the result is positive (Scenario A or B above), that's strong support — but it would not prove TSO. There are too many moving parts. The seven-path structure could be wrong even if the phase transition is real. The Fano plane geometry could be coincidence even if the lattice has the right p_c. The Pip catalog and other derived constants could be retrodictive fitting even if the phase change is observable.

What a successful test would establish: that the Wave-to-Solid boundary is a real physical phenomenon with the predicted structure. That is a substantial result. It would not establish that TSO's particular explanation of why the transition has that structure is correct.

Several things hint that the framework is touching something real, even if the explanation is incomplete: (i) TSO is consistent with Gleason's theorem on probability measures over Hilbert space; (ii) TSO's bidirectional X₁ formulation is structurally analogous to Lindblad dynamics; (iii) independent groups (Rau 2009; Bianconi-Dorogovtsev 2024; Fayfar-Bretaña-Montfrooij 2022 on protected percolation) have arrived at parts of what TSO is doing from different starting points. None of these prove TSO. All three are suggestive that the framework is gesturing at structure other physicists have also noticed.

Why this is not many-body localization
MBL requires quenched disorder and produces logarithmic entanglement growth. TSO's prediction applies to homogeneous arrays (no disorder). A homogeneous Rydberg array with no disorder showing the Tier 1 signatures (sigmoid at predicted location, floor at 2/7) is not explained by MBL. This is the decisive discriminator from MBL.
Current evidence (May 30, 2026 — v11.8 update)
Suggestive only — no dedicated test yet.
Kim et al. 2024 reanalysis: withdrawn May 2026. A prior reanalysis claiming tanh beats exponential 2.75× was based on a misidentified Kim et al. dataset. A fresh audit on the correct dataset (Kim, Kim, Park, Byun & Ahn, Sci. Data 11, 111, DOI 10.1038/s41597-024-02926-9) found that the data structure (45 distinct experiments with three-parameter variation per experiment) is not suited to the four-model AIC protocol — it does not constitute a single-axis sweep of a control variable. Rydberg evidence claim is in withdrawn status pending audit of a different dataset.
— Quandela Ascella QPU (May 2026): fractal dimension d_f = 2.0000 in quantum percolation run. Consistent with TSO prediction; geometry differs from 3D site percolation.
— IBM ibm_fez (bond percolation, May 2026): p_q > p_c confirmed (gap direction). IBM ibm_kingston (site percolation, May 2026): GHZ circuit approach hits noise floor — IBM hardware is engineered to sit above p_c by design. Confirms gap structure exists on real quantum hardware but cannot measure p_c quantitatively.
— Quandela QPU ν measurements (Linear 1.138, Deep 0.836, Belenos 1.325). Under the v11.8 reframe these are consistent with the central phase-structure claim but cannot distinguish Scenarios A from B (different platforms, different universality class implications). The Rydberg sweep is the platform that can actually cross p_c.
— Priority contacts: (1) Montfrooij group, Missouri — published 3D protected percolation universality class with γ' = 1.3066 (close to but distinguishably different from 4/3); the structural overlap with TSO's wave-to-solid mechanism is direct, and they have the experimental infrastructure to propose a Rydberg sweep through standard grant channels. Outreach planned. (2) Prof. Jaewook Ahn, KAIST — Rydberg experimental group; email sent April 2026, awaiting response. See the Rydberg protocol notebook.

2. Critical exponent κ = 4/3 from path-rotation projection RETIRED (v11.8, May 30, 2026)

Originally claimed (v10–v11.7): If a sigmoid transition is observed in Prediction 1, its width parameter κ should equal 4/3 (= 1.333…). In TSO, κ was derived from path-rotation projection at the percolation transition with effective dimensionality d_eff = 7 × p_c ≈ 2.18 — argued to "round down" into the 2D universality class, which gives ν = 4/3 exactly (CFT result, Cardy).

Why retired
Three converging reasons. (1) The framework's own April 2026 self-correction already flagged that "d_eff ≈ 2.18 rounds to 2D" was a hand-wave, not a derivation, and noted ν ≈ 0.88 from 3D universality as the alternative. (2) Direct Monte Carlo simulation of the Fano-bond percolation model on the BEST_PERM Z = 7 lattice (Notebook 3, May 30, 2026) returned ν = 0.825 (variant a, "any active line") and ν = 0.738 (variant b, "directional line") — both in the 3D universality class, neither near 4/3. The 2D-inheritance claim does not survive contact with the framework's own lattice model. (3) The bulk of empirical data from Quandela QPU runs (Linear ν = 1.138, Deep ν = 0.836) averages to 0.99 — closer to the 3D prediction (0.88) than to the 2D prediction (4/3 = 1.33).
Replaced by
Prediction 40: ν ≈ 0.88 from standard 3D percolation universality. The replacement keeps the same Rydberg test as the decisive measurement; only the predicted value changes.
What was right about the original claim
The framework was right that there is a critical exponent ν in the sigmoid formula, that it should match the percolation universality class governing the wave-to-solid transition, and that the Rydberg sweep is the decisive test for it. What was wrong was the specific value: the 2D-inheritance argument via "d_eff rounds down" was an unjustified leap. The corrected ν ≈ 0.88 falls out of the lattice geometry directly without needing that step.
What this retirement does not affect
The κ → ν renaming (notation cleanup) is a separate piece of v11.8 work and does not depend on this retirement. The Rydberg test (Prediction 1) is unchanged — only the predicted value of its critical exponent has shifted from 4/3 to ≈ 0.88. Predictions 29 and 30 (width and dV/dΓ peak location) are unchanged.

20. No spontaneous coherence revival in isolated systems FIRM

An isolated quantum system with no identifiable γ_o (opening tension) input source cannot spontaneously increase its wave fraction W. Coherence cannot be restored without energy input.

Type
PREDICTION
Source
Tension asymmetry axiom in foundation.html. This is the TSO reformulation of the second law.
Test method
Observation. Any isolated quantum system with clearly zero γ_o input showing coherence increase without energy input would refute this.
Falsified if
Such a spontaneous revival is confirmed. Spin echoes, quantum erasers, and Zeno effects do NOT count — all require active γ_o pulses.
Current evidence
Consistent with all known experiments. Note: this also constitutes a reformulation of the second law of thermodynamics, which has been tested extensively.

PARTICLES AND THE STANDARD MODEL

3. No fundamental fermion with charge outside {0, ±1/3, ±2/3, ±1} TESTABLE

Under the v11.3 bidirectional X1 bond proposal with 1/3-per-bond rescaling, every Standard Model fermion charge is a non-negative integer bond count divided by 3 (down=1/3, up=2/3, electron=3/3, neutrinos=0/3). No fundamental particle should be discovered with a charge outside this set. Any discovery of a fundamental particle with a different fractional charge (e.g., 1/2, 1/4, 1/5) would retire the bidirectional-bond framing.

Type
PREDICTION — ongoing, no counter-evidence in decades of searches
Source
v11.3 bidirectional X1 bond formalism in house.html and foundation.html. The previous derivation via Q = χ_spatial / 3 (from SO(3) invariance on three spatial paths) was retired April 10, 2026 — see retired predictions below.
Test method
Particle accelerator searches, cosmic ray detectors, quark-hunting experiments.
Falsified if
Any fundamental particle with charge outside the allowed set is discovered.
Honest caveat
The bidirectional X1 formalism accommodates the SM charge spectrum as a consistency demonstration rather than a derivation — it does not yet predict why specific particles have specific bond counts. The April 5, 2026 null hypothesis test and the April 10 brutal falsification test both flagged this. The prediction holds against the SM charge set, but its specificity to TSO is weaker than originally claimed.
Current evidence
Decades of searches have found no exception. Millikan-type experiments continue to rule out non-third-integer charges at increasingly tight bounds.

4. No colored leptons TESTABLE

Charged leptons sit in the path-identity configurations where all operational X1 bonds align directionally (framework charge = ±3, SM charge = ±1) and no minority spatial path produces a color asymmetry. Under the v11.3 bidirectional-bond formalism, this predicts leptons are color singlets. No colored lepton should ever be discovered.

Type
PREDICTION
Source
Bidirectional X1 bond proposal, house.html. Previously framed via |χ_spatial|=3 cluster enumeration, retired April 10, 2026 in favor of the path-identity reading.
Falsified if
A colored lepton is discovered, or color charge is detected in any charged-lepton class.
Current evidence
Consistent with the Standard Model. No colored leptons known.

5. Neutrinos are Majorana (self-conjugate) TESTABLE

Under the bidirectional X1 bond proposal, neutrinos have zero operational X1 bonds (framework charge = 0, SM charge = 0). With no direction state to flip under conjugation, they are predicted to be self-conjugate — i.e., Majorana fermions. The photon's self-conjugacy follows from the same mechanism.

Type
PREDICTION — awaits experimental resolution
Source
Bidirectional X1 bond proposal, house.html. The original Sector B self-conjugate-class framing is superseded but yields the same conclusion under the v11.3 reading.
Test method
Neutrinoless double beta decay experiments (GERDA, MAJORANA, CUORE, KamLAND-Zen, LEGEND). A positive detection would confirm Majorana nature.
Falsified if
Neutrinos are definitively shown to be Dirac fermions (distinct from antineutrinos).
Supported if
Neutrinoless double beta decay observed at rates consistent with Majorana masses.
Current evidence
Current lower bounds on the half-life for 0νββ are > 10²⁶ years. No definitive detection. The question remains open.

DARK MATTER AND GRAVITY

6. Dark matter halos have cored inner profiles (slope 0.8–1.2) FIRM

Dark matter is wave-state matter (S < p_c). Quantum pressure (Heisenberg uncertainty applied to wave-state mass) resists collapse to a point. DM halos should have cored inner density profiles with logarithmic slopes in the range 0.8–1.2, systematically more cored than the NFW prediction of ~0.4.

Type
PARTIAL RETRODICTION, ONGOING PREDICTION — the core-cusp problem predates TSO, but Euclid's dwarf galaxy survey provides new data
Source
TSO v6.1 and v9.2 DM analysis, unchanged through v11.6. Follows directly from the "DM is wave-state" axiom.
Test method
Weak lensing and galaxy-galaxy lensing of dwarf galaxies. Euclid (launched 2023, releases ongoing) will provide this data at unprecedented precision and sample size.
Falsified if
Euclid measures NFW-like inner slopes (~0.4) across the dwarf galaxy sample with no cored population, OR systematic slopes outside the 0.8–1.2 range.
Supported if
Euclid finds inner slopes clustering in the 0.8–1.2 range with low scatter.
Current evidence
Existing observations (de Blok 2010, and many others) show cored profiles preferentially in dwarf galaxies. The core-cusp problem is a real tension in ΛCDM. TSO is consistent with the observed direction, but Euclid will sharpen the test.

7. DM halos are spherical even for disk galaxies FIRM

Wave-state matter has no classical moment of inertia — angular momentum lives in the phase, not in bulk rotation. DM halos cannot rotate rigidly with the baryonic disk, so halos around disk galaxies should remain spheroidal rather than being flattened by rotation.

Type
PARTIAL RETRODICTION — existing data consistent; Euclid can test across much larger samples
Source
TSO v6.1 DM rotation analysis, unchanged through v11.6
Test method
Weak lensing shape measurements of DM halos around disk galaxies, correlated with disk orientation. Euclid's shear maps provide this directly.
Falsified if
DM halos show strong systematic flattening aligned with disk orientation, OR halo oblateness correlates strongly with disk rotation speed.
Supported if
Halos remain spheroidal regardless of disk orientation.
Current evidence
DM halos are observed to be roughly spherical to mildly triaxial. No strong correlation with disk orientation has been found.

8. DM self-interaction cross section σ/m < 1 cm²/g SUGGESTIVE

Wave-state matter does not undergo classical collisions. Dark matter should show effectively frictionless self-interaction, with self-interaction cross section per unit mass well below the ~1 cm²/g limit set by cluster collision observations.

Type
RETRODICTION — Bullet Cluster data existed before TSO
Source
TSO v6.1 friction analysis. The TSO-predicted friction timescale is ~15 Gyr, longer than the age of the universe.
Test method
Galaxy cluster collision observations, halo shape surveys, dwarf galaxy dynamics.
Falsified if
Multiple Bullet-Cluster-like events show DM slowing significantly, OR σ/m measured to be >> 1 cm²/g consistently.
Current evidence
Clowe et al. 2006 (Bullet Cluster) is the canonical example. Galaxy mergers, halo shapes, and satellite galaxy survival are all consistent. The one anomalous case (Abell 520 "dark core") is controversial and may have projection-effect explanations.

9. Dark matter has no classical moment of inertia FIRM

Moment of inertia I = ∫ r² dm requires mass at definite positions. Wave-state DM is delocalized and carries angular momentum in its phase, not in bulk rotation. The "rotation" observed in galaxies is baryons moving through the DM potential well, not the DM itself rotating with the galaxy.

Type
PREDICTION
Source
TSO v6.1 DM analysis, unchanged through v11.6
Falsified if
DM halos are observed to rotate as solid bodies synchronized with the disk, OR halo shapes show clear rotational flattening tracking disk rotation.
Current evidence
Consistent with observations: DM halos do not show disk-synchronized rotation. This is standard in the field and not unique to TSO, but TSO provides a physical reason for it that other DM models do not.

COSMOLOGY

10. Cosmic matter fraction Ω_m ≈ p_c = 0.3116; dark energy Ω_Λ ≈ 1−p_c = 0.6884 SUGGESTIVE

The fraction of the universe that has crystallized into matter should equal the percolation threshold p_c = 0.3116. The inactive, decoherent remainder 1−p_c = 0.6884 should equal the dark energy fraction Ω_Λ.

Type
RETRODICTION — Ω_m and Ω_Λ measurements predate TSO
Source
Phase interpretation of the cosmic state, foundation.html. Dark energy extension: inactive bonds (below classical percolation threshold) = decoherent vacuum energy. v11.6 stress test.
Test method
Improved measurements of Ω_m and Ω_Λ from Planck, Euclid, DESI, SDSS, and LSST.
Falsified if
Ω_m turns out to differ significantly from p_c under improved measurements (e.g., outside 0.28–0.34), or Ω_Λ differs significantly from 1−p_c (outside 0.66–0.72).
Current evidence (v11.6)
Planck 2018: Ω_m = 0.3111 vs p_c = 0.3116. Error 0.16%. ✓
Planck 2018: Ω_Λ = 0.6889 ± 0.0056 vs 1−p_c = 0.6884. Error 0.07%, within 1 sigma. ✓
Both matches noticed after p_c was computed from lattice geometry — not fitted.
Structural note: the percolation threshold p_c = 0.3116 appears to partition the universe: bonds active (classical matter) vs bonds inactive (dark energy). Physical derivation of why inactive bonds = cosmological constant is Open Problem 65 on roof-open.
DESI DR2 caveat: In CPL model (w₀wₐCDM), DESI DR2 prefers Ω_m ≈ 0.385 — outside the predicted range. Model-dependent. Standard ΛCDM value remains stable.
Structural upgrade
Ω_m ≈ p_c is now understood as part of a broader geometric claim: the cosmic web geometry should match 3D percolation universality class. See Prediction 33.

11. Baryon asymmetry η within 19% via metallurgical math SUGGESTIVE

Applying the Walton-Chalmers (1959) competitive crystal growth formula and Avrami (1939) phase-change kinetics to the cosmic solidification process gives η = δW^d_eff / N^(d_eff/2) × f^(1/n) ≈ 7.26 × 10⁻¹⁰. Observed: 6.1 × 10⁻¹⁰. Ratio 1.19×.

Type
RETRODICTION — observed η predates TSO
Source
Baryon asymmetry notebook indexed at notebooks.html#cosmology. Every parameter pre-fixed from lattice geometry or cosmological observation. Zero fitting.
Falsified if
Improved measurements of η shift it outside the 19% tolerance band, or if the metallurgical formalism is shown to be inapplicable to cosmic solidification.
Current evidence
η is measured precisely from BBN and CMB; the value is stable. The 19% residual is within the precision of the mushy-zone competitive-growth approximation in metallurgy.

12. CMB birefringence β ≠ 0 from cosmic chirality bias SUGGESTIVE

If cosmic solidification required a chirality bias (which is what TSO uses to explain the baryon asymmetry in prediction 11), the CMB should show a small rotation of polarization angles. The Standard Model predicts β = 0.

Type
PARTIAL PREDICTION — the sign of the effect was predicted; magnitude not specified in advance
Source
roof-chirality.html
Test method
CMB polarization analysis from Planck, WMAP, ACT, and future CMB-S4 experiments.
Falsified if
Improved CMB polarization analysis converges on β = 0 at high significance.
Current evidence
Minami & Komatsu 2020 reported β ≈ 0.35° from Planck + WMAP. ACT DR6 reports β ≈ 0.264° at 4.6–5σ. Direction consistent with TSO, but TSO does not predict the specific magnitude, which weakens the test.

13. DESI confirms dynamical dark energy (Avrami-consistent) SUGGESTIVE

The cosmic solidification process in TSO is ongoing and should produce time-evolving effective dark energy behavior consistent with Avrami crystallization kinetics. This predicts a weak but non-zero equation-of-state evolution w(z), rather than the constant w = −1 of a pure cosmological constant.

Type
PREDICTION — DESI DR2 published; full 5-year results expected 2027
Source
Pending-tests section of llms.txt. Avrami kinetics imply time-dependent growth factors.
Test method
DESI (Dark Energy Spectroscopic Instrument) DR2 and beyond. Constraint on w(z) evolution. Full 5-year survey results expected 2027 will be far more decisive.
Falsified if
DESI full 5-year results confirm w = −1 constant at high precision with no evolution.
Current evidence
DESI DR2 (released March 19, 2025; extended dark energy analysis by Lodha et al., Phys. Rev. D 112, 083511, October 2025) — gains support. BAO measurements from 14+ million galaxies and quasars show the data fit better with w₀ > −1 and wₐ < 0 — dark energy that was stronger in the past and weakening now. Combined DESI DR2 + CMB + supernovae yields a 2.8–4.2σ preference for dynamical dark energy (varying by SN compilation used). Crucially, this preference did not weaken from DR1 to DR2 — it held with the larger dataset. A principled statistical combination yields 3.1σ exclusion of ΛCDM from DESI + CMB alone, without supernovae. The direction is consistent with TSO's prediction of ongoing Avrami-type crystallization.

Honest caveat: The combined CMB+DESI+SN result is not fully robust due to tensions among those three datasets when analyzed independently. Additionally, TSO still does not provide a specific predicted w(z) curve to compare against — the prediction calls the direction (w ≠ −1, evolving) but not the shape, which weakens its distinguishing power. The 2027 full-survey results will be decisive. Status upgraded from TESTABLE to SUGGESTIVE, April 18, 2026.

BIOLOGY AT pc

14. Minimal genome ≈ 473 genes with 31.5% unknowns SUGGESTIVE

Monte Carlo of a minimal stable spanning cluster on a Z = 7 lattice gives 475 ± 36 nodes. JCVI-syn3.0 (Hutchison et al. 2016) has 473 genes, of which 149 were unknown at publication. The fraction 149/473 = 0.315 matches p_c = 0.3116 to 1.1%.

Type
RETRODICTION — syn3.0 was published before the TSO match was noticed
Source
Life-at-p_c work indexed at notebooks.html#other
Test method
Replication in other minimal-cell projects. JCVI's next-generation minimal cells, Mycoplasma florum work, and synthetic biology projects targeting minimal genomes.
Falsified if
Other minimal genomes converge on values significantly different from ~475 or unknown fractions significantly different from p_c.
Current evidence
syn3.0 is currently the only minimal genome of its kind. Replication is pending.

15. Life clusters in kBT ≈ δW band (room-temperature Goldilocks zone) SUGGESTIVE

Life should operate at temperatures where thermal coupling energy kBT approximately equals δW ≈ 0.026 eV, giving a narrow habitability band centered around 300 K. Known life spans 255 K (psychrophiles) to 395 K (hyperthermophiles), all within a factor of 1.31 of the crossing temperature.

Type
RETRODICTION — biological temperature ranges were known before TSO
Source
δW geometric calculation meets kBT. Noted after δW was computed, not fitted.
Falsified if
Life is discovered operating at temperatures where kBT differs from δW by more than a factor of ~3 without compensating mechanisms, OR silicon-based life is discovered at temperatures where the δW match fails.
Supported if
Consistent with current observations. Silicon life remains speculative and no examples exist.
Current evidence
All known life falls in the predicted band. Vattay et al. 2014 on quantum biology at the edge of chaos provides independent support that criticality at biological temperatures enhances quantum coherence.

16. syn3.0 unknown genes should remain >70% connectivity/maintenance TESTABLE

As gene function annotations improve for the 149 unknown genes in syn3.0, the fraction identified as connectivity or maintenance proteins (rather than metabolic enzymes) should remain above 70%. This is consistent with TSO's picture of a minimal cell as a spanning cluster near percolation criticality, where most genes exist to hold the topology together rather than catalyze reactions.

Type
PREDICTION — ongoing as annotations improve
Source
syn3.0 annotation audit work indexed at notebooks.html#other. Bias-corrected measurement (frozen mechanical classifier, not hand-labeled): ~48% connectivity/maintenance vs ~26% baseline, odds ratio 2.6, p ≈ 4×10⁻⁵. An earlier 73% hand-classified estimate was retired for bias.
Test method
PROST gene-by-gene verification, ongoing annotation updates, functional characterization studies.
Falsified if
The bias-corrected enrichment vanishes — i.e., the connectivity fraction drops to the ~26% baseline (no enrichment) as annotation improves, or the odds ratio falls to ~1. (The bias-corrected value is already ~48%, about half the retired hand-classified figure; the surviving claim is the enrichment over baseline, OR 2.6, not a specific high percentage.)
Current evidence
~48% connectivity/maintenance vs ~26% baseline (OR 2.6, p ≈ 4×10⁻⁵), bias-corrected. The robust piece is the scale-free PPI topology; the single-number fraction match (149/473 ≈ pc) is weak on its own.

OBSERVATIONAL COSMOLOGY

17. JWST findings consistent with cosmic percolation SUGGESTIVE

Five JWST findings are consistent with TSO's cosmic phase diagram: early massive galaxies (crystallization nucleation sites), Little Red Dots as dust-phase objects, cosmic web structure at percolation threshold, unexpected metal enrichment timing, and the absence of expected population III evidence.

Type
RETRODICTION — JWST data is being re-interpreted rather than predicted
Source
jwst.html
Test method
Continued JWST observations; direct comparison to ΛCDM predictions for the same phenomena.
Falsified if
JWST observations converge on explanations that specifically contradict TSO's phase structure (e.g., Little Red Dots turn out to be mundane dust-obscured AGN with no phase-transition signature).
Current evidence
Five findings described on the JWST page are consistent with TSO. None is a decisive test. This is the weakest category of support — "not contradicted."

THE PIP FRAMEWORK

18. J/Pip is universal across hardware platforms CONDITIONAL

If the Pip framework is physically meaningful, the energy cost per Pip of γ_o should be approximately the same (within an order of magnitude) across independent hardware platforms: photonic beam splitters, superconducting qubits, trapped ions, Rydberg arrays, and NV centers. The photonic anchor gives J/Pip ≈ 4.76 × 10⁻²² J at 800 nm.

Type
PREDICTION — conditional on independent calibrations being extracted
Source
Pip catalog work, April 2026. Current state: only photonic anchor is rigorously extracted; biological and other estimates rely on analogical reasoning and are not independent.
Test method
Fit published decoherence curves from superconducting qubit, ion trap, Rydberg, and NV center platforms to the percolation sigmoid form. Extract effective γ per event for each. Compute J/Pip per platform. Check whether values cluster.
Falsified if
Independently-extracted J/Pip values from 3+ hardware platforms span more than 3 orders of magnitude. In this case, the Pip unit is per-platform bookkeeping and should be labeled as such.
Supported if
Independent values agree within ~1 order of magnitude. This would promote "Pip" from accounting convention to a candidate physical quantity.
Current evidence
Only one independent measurement (γ_BS from Quandela). The null hypothesis test of April 5, 2026 showed that analogical estimates for ATP and ion channels are circular and do not constitute independent calibrations. Pending: IBM gate-depth experiment (prediction 19).

19. IBM gate-depth sweep reveals sigmoid transition TESTABLE

A sequential gate fidelity experiment on IBM superconducting qubits, sweeping the number of sequential two-qubit gates, should show a sigmoid transition in fidelity as cumulative Γ_C crosses −p_c. The fit should yield γ per gate as an independent Pip calibration point, complementary to the Quandela γ_BS measurement.

Type
PREDICTION — IBM credits available; experiment pending design and execution
Source
April 5, 2026 session: the original retirement of IBM as a sigmoid test platform was based on idle T2 measurements. A sequential-gate sweep is analogous to Quandela's beam-splitter sweep and should be able to reach the critical coupling via cumulative Γ_C.
Test method
Run sequential CNOT or entangling-gate sequences of depth N = 1 through 20 on 2–4 qubits. Measure fidelity at each depth. Fit both exponential decay and percolation sigmoid. Compare AIC. See IBM notebooks.
Falsified if
Pure exponential fidelity decay dominates with no sigmoid knee — confirming the original retirement.
Supported if
Sigmoid fit beats exponential, AND the extracted γ/gate gives a J/Pip value consistent with the Quandela anchor (within order of magnitude).
Current evidence
IBM v2 site percolation (ibm_kingston, May 2026) hit noise floor before signal emerged — hardware is engineered above p_c. The gate-depth sweep variant remains untested. See IBM v2 percolation notebook.

SPECULATIVE PREDICTIONS

These follow from TSO's axioms but are not considered load-bearing. Each could fail without retiring the framework, but each is in principle falsifiable.

21. Casimir-assisted coherence anomaly near 1 μm SPECULATIVE

If the earlier Casimir-at-1μm result survives rederivation, free-space cavities with separations near 1 μm should show an anomaly in their vacuum noise behavior or coherence times compared to cavities at 100 nm or 10 μm. The γ_Casimir per vacuum mode is π/360 ≈ 28 Pips — geometric and distance-independent per mode, but the mode count depends on geometry.

Type
PRE-EMPIRICAL
Source
April 4, 2026 Casimir re-derivation in the Pip catalog work
Falsified if
Precision coherence measurements across 100 nm–10 μm cavity spacings show monotonic behavior with no feature near 1 μm.
Current evidence
None. This prediction has not been extracted from existing cavity QED data.

22. DM diffraction around kpc-scale structures SPECULATIVE

Wave-state DM with coherence length ξ ~ 1 kpc should diffract around structures smaller than ξ. Dwarf galaxies at r ~ 1 kpc should show anomalously extended halos compared to naive scaling from larger galaxies. Structures much larger than ξ (big galaxies) can hold DM normally; structures at or below ξ experience diffraction.

Type
PREDICTION
Source
TSO v6.1 DM optics analysis
Test method
Comparison of DM halo extent versus baryonic radius across a wide mass range, specifically looking for deviations at the dwarf galaxy scale.
Falsified if
Halo extent scales smoothly with baryonic radius across all mass scales with no anomaly at kpc.
Current evidence
Dwarf galaxies do show relatively extended halos, but this could have many explanations. The ξ value in TSO is not sharp enough to make this a decisive test.

23. Quantized vortex structures in DM halos SPECULATIVE

If DM halos carry angular momentum, wave-state matter cannot rotate classically but can form quantized vortex lines (analogous to superfluid helium). Vortex substructure should be detectable via gravitational lensing or stellar velocity anomalies.

Type
PREDICTION
Source
TSO v6.1 superfluid DM analogy
Test method
High-resolution lensing of galaxies with measurable angular momentum. Detection of periodic density fluctuations or velocity features.
Falsified if
High-precision lensing shows smooth DM distribution with no vortex signatures in rotating halos.
Current evidence
None at required precision.

24. Wave-wave gravitational coupling (open question) SPECULATIVE

Coherent light might couple to wave-state DM differently than incoherent light does, because interaction with solid matter can cause partial decoherence of the test particle. This could manifest as different effective lensing for coherent versus thermal light sources through the same DM distribution.

Type
OPEN QUESTION — not a sharp prediction; included for completeness
Source
TSO wave-wave coupling exploration. Explicitly labeled in that document as "speculative, not a prediction."
Falsified if
Coherent and incoherent light show identical lensing through the same source.
Current evidence
No direct test exists. The required experiments (coherent laser through DM-dominated regions) are currently beyond technology.
Honest note
This prediction has no derived mechanism and is held very loosely. It is included here only so it is not silently dropped from the framework's history.

27. Percolation-critical metamaterial with anomalous inertial and EM properties SPECULATIVE

A material engineered to have effective connectivity Z_eff ≈ 7 and tuned (via doping, pressure, temperature, or quantum critical control parameter) so that its wave fraction W approaches p_c should display measurable anomalies in three properties simultaneously: reduced effective inertia, anomalous electromagnetic transparency, and amplified sensitivity to external Γ perturbations. None of these effects is predicted by standard condensed matter theory for a conventional material at its critical point; they would be specific signatures of the percolation-criticality picture of inertia and gauge coupling.

Type
PRE-EMPIRICAL — pre-registered April 18, 2026, before any candidate material has been synthesized
Source
TSO three-phase model and the criticality-amplification argument in foundation.html. Inertia emerges from full crystallization; partial decrystallization should reduce it. EM coupling requires definite spatial position; partial wave-state restoration should reduce it. Near a critical point, small external perturbations produce large responses.
Predicted anomalies
(a) Reduced effective inertia. Inertia is a fully-crystallized-phase property in TSO. A material at W ≈ p_c is ~31% de-crystallized, meaning its resistance to acceleration should be measurably lower than its rest mass would predict under classical mechanics.

(b) Anomalous EM transparency. Wave-state matter (high W) does not couple to classical EM fields — this is why dark matter is electromagnetically invisible in TSO. A material tuned to p_c should show partial EM transparency: reduced reflectivity, anomalous skin depth, and reduced radar cross-section relative to a conventional material of the same mass and geometry.

(c) Criticality amplification. Near p_c, small external Γ perturbations produce disproportionately large W responses. The material would be anomalously sensitive to electromagnetic, gravitational, or decoherence inputs — a candidate for highly efficient field-coupling applications.
Test method
Synthesize candidate materials near known quantum phase transitions (heavy-fermion compounds, quantum spin liquids, topological semimetals near Lifshitz transitions) and measure: (1) effective inertial mass via precision pendulum or torsion balance versus gravitational mass, looking for m_inertial / m_gravitational ≠ 1; (2) EM reflectivity and skin depth as a function of proximity to the quantum critical point; (3) sensitivity to weak external field perturbations as a function of tuning parameter (pressure, doping, magnetic field) through the critical point.
Falsified if
Materials tuned through quantum critical points show no anomaly in the inertial-to-gravitational mass ratio, no anomalous EM transparency, and no amplified sensitivity to external perturbations — i.e., all properties scale continuously and conventionally through the transition with no feature at p_c specifically.
Supported if
Any of the three predicted anomalies is measured at or near a quantum critical point in a material whose effective connectivity approaches Z = 7. A non-unity m_inertial / m_gravitational ratio at the critical point would be the most decisive single result, as it is the most specific to TSO and the hardest to explain by conventional means.
Honest caveat
This is firmly Roof-level speculation. The jump from TSO's mathematical W field to an engineered material with tunable W is large and the path is not derived — it is analogical. The prediction that quantum critical materials should show these anomalies is not unique to TSO; some of these effects (anomalous EM properties near QCPs, enhanced susceptibility) are already studied in condensed matter physics under different theoretical frameworks. What TSO adds is the specific prediction of a non-unity inertial-to-gravitational mass ratio, which is not predicted by standard condensed matter theory and would be a genuinely TSO-specific result. Do not cite this prediction as established TSO — it is an extrapolation from the framework, not a consequence of its core axioms.

LRD SUBLIMATION AND THE LEL CASCADE

These two entries were added April 18, 2026, following a numerical test of the LRD density distribution and the recovery of the Lower Entanglement Limit (LEL) cascade mechanism from TSO v6.3. They are related: prediction 26 gives the mechanistic reason prediction 25 expects a sigmoid rather than an exponential.

25. LRD number density follows a sigmoid on the decline side (sublimation test) TESTABLE

Little Red Dot (LRD) comoving number density n(z) should follow a sigmoid curve on the decline side (z ≈ 4.5 → 1.5), not a simple exponential or power law. The decline decelerates and flattens at low redshift rather than continuing log-linearly. This is because LRD disappearance is driven by a cascade sublimation mechanism — dust-phase nodes converting to wave-phase as surrounding solid-phase Γ_c pressure builds — not by independent random dissolution. Phase transitions triggered by cascade/nucleation produce sigmoid density curves; independent random dissolution produces exponential.

Type
PREDICTION — pre-registered April 18, 2026, before the z=1–2 data is published
Source
TSO three-phase model (jwst.html): LRDs are dust-phase nodes (W < 2/7). As the early universe cooled into the solid phase, Γ_c pressure increased and drove sublimation (dust → wave, bypassing solid). Mechanistic basis: LEL cascade (prediction 26). The cascade structure is what makes the decline sigmoid-shaped rather than exponential.
Specific claim
The sigmoid inflection point falls at z ≈ 2.5–3.5 (cosmic time t ≈ 2.0–2.5 Gyr). At z ~ 1–1.5, n(z) should noticeably flatten — the decline rate should decelerate relative to what a straight log-linear fit through the z=2–5 data would predict.
Test method
LRD counts at z = 1–2 from ground-based surveys (HSC/COSMOS, CDFS). Ma et al. 2025 already reaches z~1.7. One additional bin at z ~ 1.2 would likely resolve the test. A sigmoid is distinguishable from an exponential at its tail — where the decline decelerates and flattens — not at the peak. The Kocevski et al. 2025 histogram (if binned at 8–12 bins rather than the 4–5 redshift bins currently publicly available in summary form) would also suffice.
Falsified if
n(z) at z = 1–2 continues declining log-linearly through the range, with no deceleration or flattening — i.e., the decline is consistent with pure exponential or power-law at all sampled redshifts. A straight line in log(n) vs. t space all the way to z ~ 1 would retire the sublimation mechanism.
Supported if
n(z) shows a statistically significant deceleration in its decline below z ~ 2, with the sigmoid fit (R²) beating the exponential fit by ΔR² > 0.05 on a dataset with ≥ 6 decline-side bins.
Current evidence
Numerical test run April 18, 2026, using published data from Kocevski et al. 2025 (341 LRDs, z=2–11) and Ma et al. 2025 (ground-based z < 4). Result: 4 data points on the decline side — sigmoid and exponential statistically indistinguishable (both R² = 0.9484, RMSE = 0.105 dex). Power-law marginally better (R² = 0.9833). The sigmoid optimizer found an unphysical inflection at t₀ = −10 Gyr, indicating no S-curve inflection is yet visible in the available data. The test is data-limited, not model-limited. Diagnosis: the z = 1–2 tail data needed to see the flattening is precisely the range that ground-based surveys are now beginning to probe. One more data point at z ~ 1.2 likely resolves the test.
Honest caveat
This prediction is labeled TESTABLE rather than FIRM because the LRD dust-phase interpretation is from March 2026 (newer and less tested than the percolation core). The sublimation mechanism is physically motivated but not yet independently validated. A sigmoid result would be strong support; an exponential result would retire the sublimation mechanism but not necessarily the dust-phase classification of LRDs.

26. LEL cascade as crystallization trigger — updated S-field equation CONDITIONAL

Crystallization in TSO is not simply driven by Γ exceeding Γ_c. It requires local entanglement entropy E to drop below a Lower Entanglement Limit (LEL). The original S-field equation treats the decoherence term as always-active; the LEL-revised equation adds a Heaviside step function that makes crystallization conditional on the entanglement state of the local region:

∂S/∂t = DS∇²S + (Γ/Γc) × Θ(ELEL − E) − λS(1 − Γ/Γc) − V₀S(S − pc)(S − 1)

where Θ is the Heaviside step function, E is local entanglement entropy E(x) = −Tr(ρlocal ln ρlocal), and ELEL is the lower threshold. The term is active (= 1) only when E < ELEL — i.e., when entanglement has dropped below the level needed to maintain quantum coherence. The decoherence dynamics of entanglement are governed by dE/dt = −Γ × E + (generation rate), so high Γ drives E down toward the threshold.

Type
PRE-EMPIRICAL — theoretical update; the equation form is a prediction about the structure of crystallization dynamics
Source
TSO v6.3 (Lower Entanglement Limit section, recovered April 18, 2026). The LEL concept was part of an earlier version of TSO and predates the current percolation/three-phase formulation, but was not yet incorporated into the main S-field equation. The analogy: LEL in combustion physics is the concentration below which a flame cannot propagate; TSO LEL is the entanglement below which quantum coherence cannot be maintained and crystallization becomes self-sustaining.
Physical consequences
(a) Crystallization is a cascade: a local region that drops below LEL crystallizes, which reduces entanglement in neighboring regions, which may then also cross LEL. This is why the density curve is sigmoid rather than exponential (prediction 25).

(b) DM is wave-state permanently because Γ_DM ≈ 0 means E_DM never drops below LEL. The step function never activates for DM. This gives a mechanistic reason (not just a label) for why DM doesn't crystallize.

(c) Baryons cross LEL almost immediately after the Big Bang because Γ_baryon >> 0. The initial cascade from ψ-space → classical spacetime was a LEL cascade, not a smooth uniform transition.
Test method
Numerical simulation: implement the LEL S-field equation and compare density evolution curves to the original equation without the step function. The LEL version should produce sigmoid-shaped density curves; the original should produce approximately exponential. If the LRD redshift distribution (prediction 25) turns out to be sigmoid, this is indirect support for the LEL mechanism over the continuous Γ model.
Falsified if
Prediction 25 fails (LRD decline is exponential, not sigmoid), AND the Rydberg sigmoid test (prediction 1) shows that coherence decay is continuous with no threshold behavior. A smooth, threshold-free decoherence curve would be inconsistent with the step function form.
Supported if
LRD decline is sigmoid (prediction 25 confirmed), AND the Rydberg experiment shows a sharp onset of sigmoid behavior rather than a gradual onset — consistent with a threshold mechanism.
Conditional note
This entry is CONDITIONAL on prediction 1 (Rydberg sigmoid) being confirmed. The LEL step function is a natural theoretical extension, but its empirical necessity over the simpler continuous Γ model has not been established. It is included here to pre-register the equation form before any simulation or experiment tests it.

HEISENBERG, PROJECTION, AND THE SPACE ROAR

These five entries follow from a single theoretical development: Heisenberg Uncertainty is not an axiom but a consequence of wave-state objects projecting into 1 or 2 spatial dimensions rather than all 3 simultaneously, drawing from a finite probability fuel budget. A wave-state object doesn't have a simultaneous x, y, z address — not because we can't know it, but because it isn't there to be known. Full observability requires x, y, z extension, which requires the spanning cluster to close in all three dimensions. Virtual particles never close. Semi-crystallised matter partially closes, bobs under γ_c fluctuations, and radiates by Larmor's formula. Predictions 29 and 30 are testable with the same Rydberg experiment as Prediction 1. The projection falsification suite that generated all five entries is indexed at notebooks.html#rydberg.

28. Space Roar as Larmor radiation from W-space bobbing SUGGESTIVE

The ARCADE 2 experiment (2006) detected an isotropic radio background six times louder than all known sources combined — unresolved for nearly two decades. TSO identifies the source as Larmor radiation from electrons in semi-crystallised equilibrium. These electrons are held at W ≈ p_c by the balance between Γ = Σγ_c tension (pulling toward crystallisation) and exhausted probability fuel (insufficient to complete it). Individual γ_c fluctuations jostle each electron's W value — this is W-space bobbing. A bobbing charge is an accelerating charge. Larmor's formula gives the power: P = q²a² / (6πε₀c³). Across cosmological volumes of semi-crystallised matter, this is a continuous, isotropic, synchrotron-spectrum signal from no point source — exactly matching the Space Roar's observed character.

Type
RETRODICTION — Space Roar detected 2006; TSO interpretation derived April 2026
Source
Projection falsification suite, Test 5. Γ = Σγ_c (not a uniform field); observability requires x, y, z extension; W-space bobbing → Larmor emission. The ball-in-airstream analogy: air stream too weak to push the ball out of the tube, but strong enough to hold it at some level. Fluctuations in the stream make the ball bob. The bob is the emission.
Numerical estimate
Larmor power density from semi-crystallised cosmic electron density, W-fluctuation amplitude δW = dW = 0.02589, bobbing frequency ω_bob = kT_CMB/ℏ ≈ 3.6 × 10¹¹ Hz: estimated power density ≈ 1.75 × 10⁻³² W/m³. ARCADE observed excess ≈ 10⁻³⁴ W/m³. Ratio ≈ 175× (2.2 orders of magnitude). For a rough first estimate with no free parameters fitted, this is order-of-magnitude consistent. Parameter refinement — particularly the bobbing frequency and the semi-crystallised fraction — could close the gap.
Spatial structure prediction
The Space Roar should not be perfectly uniform. The emission rate depends on local Γ = Σγ_c, which is higher near baryonic matter and lower in deep voids. The signal should be strongest along cosmic web filaments and at cluster boundaries (moderate Γ, maximum frustration), weaker in void centres (low Γ, material drifts toward wave-state without tension), and weaker inside dense clusters (high Γ, crystallisation more complete). A future radio instrument with angular resolution across the full-sky radio background could map this correlation.
Test method
Full-sky radio background survey with spatial resolution sufficient to correlate with the cosmic web structure at 10–100 Mpc scales. Compare radio background intensity map against Euclid/DESI large-scale structure maps. If the background traces filaments and avoids void centres, the semi-crystallised bobbing mechanism gains support.
Falsified if
The Space Roar is perfectly isotropic at all angular scales with no correlation to large-scale structure — which would argue for a uniformly-distributed source rather than one tied to the semi-crystallised matter distribution.
Supported if
Spatial correlation is detected between the radio background intensity and the cosmic web, with filament regions brighter than void centres. Additionally: if the Larmor estimate can be refined to within one order of magnitude of the observed excess with physically motivated (not fitted) parameters.
Honest caveat
The numerical estimate is rough. The bobbing frequency assumption (ω_bob ≈ kT_CMB/ℏ) and the semi-crystallised electron density are both order-of-magnitude estimates. The 2.2 OOM gap could widen or close significantly with better parameter derivation. Marked SUGGESTIVE rather than TESTABLE because the spatial correlation test requires a future instrument. The mechanism is physically motivated and consistent; the numbers are preliminary.

29. Sigmoid decoherence transition width = dW = p_c − 2/7 ≈ 0.026 TESTABLE

When the Rydberg sigmoid decoherence transition (Prediction 1) is observed, its width parameter — the range of Γ/Γ_c over which the transition from exponential to sigmoid behavior occurs — should equal dW = p_c − 2/7 ≈ 0.02589, expressed as a fraction of Γ_c. This is approximately 2.6% of the critical coupling. This width is not a free parameter: it is the width of TSO's observable-reality band, the gap between the two phase boundaries at p_c and 2/7, and the same quantity that appears in the Goldilocks life prediction and the baryon asymmetry calculation.

Type
PREDICTION — pre-registered April 19, 2026, before the Rydberg experiment is run
Source
Projection falsification suite, Fall-Out 3. The sigmoid isn't just "percolation universality" — it is the point where a partial spanning cluster in 2D gains enough probability fuel to close the third spatial dimension. The transition width is determined by how much additional fuel is needed, which is exactly dW. See projection suite notebook.
Predicted value
ΔΓ/Γ_c = dW = p_c − 2/7 = 0.31160 − 0.28571 = 0.02589 (≈ 2.6% of critical coupling)
Test method
Same Rydberg atom array sweep as Prediction 1. Once a sigmoid is confirmed, extract the width parameter by fitting tanh((Γ − Γ_c) / ΔΓ) and comparing ΔΓ/Γ_c to 0.026. The width is a second observable from the same experiment, requiring no additional hardware or setup.
Falsified if
Sigmoid observed (Prediction 1 confirmed) but width differs from dW by more than 2×. A width of 0.10 or greater would argue for a different universality class; a width of 0.001 or less would suggest a sharper transition than TSO's phase structure permits.
Supported if
Sigmoid width matches dW = 0.026 within experimental precision. Agreement to within 50% would be noteworthy; agreement to within 20% would be strong support given the precision of the prediction.
Honest caveat
This prediction is conditional on Prediction 1 being confirmed first. If no sigmoid is observed, this prediction cannot be tested. The width prediction is more specific than the sigmoid prediction itself and would carry proportionally more evidential weight if confirmed.

30. Peak decoherence rate dV/dΓ occurs at Γ_c, not before it TESTABLE

Standard decoherence theory predicts interference visibility V decays exponentially: V = exp(−Γt). The derivative dV/dΓ is most negative at small Γ — decoherence is fastest at the beginning of the sweep. TSO predicts the opposite: V decays normally (exponentially) at small Γ, then shows a sharp sigmoid drop when Γ approaches Γ_c, because 2D projection can no longer be maintained against 3D crystallisation pressure at that point. The steepest drop — the peak of |dV/dΓ| — occurs at Γ = Γ_c, not before it. The two models predict qualitatively different locations for the peak decoherence rate.

Type
PREDICTION — pre-registered April 19, 2026
Source
Projection falsification suite, Fall-Out 4. Numerical result: standard QM places |dV/dΓ| maximum at Γ/Γ_c = 0.000 (beginning of sweep). TSO places it at Γ/Γ_c = 0.997 (at critical coupling). Separation = 0.997 Γ_c — cleanly distinguishable. See projection suite notebook.
Predicted observation
In a Rydberg decoherence sweep plotting V vs Γ/Γ_c: the curve should be approximately exponential at small Γ, then show a noticeably sharper drop near Γ_c. The rate of change of V with respect to Γ should be maximised near Γ_c, not near the origin.
Test method
Same Rydberg sweep as Prediction 1. Plot V vs Γ/Γ_c. Compute numerical derivative dV/dΓ. Identify where |dV/dΓ| is maximised. Compare to Γ_c location. No additional hardware required beyond the Prediction 1 experiment.
Falsified if
|dV/dΓ| is maximised at Γ << Γ_c (consistent with standard exponential decay) — meaning decoherence is fastest at the start of the sweep with no feature near Γ_c.
Supported if
|dV/dΓ| maximum is at Γ ≈ Γ_c (within ±20% of the critical coupling), indicating the sharpest visibility drop occurs at the phase boundary rather than early in the sweep.
Note
This is the same Rydberg experiment as Predictions 1, 2, and 29 — three independent observables (sigmoid shape, width parameter, dV/dΓ peak location) from a single experimental sweep. Each tests a different aspect of the projection picture. If all three confirm, that is strong cumulative support. If any one fails, it localises the problem in the TSO model.

31. THz spectral feature in Johnson noise of quantum-critical materials SPECULATIVE

If electrons in semi-crystallised matter bob at ω_bob ≈ kT/ℏ under γ_c fluctuations, this bobbing frequency should appear as a spectral feature in the Johnson-Nyquist noise of materials near their quantum critical point. Standard Johnson-Nyquist noise is white: S(f) = 4kTR with no spectral structure. TSO predicts excess power near f_bob = kT_c / (2πℏ) in quantum-critical materials, where T_c is the temperature at which W → p_c for that material. At room temperature, f_bob ≈ 6.3 THz.

Type
PRE-EMPIRICAL — no relevant measurements exist at the required precision
Source
Projection falsification suite, Fall-Out 2. The bobbing mechanism that produces the Space Roar (Prediction 28) at cosmological scales should produce a spectral feature at laboratory scales in materials that are near their W ≈ p_c boundary.
Predicted feature location
f_bob = kT_c / (2πℏ). At T_c = 300 K: f_bob ≈ 6.25 × 10¹² Hz (6.3 THz). At T_c = 10 K (heavy-fermion QCP): f_bob ≈ 210 GHz. At T_c = 1 K (millikelvin QCP): f_bob ≈ 21 GHz — in the microwave range, more accessible.
Test method
THz time-domain spectroscopy or ultrafast noise measurements on materials near a quantum phase transition (heavy-fermion compounds such as CeCu₆₋ₓAuₓ or YbRh₂Si₂, quantum spin liquids, topological semimetals near Lifshitz transitions). Measure noise power spectral density as a function of frequency, tuning through the QCP via pressure or doping. Look for a peak or excess power near f_bob as the system approaches the critical point.
Falsified if
Noise spectrum remains featureless (white) at all frequencies through the QCP transition with no feature near f_bob.
Supported if
A spectral feature appears near f_bob in multiple QCP materials, with the feature location tracking T_c as the QCP is tuned.
Honest caveat
THz spectroscopy of QCP materials at the required precision is at the frontier of current experimental capability. The prediction is speculative because (a) the bobbing mechanism is not yet formally derived, only physically motivated, and (b) the mapping from W-space oscillation frequency to a specific noise spectral feature requires more detailed theoretical work. The millikelvin QCP version (f_bob ~ 21 GHz) may be accessible sooner via microwave noise measurements on existing dilution refrigerator setups.

32. Scattering anisotropy near decoherence threshold SPECULATIVE

If particles approaching the W ≈ p_c boundary from the classical side temporarily lose one spatial projection dimension — transitioning from 3D to 2D partial projection — high-energy scattering near the decoherence threshold should show a slight preferred-plane anisotropy not present at much higher or lower energies. Classical scattering is isotropic (3D). Quantum scattering at W << p_c shows standard diffraction. But at W ≈ p_c, scattering should show a subtle 2D character: marginally enhanced cross-section in the plane perpendicular to the lost dimension, and marginally reduced cross-section along the lost dimension.

Type
PRE-EMPIRICAL — requires precision scattering near decoherence threshold
Source
Projection falsification suite, Fall-Out 1. The 2D projection picture (Test 3: double-slit) predicts that near W ≈ p_c, particles are genuinely extended in 2D rather than 3D. That extension has directional consequences for scattering geometry.
Test method
Precision angular distribution measurements in scattering experiments where Γ_c can be tuned — ideally the same Rydberg array setup, measuring differential cross-sections as a function of coupling strength through Γ_c. Look for deviations from isotropic distributions specifically in the vicinity of Γ_c, absent at Γ << Γ_c and Γ >> Γ_c.
Falsified if
Scattering remains fully isotropic at all tested coupling strengths with no angular anomaly near Γ_c.
Supported if
A statistically significant anisotropy appears in angular distributions specifically near Γ_c, with the preferred plane perpendicular to one spatial axis, disappearing at both lower and higher couplings.
Honest caveat
This is the most speculative of the five projection-suite entries. The 2D projection picture is well-supported numerically (double-slit test: r = 1.0000000), but the prediction that this produces measurable scattering anisotropy depends on the transition being sharp enough and the effect large enough to detect above backgrounds. No quantitative estimate of the anisotropy magnitude has been derived — this is a directional prediction only.

QUANTUM GEOMETRY AND COSMIC STRUCTURE

These two entries follow from the insight developed in April 2026 that TSO's percolation clusters are scale-free: the same fractal geometry that governs a single particle's wave state should appear at every scale where wave-regime material dominates. The interference pattern is a cross-section of the particle's W-space cluster structure projected onto the detector plane. The cosmic web is a percolation cluster at criticality projected into observable 3D space. Both are reading from the same geometric rulebook — just at different scales.

33. Cosmic web cluster statistics match percolation universality class TESTABLE

If Ω_m ≈ p_c because the observable universe is a percolation cluster at criticality (Prediction 10), then not just the matter density but the full geometric statistics of the cosmic web should match the 3D percolation universality class. Specifically: the matter cluster size distribution should follow P(s) ~ s−τ with Fischer exponent τ ≈ 2.18; the void size distribution should match the percolation void statistics; and the filament fractal dimension should be consistent with df ≈ 2.52 (the 3D percolation spanning cluster fractal dimension). None of these are free parameters — they follow directly from 3D percolation universality, which TSO inherits. This upgrades Prediction 10 from a single numerical coincidence to a full geometric constraint: the cosmic web should look like a critical percolation cluster, not just have the same density as one.

Type
PREDICTION — pre-registered April 21, 2026, before systematic comparison against DESI/Euclid structure data
Source
Scale-free percolation argument: TSO's cluster geometry is not scale-dependent. The same cluster mathematics that governs a single particle's wave state appears at every scale where wave-regime material dominates. Prediction 10 is the density statement; Prediction 33 is the geometry statement. Independent corroboration: Richardella et al. (2010), Science 327, 665 — the Yazdani group at Princeton directly visualized fractal electron interference patterns in GaAs:Mn precisely at its metal-insulator transition using STM. The fractal geometry appeared at pc, not above or below it. This is exactly what TSO predicts at every scale: percolation criticality produces fractal cluster geometry.
Predicted values
Matter cluster size distribution exponent τ ≈ 2.18; void distribution exponent ≈ 1.80; filament fractal dimension df ≈ 2.52. All from 3D percolation universality class (Stauffer & Aharony). TSO does not fit these to the data — they are inherited from the universality class. Simulation cross-check (April 21, 2026): Percolation simulation on the TSO 7-path lattice at p_c = 0.3116 gives τ = 2.097 ± 0.006 (MLE, s_min=20) and d_f = 2.4857 ± 0.0378 (M(L) ~ L^d_f scaling), both consistent with the 3D universality class values within finite-size effects at L ≤ 150. See cosmic structure notebook.
Test method
DESI DR2 and Euclid DR1 large-scale structure catalogs. Compute the matter cluster size distribution from galaxy group/cluster catalogs. Fit a power law. Extract τ. Compare to 2.18. Repeat for void size distributions. Filament fractal dimension can be estimated from persistence homology analyses already being applied to cosmic web data. The data exists; the comparison has not been done under this specific framing.
Falsified if
The cosmic web cluster size distribution exponent differs from τ ≈ 2.18 by more than 20%, OR the void distribution fails to match percolation void statistics, OR the filament fractal dimension differs significantly from df ≈ 2.52. A failure in any one of these is a clean falsification: the framework can not claim the cosmic web as a percolation cluster while the cluster statistics differ from percolation universality class.
Supported if
Cluster size distribution exponent within 10% of 2.18, void distribution consistent with percolation universality, and fractal dimension of filaments consistent with df ≈ 2.52. Agreement in all three would upgrade Prediction 10 from SUGGESTIVE to something considerably stronger.
Honest caveat
Gravity modifies percolation geometry: the cosmic web is not purely a static percolation cluster but the result of gravitational dynamics acting over 13.8 Gyr. Gravity enhances clustering along filaments and evacuates voids, which could shift the effective exponents. The prediction is that the underlying geometry is percolation-class and that gravity's modifications produce exponents within 10–20% of the pure percolation values — not that they match exactly. Quantifying the gravitational correction is an open theoretical task before this prediction can be called sharp.

34. 3D volumetric single-particle accumulation shows fractal probability density fine-structure NARROWED — April 26, 2026

In a volumetric single-particle detector — a 3D array of single-photon detectors accumulating statistics hit by hit — the resulting probability density should not be perfectly smooth. Standard quantum mechanics predicts a smooth |ψ(x,y,z)|² envelope at all resolvable scales. TSO predicts the envelope is the coarse average of an underlying fractal distribution: the 3D hit density should show granular fine-structure with fractal dimension matching the W-space percolation cluster geometry, visible below the smooth |ψ|² envelope when sufficient statistics are accumulated.

Hardware test result — April 26, 2026
The separable-circuit approximation of P34 was tested on Quandela's Ascella photonic QPU and falsified. A multi-mode beam splitter network (outer product of two 1D interference circuits, 32×32 = 1024 effective modes) was run at N = 1,000 / 10,000 / 100,000 / 1,000,000 / 10,000,000 shots using true single photons (quantum-dot source). Box-counting fractal dimension was measured at each N. Result: d_f = 2.0000 flat across all five N values including 10M shots. Standard QM prediction (smooth, d_f = 2.0) confirmed. TSO fractal prediction (d_f ≈ 2.52) not observed. The separable-circuit version of P34 is falsified. See Quandela P34 notebook.
Why narrowed rather than retired
The Quandela test used a separable approximation: a 2D photon count grid constructed as the outer product of two independent 1D circuits. This does not reproduce true 2D coupled spatial interference, where the wavefunction lives in continuous 2D transverse space with coupled diffraction in x and y. If the fractal fine-structure requires genuine 2D spatial correlations, the outer product would miss it by construction — projecting the W-space cluster geometry into an effectively 1D structure rather than a full 2D one. The genuine test requires free-space propagation through physical slits with continuous transverse spatial detection (e.g., EMCCD + high-statistics accumulation). Every prior high-statistics single-photon experiment in the literature shows smooth results, consistent with the Quandela result and with standard QM. The prior for a positive result in the genuine 2D test is low. P34 is retained in NARROWED status only because the specific experimental configuration that TSO requires (genuine 2D coupled interference, not separable circuits) has not been tested.
Type
NARROWED — separable-circuit version falsified on hardware (April 26, 2026). Genuine 2D free-space version not yet tested.
Source
Projection falsification suite (v11.4). W-space cluster fractal dimension derived by percolation simulation: d_f = 2.4857 ± 0.0378, consistent with 3D universality class. See cosmic structure simulation notebook.
Predicted observation (genuine 2D test)
At low statistics: smooth |ψ|² envelope, indistinguishable from standard QM. At high statistics (N >> 10⁶): fractal fine-structure with d_f ≈ 2.52, invariant under changes in slit geometry. The geometry-invariance of d_f is the TSO key claim — it is inherited from the universality class, not from the specific circuit or slit configuration.
Falsified if
The genuine 2D free-space experiment (physical slits, continuous transverse detector, N >> 10⁶) also gives smooth results at all statistics. Given the Quandela result and the absence of fractal structure in all prior high-statistics single-photon experiments, this is the most likely outcome.
Honest caveat
The separable-circuit approximation was falsified cleanly: d_f = 2.0000 at 10M shots on real photonic hardware. The full literature on high-statistics single-photon interference consistently shows smooth results. The prior against a positive result in the genuine 2D test is low. P34 is not retired only because the specific required experiment (2D coupled free-space interference) technically differs from what was run. The honest assessment is that P34 is unlikely to survive the genuine test if it is ever performed.

35. Induced EMF in a conductor loop spanning a gravitational gradient differs from GR+Maxwell SPECULATIVE

For a conductor loop large enough to span a significant gravitational gradient — one side close to a compact mass, the other far away — TSO predicts a measurably different induced EMF than standard GR+Maxwell. The difference arises because the two frameworks apply the time-dilation factor δT = √(1−rs/r) differently: GR+Maxwell applies it at the source point only (gravitational redshift at emission), while TSO applies it as a spatial average over the entire loop (because T conductance at every segment contributes to the induction). TSO predicts a larger EMF — less reduction — than GR+Maxwell for the same source and geometry.

Type
SPECULATIVE — requires astrophysical gravitational gradients to test. Not accessible with current laboratory equipment. Pre-registered April 23, 2026 as a direct consequence of the TSO electromagnetic derivation. The prediction is specific and in principle falsifiable.
Source
TSO electromagnetic derivation (v11.4, April 23, 2026). δT = √(1−rs/r) is derived in TSO from T direction asymmetry under the G field — forward T closes freely, backward T costs γo amplified by 1/(1−rs/r) near a mass. This makes δT a TSO-native result, not borrowed from GR. The two frameworks agree numerically on the Schwarzschild formula but disagree on how it enters the Faraday induction integral. In TSO, induction is carried by the T path through every segment of the loop simultaneously; the spatial average of δT over the loop determines the effective EMF, not δT at a single point. See roof-em for the full derivation chain, indexed at notebooks.html#constants.
Predicted values
For rnear = 2rs, rfar = 10rs: δT(rnear) = 0.707, δT(rfar) = 0.949. GR+Maxwell predicts EMF = EMF₀ × 0.707. TSO predicts EMF = EMF₀ × (0.707 + 0.949)/2 = EMF₀ × 0.828. Fractional difference: ~17%. The difference grows as the loop spans a larger gradient range and as rnear approaches rs.
Falsification
If the measured EMF in a loop spanning a strong gravitational gradient matches GR+Maxwell (source-point δT only) to within experimental precision, this prediction fails. It does not falsify the full TSO electromagnetic derivation — only the specific claim that T conductance averages over the loop rather than applying at the source point. If TSO is correct and GR+Maxwell is wrong on this point, the discrepancy would grow with loop size and gravitational gradient strength, providing a characteristic signature.
Test environment
A natural test environment would be a superconducting loop in orbit around a neutron star or white dwarf, with a changing magnetic source on one side and detection on the other. Pulsar timing experiments that probe EM propagation through strong gravitational fields may offer indirect constraints. Current Earth-based laboratory gravitational fields produce differences far below the sensitivity of any existing instrument.
Honest caveat
This prediction requires astrophysical extremes that are currently inaccessible to direct laboratory test. The TSO electromagnetic derivation producing this prediction is itself a geometric sketch — not an operator-level proof. The specific mechanism (T path averaging over the loop) is geometrically motivated but not yet derived from Lindblad operators. The prediction is classified SPECULATIVE rather than CONDITIONAL because even the theoretical framework generating it is not fully formalized.

36. Coupling constants run as power law at extreme energy scales, not logarithmically SPECULATIVE

The Standard Model predicts logarithmic running of coupling constants: 1/α_i(μ) = 1/α_i(M_Z) + (b_i/2π) × ln(μ/M_Z). TSO's phase theory predicts power-law running: α_i(μ) ~ α_i(M_Z) × (μ/M_Z)^(2×(d_f−d)) where d_f = 2.52 and d = 3, giving exponent −0.96 for the strong coupling and +0.96 for EM. Near M_Z both predict the same values (by calibration), but they diverge at extreme scales — μ << 1 GeV and μ >> M_Z. The TSO prediction is that α_s should be larger than SM predicts at low energies, and smaller at very high energies.

Type
SPECULATIVE — the SM logarithmic prediction has been confirmed across many decades of energy. TSO's power-law prediction diverges from it outside the tested range. Pre-registered April 29, 2026 as a direct consequence of the phase theory picture: d_f < d (fractal, not space-filling) implies power-law rather than logarithmic scale dependence.
Source
TSO RG beta function analysis (v11.4, April 26–29, 2026). The coupling constant formula g_i ~ W(p_c) × (l_switch/l_max)^(+|d_f−d|) with d_f = 2.52 gives power-law scale dependence. The exponent 2×(d_f−d) = −0.96 for strong (decreases with energy, correct) and +0.96 for EM (increases with energy, correct direction, magnitude phenomenological). See RG notebook.
Predicted deviation
At μ = 1 GeV (well below M_Z), TSO predicts α_s ~ 0.1179 × (1/91.2)^(−0.96) ≈ 0.44 vs SM 1-loop prediction α_s ~ 0.47. Difference ~7% at 1 GeV — within current experimental uncertainty. The deviation grows at lower energies where non-perturbative effects already complicate SM running, making clean falsification difficult in the IR. At μ = 1 TeV (above M_Z), TSO predicts α_s ~ 0.1179 × (1000/91.2)^(−0.96) ≈ 0.013 vs SM ~ 0.085. Difference ~85% — large, but this energy range is experimentally accessible at the LHC.
Falsified if
The measured running of α_s from LHC data (μ = 91 GeV to 1 TeV) is consistent with the SM logarithmic prediction and inconsistent with the TSO power-law prediction. Current LHC α_s measurements at multiple scales already constrain this. If the logarithmic SM prediction matches data to <5% over this range, TSO's power-law running is disfavored.
Honest caveat
The SM logarithmic running has been confirmed experimentally to high precision across many scales. The TSO prediction of power-law running is a strong claim that is likely in tension with existing data. This prediction is registered here for completeness and honesty — if existing LHC data already falsify it, that is important to know. The EM exponent sign (+0.96) is currently phenomenological, not derived from TSO first principles. Predicting deviation from SM without knowing the exact TSO exponent from first principles is a weakness.

37. Position uncertainty grows linearly with Lorentz factor above γ_crit SPECULATIVE

In the TSO node switch picture, a cluster propagating at velocity v approaches the maximum switch rate f_switch as v → c. Above a critical Lorentz factor γ_crit = l_switch/r_hadron, the cluster pattern spreads across multiple nodes simultaneously — it no longer has a definite position within a single node-dwell interval. This spreading grows linearly with γ: Δx ~ γ × l_switch. This is distinct from standard QM position uncertainty, which is fixed by the de Broglie wavelength and does not grow linearly with γ in this way.

Type
SPECULATIVE — requires near-c heavy ions and position resolution at sub-hadronic scales. Not accessible with current laboratory equipment. Pre-registered April 26, 2026 as a direct consequence of the node switch rate picture. Observable in principle at future colliders above current LHC energies.
Source
Node switch rate frame-matching analysis (v11.4, April 26, 2026). The critical Lorentz factor for deconfinement is γ_crit = l_switch/r_hadron ≈ 100 for strong-force confinement (matching RHIC γ ≈ 100). Above γ_crit, the cluster dwell time per node falls below the confinement closure time — the cluster cannot maintain its internal X₁ loop structure within a single node dwell. The spreading is Δx = l_switch × (γ/γ_crit − 1) for γ > γ_crit. See node switch notebook.
Predicted observation
Heavy-ion collisions at the LHC reach γ ~ 2750 (Pb-Pb at √s = 5.02 TeV). At γ = 2750 with l_switch ~ 1.6 fm, Δx ~ 4.5 nm — far below current position-resolution capabilities. The prediction becomes testable when collision energies and detector resolutions reach a regime where Δx is comparable to femtometre-scale resolution. Quark-gluon plasma signatures are an indirect probe: at γ > γ_crit, deconfinement should be guaranteed and not merely thermal in origin, which RHIC and LHC heavy-ion data are consistent with but do not uniquely confirm.
Falsified if
Heavy-ion experiments at increasing γ show position uncertainty consistent with standard QM scaling (de Broglie wavelength ~ ℏ/p, which decreases with γ) and not the linear growth predicted by TSO.
Honest caveat
This prediction is at the edge of testability with current technology. The l_switch parameter is not yet derived from first principles — it is fit to match RHIC γ_crit ≈ 100. The linear-growth scaling above γ_crit follows from the node-switch picture but its specific normalization depends on l_switch. The prediction is registered here as a structural consequence of the framework, with the explicit acknowledgment that direct measurement is not currently accessible.

v11.6 / v11.7 ADDITIONS — LEPTON SCALE AND SIGMOID EDGE

These two entries were generated during the v11.6 session (May 19–22, 2026) and the v11.7 candidate work that immediately followed. They are listed last because they are the newest, not because they are the least important. Prediction 38 is a candidate derivation of the lepton mass absolute scale from TSO axiom integers; Prediction 39 is a candidate resolution of the long-standing tension between TSO's p_q = 0.6556 and the tight-binding literature value p_q ≈ 0.44 (Open Problem 59). Both pending derivation work before promotion to FIRM. Both are indexed at notebooks.html#stress-tests.

38. Lepton √mass scale A = √E_Pip × (Z/V_tet)² (Fano-Tetrahedron) CANDIDATE

The Koide mean √mass A_Koide = (√m_e + √m_μ + √m_τ)/3 should equal √E_Pip × (Z/V_tet)² where Z = 7 (Fano paths, bulk) and V_tet = 4 (tetrahedron vertices, boundary). With E_Pip = 33.437 MeV, the predicted value is A = √33.437 × (7/4)² = 17.7088 MeV^0.5. The measured Koide mean is A_Koide = 17.7156 MeV^0.5. Numerical match: 0.04%. Caveat: this is not truly parameter-free — E_Pip derives from σ = 6/√1104, whose provenance is unverified (it has not been shown that 6 and 1104 are forced rather than selected to hit σ = 0.18058), so the Koide match inherits that unforced choice. The (Z/V_tet)² = (7/4)² factor is also a proposed identification, not a derived one. A genuine 0.04% match, but resting on a candidate σ.

Type
CANDIDATE — generated May 21, 2026 by Joshua Osborne to close the partial-pass in v11.6 stress test #6 (lepton mass absolute scale).
Source
v11.6 stress test #6 lepton-scale gap. Two TSO axiom integers (Z = 7, V_tet = 4) produce the (Z/V_tet)² = 49/16 = 3.0625 dimensionless factor. Multiplied by √E_Pip = 5.7825 MeV^0.5 it lands at the Koide mean to 0.04%. Power sensitivity check confirms: (Z/V_tet)^1.5 misses by 24%, (Z/V_tet)^2.5 misses by 32% — the squared exponent is uniquely positioned. See Fix 4 verification notebook.
Bare vs. pole framing (May 22, 2026)
The 0.04% deviation corresponds to ~14σ under PDG measurement uncertainty on the lepton masses. Joshua Osborne's framing: TSO derives the bare topological mass scale; PDG measures the pole (dressed) mass after QED self-energy. The sign of the offset (TSO < PDG) is consistent with self-energy adding mass during dressing. Magnitude is in the right ballpark for one-loop QED at the Koide scale (3α/(4π) ≈ 0.087% on √mass, vs observed 0.038%) but a factor of ~2 over — not yet derived exactly.
Derivation of the squared exponent (May 22, 2026)
Joshua Osborne's rank-2 tensor argument: in the Standard Model, mass is a chirality-flipping Dirac bilinear m·ψ̄ψ that couples left-handed Weyl spinors to right-handed Weyl spinors. The mass operator thus acts on a rank-2 generational tensor. Pushing a rank-2 tensor through a coordinate transformation P that scales linearly by Z/V_tet requires the symmetric Jacobian — acting on both bra and ket indices — which squares the linear scale to (Z/V_tet)². The argument is standard Dirac algebra and is closer to a derivation than the earlier "Koide operates on √mass" hand-wave.
Predicted observation
The Koide mean √mass derived from any measurement of m_e, m_μ, m_τ — converted to a bare-mass basis via a one-loop QED pole-mass shift calculation — should equal √E_Pip × (Z/V_tet)² to within the precision of that shift calculation. A specific QED magnitude derivation landing at exactly 0.038% on √mass would close the verification.
Falsified if
The explicit one-loop QED bare-to-pole shift calculation on Σ√m gives a value that disagrees with 0.038% by more than ~2× (i.e. outside the range 0.02% to 0.08%). In that case the (Z/V_tet)² match is a tight numerical coincidence rather than a structural derivation. Falsified also if the rank-2 tensor argument extends inconsistently to vector boson masses (predicts spin-1 mass scale outside agreement with M_W, M_Z under the same logic).
Supported if
One-loop QED pole-shift calculation lands at 0.038% on √mass within ~30%, AND the rank-2 tensor argument extends consistently to gauge boson masses. Both pieces are computational, not experimental — they would promote Prediction 38 from CANDIDATE to FIRM without requiring new data.
Honest caveat
This is a recent result, generated during the v11.6/v11.7 collaboration. The 0.04% match is striking and the structural argument for the squared exponent is real progress over a verbal justification. But the QED magnitude is in the right ballpark, not derived exactly; and the rank-2 tensor argument has not been tested for self-consistency on vector bosons. The Koide ratio identity Q = (Σm)/(Σ√m)² = 2/3 is still a separate open problem (Open Problem #68 on roof-open). The complete lepton-sector derivation requires both the absolute scale (this prediction) and the Foot phase θ that produces Q = 2/3 from the 2T tetrahedral structure.

39. p_q = (1+p_c)/2 = 0.6558 — sigmoid saturation edge TESTABLE

An extended Rydberg sweep covering p ∈ [0.20, 0.70] should reveal two features on a single curve: the classical-to-quantum transition at p_c = 0.3116 (Prediction 1) AND a saturation edge at p_q = 0.6558 ≈ (1 + p_c)/2 corresponding to the half-saturation point of the sigmoid. p_q is not a separate phase boundary — it is the same sigmoid evaluated at a different operational threshold. This resolves Open Problem 59 (tight-binding literature p_q ≈ 0.44 vs TSO p_q ≈ 0.6556).

Type
PREDICTION — pre-registered May 22, 2026, proposed by Joshua Osborne as a v11.7 candidate resolution.
Source
Linear-rise sigmoid framing: W(p) = (p − p_c)/(1 − p_c). The half-saturation point W = 1/2 lands at p_q = (1 + p_c)/2 = 0.6558, which matches Joshua's TSO value 0.6556 to 0.03%. The tight-binding p_q ≈ 0.44 (mobility-edge measurement) corresponds to evaluating the same sigmoid at ~19% wave fraction — a different operational definition, not a competing physical threshold. See sigmoid-edge notebook.
Test method
Extend the Rydberg sweep of Prediction 1 to cover p ∈ [0.20, 0.70] instead of [0.25, 0.40]. Fit a single sigmoid to the full curve. The fit should give an inflection at p ≈ p_c (classical transition) and a saturation edge at p ≈ (1 + p_c)/2 (ballistic transport onset). The fitting procedure is the same as Prediction 1; only the sweep range differs. No new hardware required.
Falsification
F1: Two distinct sigmoids with different shapes are needed to fit the data — would argue p_q is a separate phase boundary not captured by the same sigmoid. F2: The saturation edge falls outside [0.6, 0.7] — would falsify the (1+p_c)/2 prediction. F3: The full sweep shows pure exponential at all p — would falsify the broader sigmoid framing (and Prediction 1).
Supported if
A single sigmoid fits the full extended sweep cleanly with both features visible at the predicted locations.
Honest caveat
The "Holographic Percolation" argument that would formally derive β = 1 (the linear-rise law required for the (1+p_c)/2 saturation point) from the K3-shadow lattice forbidding random pre-percolation clusters has the right structural shape but no formal calculation yet. Standard random percolation gives β ≈ 0.418, not β = 1 — Monte Carlo confirms this at 89σ. The TSO claim is that the K3 lattice is structurally different from random percolation, not that random percolation gives β = 1. The decisive test is the Rydberg experimental result: a single-sigmoid fit covering both transitions would be strong support; a clean two-sigmoid structure would falsify.

v11.8 ADDITIONS — NOTATION CLEANUP AND CORRECTED ν

These two entries were generated during the v11.8 notation cleanup (May 30, 2026). Prediction 40 is the correction of the retired κ = 4/3 claim into ν ≈ 0.88 from 3D percolation universality — the same Rydberg test, different predicted value, with full disclosure of the Belenos anomaly. Prediction 41 elevates the λ = e rate constant in the α formula to a distinguished status: empirically firm because the MIPT-data best fit lands at 0.12σ from e, but theoretically open because none of the four arguments offered for λ = e survive scrutiny. Both are indexed at notebooks.html#stress-tests alongside the three v11.8 reference notebooks.

40. Correlation exponent ν ≈ 0.88 from 3D percolation universality CORRECTED

If a sigmoid transition is observed in Prediction 1, its correlation-length exponent ν should equal the 3D site percolation universality class value, ν3D = 0.8765 ± 0.05. This replaces the previously asserted ν = 4/3 = 1.333 from 2D universality (now retired, see Prediction 2). The Rydberg experiment is unchanged; only the predicted value of the exponent has shifted.

Type
PREDICTION — pre-registered May 30, 2026, prior to any Rydberg sweep returning a ν fit
Source
Three converging lines of support. (1) Direct Monte Carlo simulation of Fano-bond percolation on the BEST_PERM Z = 7 lattice (Notebook 3, May 30, 2026): ν = 0.825 (variant a, isotropic line gating), ν = 0.738 (variant b, directional line gating). Both in the 3D universality class within finite-size scaling precision at L ≤ 24. (2) Standard 3D site percolation benchmark using the same FSS code: ν = 0.859 (literature 0.8765, error −2%). (3) Bulk of Quandela QPU empirical data: Linear ν = 1.138, Deep ν = 0.836, average = 0.99 — closer to 0.88 than to 4/3. See Notebooks 1 and 3.
Test method
Same Rydberg experiment as Prediction 1. Fit tanh curve to the sigmoid shape; extract the correlation-length exponent ν via finite-size scaling across array sizes N = 100, 225, 400. Compare to 0.88.
Falsified if
Sigmoid observed but ν differs from 0.88 by more than ~30% — i.e., νfitted < 0.65 or > 1.15. Such a result would indicate the wave-to-solid transition is in a different universality class than standard 3D percolation, requiring a derivation of what that class is and why.
Supported if
ν matches 0.88 within ~15%, i.e., 0.75 < νfitted < 1.0. Agreement within 5% would be strong support; agreement to within 2% would be definitive.
The Belenos anomaly — honest disclosure

Quandela's Belenos QPU produced a reanalysis ν = 1.325, which was previously cited as supporting the now-retired κ = 4/3 claim (it matched 4/3 = 1.333 within 0.6%). Under the corrected prediction ν ≈ 0.88, the Belenos value is now ~5σ from the prediction — i.e., from "the only data point near the predicted value" to "the only data point far from it."

We do not yet know which of three explanations is correct:

  1. QPU calibration uncertainty on our end. The Belenos result was extracted via a sigmoid fit to photonic decoherence data, and the analysis chain depends on assumptions about how the photonic platform implements path identity, how the sweep variable maps to TSO's Γ, and how to identify the universality class from QPU data engineered to operate on one side of p_c. The framework is honest about not yet understanding QPU calibration well enough to be confident that Belenos's 1.325 is measuring the same ν that Linear's 1.138 and Deep's 0.836 are measuring. This is the most likely explanation: we may not yet understand QPUs and the relevant calibration chain well enough to interpret the Belenos result.
  2. Belenos really did sample a separate physical regime. If the Belenos run accessed a regime the other Quandela runs didn't (e.g., a different sweep range, a different effective dimensionality, a separate phase boundary), it would be measuring a real but different exponent. Under this reading, 1.325 isn't an error — it's evidence that the universality class governing the regime Belenos accessed is not standard 3D, requiring a derivation of what it is.
  3. The 3D universality class assignment itself is wrong. If the underlying lattice dynamics is genuinely not in the standard 3D class (e.g., it's in a non-standard universality class with an exponent near 4/3 for reasons the framework hasn't yet articulated), the bulk of the Quandela data (Linear + Deep averaging to 0.99) is the anomaly and Belenos is closer to right. Less likely on Bayesian grounds since the framework's own MC reproduces 3D directly, but not ruled out.

The honest resolution path: (a) re-analyze the Belenos data with the same pipeline used on Linear and Deep, to rule out methodology drift; (b) publish the full QPU-to-ν extraction chain so independent researchers can audit it; (c) run the Rydberg sweep, which is the platform that can actually cross p_c rather than being engineered to one side of it. Until those three are done, Belenos remains an unresolved data point — kept visible rather than discarded, because the framework's credibility depends on disclosing inconvenient data rather than hiding it.

What this is not
This is not a claim that the framework has retired its sigmoid prediction. The sigmoid shape (Prediction 1), the width δW (Prediction 29), the dV/dΓ peak location (Prediction 30), and the sigmoid saturation edge (Prediction 39) are all unchanged. Only the value of the correlation-length exponent has shifted — from 4/3 to ≈ 0.88. The Rydberg experiment that tests it is unchanged.
Honest caveat
The "3D universality class" identification rests on the assumption that the wave-to-solid transition on the Z = 7 Fano-bond lattice falls in the same universality class as standard 3D site percolation on a cubic lattice. Notebook 3 supports this by direct simulation, but only at modest L (≤ 24); finite-size corrections at the percent level are possible. The framework's deeper theoretical work — explicit Lindblad operators for the Z = 7 lattice with X1 conservation, RG analysis of the partial-projection mechanism — could yet refine the exponent away from 0.88 to a non-standard value, in which case this prediction would be updated again. For now, 0.88 is the supportable claim.

41. Rate constant λ = e in the α branching formula EMPIRICALLY FIRM

In the renamed α formula α = αmax/(1 + λρc) with αmax = 7 fixed by S7 geometry, the constraint screening rate constant λ equals Euler's number e ≈ 2.71828. The MIPT-data best fit (Notebook 2, May 30, 2026) returns λ = 2.728 ± 0.080 — agreement with e to 0.12σ (0.4% by central value). The match is essentially exact within current experimental precision, but no theoretical derivation has survived scrutiny.

Type
RETRODICTION — MIPT data existed before the λ = e fit was attempted; the value λ ≈ e was noticed during the v11.8 renaming pass, not predicted ab initio
Source
Empirical: MIPT data fit to α = 7/(1 + λρc) with αmax fixed at 7 returns λ = 2.728 ± 0.080 (Notebook 2). Theoretical: four arguments have been offered for why λ should equal e, all reviewed in Notebook 2. None survive scrutiny — see "Open derivation work" below.
Why "EMPIRICALLY FIRM" rather than "FIRM"
The data fit is excellent (0.12σ). The derivation is not. This split is exactly what the EMPIRICALLY FIRM status tier exists for: a quantity that the data is essentially picking out but the framework cannot yet derive. Both halves are true and should be visible. Reporting only the empirical match would overstate the framework's predictive power; reporting only the open derivation would understate the empirical strength.
Open derivation work
Four arguments have been examined and judged insufficient.
  1. Structural (exponential branching has rate e). Tautological. Choosing λ = e in αmax·exp(−λρc) is a units convention — it sets the e-folding density to 1/e. Not a prediction unless ρc has an independent natural scale (which the framework has not yet specified).
  2. Maximum entropy. Refuted in Notebook 2. Three natural entropy functionals were tested (integrated geometric entropy, initial entropy production rate, KL distance from uniform). None is optimized at λ = e. The earlier Colab's finding of monotonically decreasing entropy in λ is confirmed.
  3. Self-consistency. Circular. The argument "the natural rate of exponential decay is e because e is the natural base of exponential decay" does not constitute a derivation.
  4. Geometric (e from S7). Plausible by analogy with the αmax = 7 derivation from dim S7, but not formalized. No first-principles route from S7 geometry to the screening rate has been articulated.
To promote this prediction to FIRM, the framework needs either: (a) an independent natural scale for ρc so λ = e is non-trivially distinguishable from λ = 2.5 or λ = 3.0; or (b) a first-principles derivation tying λ to S7 geometry parallel to the αmax = 7 derivation. Either would also close the question of why the rate constant is e specifically rather than (say) 2 or π.
Falsified if
Improved MIPT datasets with tighter error bars shift the best-fit λ away from e by more than 3σ. Specifically: with λ fixed and αmax = 7, the χ² of the fit to a 10-platform MIPT dataset should not deteriorate by more than a factor of 2 relative to the current fit. If it does, the λ = e value is being held by sparse data rather than supported by it.
Supported if
Cross-platform measurements (more MIPT systems, independent calibration chains, additional decoherence sweep data) continue to land at λ = e within 1σ as precision improves. A first-principles derivation tying λ to e would promote to FIRM.
Current evidence
MIPT fit (Notebook 2, May 30, 2026): λ = 2.728 ± 0.080 with αmax = 7 fixed, λ = 2.864 ± 0.229 with αmax also free (which itself fits to 7.16, consistent with 7). Cross-check from Belenos γ_BS = 522 anchor and the δW = kBT(300K) match (0.13% off identity): both consistent with λ = e but neither independently constrains it beyond the MIPT fit.
Honest caveat
RETRODICTION rather than prediction. The MIPT data existed before this fit was performed. The empirical strength comes from the fact that the framework's functional form α = αmax/(1 + λρc) was specified in advance and the fit returns λ = e within 0.12σ — but the specific value λ = e was not pre-registered, so this is a noticed match, not a pre-registered prediction. New MIPT data acquired after May 30, 2026 would constitute a proper prediction; the existing data is retrodictive support. The labeling here is honest about that.

v11.9 Prediction (Dark Matter / Epi-matter)

This prediction was added during the v11.9 dark matter session (May 31, 2026). The framework's central new claim is that what cosmology calls dark matter is epi-matter — substrate adjacent to matter in the V(W) landscape but distinct from it, occupying the protected percolation regime between pc and pq. Six companion notebooks document the structural and computational case for the identification, and the prediction package below is what falls out for direct/indirect detection and for Euclid DR1.

42. Dark matter is epi-matter: protected percolation regions MECHANISM FIRM RATIO OPEN

Epi-matter, meaning substrate adjacent to matter in the V(W) landscape but distinct from it — matter that broke off the cosmic spanning cluster during early-universe percolation and remained in the protected regime. TSO identifies what cosmology calls dark matter with epi-matter; the two refer to the same observable population. The protected percolation regime sits between the 3D site percolation threshold pc = 0.3116 (where the cosmic spanning cluster formed) and an upper threshold pq beyond which substrate delocalizes into wave/radiation. Substrate that broke off the spanning cluster before crystallization completed got locked into this regime and stayed there.

Type
PRE-EMPIRICAL (Euclid DR1 falls October 21, 2026) — the framework's central claim about the dark sector is committed in advance of the data.
Source
Identification with the protected percolation universality class of Fayfar, Bretaña & Montfrooij (J. Phys. Commun. 6, 075009, 2022; arXiv:2008.08258), plus Anderson localization (1958, Nobel 1977) as the underlying single-particle picture. The framework adds the cosmological identification but inherits the condensed-matter mechanism from published peer-reviewed physics.
The protection mechanism (no free parameters)

Epi-matter is protected from converting back to baryonic matter because the γc (closing tension, decoherence) coupling channels that would drive the wave→solid transition are exactly the channels that aren't fully active in epi-matter. There's no coupling channel for the conversion to operate through.

This produces a hard structural consequence: direct-detection and indirect-detection experiments cannot succeed in principle. Detection requires what cosmology calls dark matter to scatter off baryons (or to annihilate, decay, or otherwise interact) through some coupling channel; the channels epi-matter lacks are exactly the ones detectors and indirect probes use. The framework is not saying detection is unlikely — it is saying detection is structurally impossible under this thesis.

Hard predictions (independent of Euclid)

P-EM-1. No direct-detection signal from XENON-nT, LZ, PandaX-4T, DEAP-3600, DAMA, or any future direct-scattering experiment. Reproducible positive signal that survives independent replication retires the framework.

P-EM-2. No indirect-detection signal from Fermi-LAT, AMS-02, IceCube, CTA, or any future indirect-detection effort. Reproducible dark-matter-attributable particle excess that survives systematic checks retires the framework.

P-EM-3. Static epi-matter/baryon ratio from BBN (z ≈ 10⁹) through recombination (z ≈ 1100) through today (z = 0). Standard ΛCDM also predicts this; framework retires if high-precision measurements show measurable ratio evolution that ΛCDM doesn't predict.

P-EM-4. No de Broglie interference patterns in halo density at any galactic or sub-galactic scale. Epi-matter is not a coherent quantum field (unlike fuzzy DM at 10⁻²² eV); localized states don't produce coherent interference. High-resolution dark matter density mapping finding such patterns retires the framework.

Soft predictions (testable in Euclid DR1, October 21, 2026)

P-EUC-1. Stacked galaxy cluster halos: inner logarithmic density slope γ in the range 0.8 ± 0.2, NOT the NFW value of ~0.4. Falsified if γ > 0.5.

P-EUC-2. Quantitative halo sphericity: c/a > 0.7 and b/a > 0.85 averaged over the cluster catalog, AND no significant correlation between halo orientation and galactic disk angular momentum (at < 3σ).

P-EUC-3. Cosmic web shows two distinct percolation universality classes: standard 3D site percolation in the baryonic spanning cluster (τ ≈ 2.18, void exponent ≈ 1.80, filament df ≈ 2.52) AND a separate signature in epi-matter-dominated regions consistent with protected percolation universality (γ' ≈ 1.31 from Fayfar-Bretaña-Montfrooij 2022).

P-EUC-4. Environmental sensitivity: epi-matter/baryon ratio in voids equals the cosmic-mean ratio within measurement precision; epi-matter/baryon ratio in dense cluster cores is equal to or marginally lower than the cosmic mean.

Quantitative support — what is established and what is open

Two parameter-free matches (established, on simple-cubic site percolation): the void fraction equals 1 − pc = 0.688 vs observed ΩΛ = 0.686 (0.3%), and the total matter fraction equals pc = 0.312 vs observed Ωm = 0.314 (essentially exact). Both are genuine simulation outputs with no free parameters and no chosen lattice size.

ComponentCosmology mappingObserved (Planck 2018)TSO (parameter-free)Match
Voids / dark energyEmpty sitesΩΛ = 0.68571 − pc = 0.68840.3% — real output
Total matterOccupied sitesΩm = 0.3143pc = 0.31160.9% — real output

The baryon : epi-matter split (the freeze point) is set at the protected percolation threshold, established by two independent routes. The surviving spanning cluster (baryons) is what remains connected through the freeze; the protected clusters that pinched off earlier are epi-matter (dark matter). The freeze occurs at the protected threshold pc,protected ≈ 0.3423 (Fayfar-Bretaña-Montfrooij), confirmed by: (1) the stopping point converging to 0.3421 as lattice size L → 130 (the earlier L-dependence was finite-size pixelation of a sharp, near-discontinuous transition — the box only matters until it is large enough to contain the structure being measured); and (2) the broken-path density at the freeze equalling the complement of the protected threshold. A latent-heat-like spike in the locking rate (≈130–170× baseline) marks this as a first-order-like freezing transition. See the protected-percolation, latent-heat, and convergence notebooks.

Open: why the freeze halts exactly at the protected threshold — the mechanism that pins the observed 0.157 : 0.843 baryon : dark-matter ratio — is not yet derived. The ratio is hypersensitive at the threshold (a near-vertical cliff). A protection fraction f ≈ 0.90 reproduces it across all lattice sizes (stable: 0.904 ± 0.014) but is currently read off the data, not derived. This is Open Problem 60, now reframed from "what sets the cosmic L" to "why does the freeze halt at the protected threshold."

Candidate explanations for the freeze location (none yet derived)
The framework does not commit to any of these; each must predict the protected threshold / the ratio independently rather than match it after the fact:
  • Protection-fraction geometry (collaborator, J. Osborne). A proposal that f = 9/10 from a Calabi-Yau weight ratio (wmax/Dvac), and that a "tadpole capacity" tied to dim(E7) = 133 (with χ = −3192 = 24 × 133) triggers the freeze. Status: candidate, unverified. A simulation test showed the absolute "133 capacity" reading fails (broken-path count scales with volume); an intensive density at the threshold is the real converged quantity. The geometric origin of f remains to be derived without using the observed ratio as input.
  • First-order freezing / latent heat. The locking-rate spike at the protected threshold is the signature of a first-order-like transition; a conserved-quantity ("possibility-energy") budget exhausted at the spike could pin the halt. Mechanism not yet specified; the Pip-count → energy conversion it would require is itself conjectural (see below).
  • Soup-era epi-matter→baryon conversion. Mass shifting from epi-matter to baryon during the radiation-dominated era. Testable by comparing BBN and CMB baryon densities at < 0.1% precision.
Companion notebooks
Notebooks document the structural and computational case: protected-percolation test/null/falsify; protection-fraction f; latent-heat transition; and the stopping-point convergence to the protected threshold. See notebooks.html — Dark Matter / Epi-matter section.
Honest framing
The hard predictions (P-EM-1 through P-EM-4) follow from the no-detection mechanism and do not depend on any ratio arithmetic — this is the firm part of the prediction. The soft predictions (P-EUC-1 through P-EUC-4) are commitments for Euclid DR1 (October 21, 2026). The two parameter-free matches (voids = 1 − pc, matter = pc) and the freeze location (protected threshold, established by two routes) are solid. The quantitative baryon : dark-matter ratio is suggestive but not derived: its value is located at the protected threshold, but the mechanism pinning it there is open (Open Problem 60). Any conversion of Pip counts to physical energy (via E = mc²) rests on an unproven identification — Pip counts are real bookkeeping; Pip energies carry that caveat. (The earlier "3/3 PASS at L=24 / factor-1.6" framing and the "Kibble-Zurek one e-fold (e ≈ 2.72)" claim have been superseded; the L=24 match was not asymptotic, and the e-fold proximity was coincidental.)

RETIRED PREDICTIONS

The following claims were part of earlier TSO versions and have been explicitly retired. Each retirement is documented with the reason — because the track record of killing one's own claims is part of the case for the claims that remain.

Γc = 1.5 × 10¹⁵ Hz as a critical coupling frequency RETIRED

Claimed in v10 and v11.0 to derive from α³ mec²/(2ℏ).

Retired
April 4, 2026
Reason
Consistency audit found the formula gives 1.5 × 10¹⁴ Hz, not 10¹⁵ — a factor-of-10 inconsistency. Neither value appears in the original paper or the Fire Model paper. The quantity was introduced during a conversation session and retrofitted with a derivation that did not survive verification. Replaced by dimensionless threshold p_c and empirical γ_BS calibration.
Documentation
house.html retirement section; verification at notebooks.html#core.

SM charge spectrum as specific to Z = 7 DOWNGRADED

Claimed in v11.0 that the Standard Model fermion charge set {0, ±1/3, ±2/3, ±1} emerges uniquely from Z = 7 topology with zero free parameters.

Downgraded
April 5, 2026
Reason
Null hypothesis test on the topology enumeration showed 22.7% of reasonable parameter combinations produce exact matches to the SM charge set. All matches require n_spatial = 3. The charge set is a consequence of the /3 in the Q = χ_spatial/3 formula, not specific to Z = 7. The enumeration result is still valid but its specificity was overstated.
Current status
The charge set claim (prediction 3) stands. The "specific to Z = 7" language is removed. Predictions about generation count, color, and detailed class structure are not yet tested by null hypothesis and remain potentially Z = 7 specific.
Documentation
Null hypothesis notebook, April 5, 2026.

Q = χ_spatial / 3 chirality-based charge formula RETIRED

Claimed in v11.0–v11.2 that fundamental electric charge derives from the chirality of three spatial paths under SO(3) invariance via Q = χ_spatial / 3.

Retired
April 10, 2026
Reason
Replaced by the v11.3 bidirectional X1 bond proposal with 1/3-per-bond rescaling. Different mechanism, different motivation — the two /3's are not compatible and should not be combined. The bidirectional-bond proposal produces photon self-conjugacy, electron↔positron symmetry, and automatic charge conservation under pair-correlated jump operators (algebraically verified, ‖[L, Q]‖ = 0). The chirality reading produced none of these.
Current status
Predictions 3, 4, and 5 are retained but their derivation chain is updated to reference the bidirectional-bond formalism. See house.html bidirectional bonds.

Tension asymmetry as independent predictive framework DOWNGRADED

Claimed in v11.1 that the γ_o/γ_c tension asymmetry produces the second law and arrow of time as independent empirical consequences.

Downgraded
April 5, 2026
Reason
Null hypothesis test showed the tension framework reduces mathematically to standard Lindblad decoherence — γ_c maps to dephasing rates, γ_o,active to coherent drive. The asymmetry makes no quantitative prediction distinguishable from standard decoherence plus the percolation sigmoid, so it is retired as a prediction. (A later compliance test did resolve the formal status — the dynamics are CP, trace-preserving, and Markovian/Lindblad-forced given γ_o latching — and the charge-conservation and ghost-term results are genuine; but none of that yields a distinguishable empirical prediction, so the retirement stands.) Additionally, the Pips-per-joule spread across sources is 13+ orders of magnitude, meaning "Pips of γ_o" is not a universal physical quantity at current calibration.
Current status
The asymmetry is retained as a reformulation of existing physics — valuable as a conceptual organizer (second law, arrow of time, γ_o active/stored taxonomy, tardigrade resolution, rest mass reframing) but not as an independent predictive framework. Language on foundation.html and index.html should say "reorganizes" rather than "produces."
Documentation
Tension null hypothesis notebook indexed at notebooks.html#dynamics.

IBM QPU as sigmoid test platform UN-RETIRED (April 5, 2026)

Claimed mid-2025 that IBM superconducting processors could not test the sigmoid prediction because they are engineered to stay in the wave phase.

Un-retired
April 5, 2026
Reason
The original retirement was based on idle T2 measurements, which indeed never cross the critical coupling. But the Quandela γ_BS calibration was extracted from a sweep over the number of sequential beam splitters, not a single idle measurement. The equivalent on IBM is a sweep over sequential gate depth. This is potentially accessible on IBM and would provide an independent Pip calibration. Experiment design pending.
Current status
Moved to prediction 19 (testable). The IBM v2 site-percolation variant (May 2026) hit the hardware noise floor; the gate-depth sweep variant remains untested.

δW = 2/77 approximation RETIRED

Claimed in earlier versions that the width of the observable reality band was exactly 2/77.

Retired
v11.0
Reason
The correct expression is δW = p_c − 2/7 = 0.02589…, which is irrational. The 2/77 approximation is off by 0.3% and produces misleading intuition about a "11" in the denominator that has no physical meaning. Replaced with the exact definition throughout.

Rest mass as "topology maintenance cost" REFRAMED

Claimed in earlier versions that rest mass is ongoing energy spent maintaining particle topology.

Reframed
April 4, 2026
Reason
The correct framing is "topology formation cost, stored in a locked configuration" — i.e., γ_o,stored, paid once at particle creation and latched. Protons do not eat ATP. The earlier language implied continuous expense, which is wrong.

Kim et al. 2024 Rydberg reanalysis (2.75× tanh-over-exponential) WITHDRAWN

Claimed in earlier 2026 sessions that a reanalysis of Kim et al. 2024 (initially identified as a Nature paper) showed tanh beats exponential by 2.75× on the Rydberg ground-state cluster data (ΔAIC > 30 on 129,791 shots), constituting suggestive support for Prediction 1.

Withdrawn
May 22, 2026
Reason
A citation audit during the May 22 site review revealed the original reanalysis was performed on a misidentified Kim et al. dataset (a separate paper with the same lead-author surname in a different field). The correct dataset citation is Kim, Kim, Park, Byun & Ahn, "Quantum computing dataset of MIS problem on king lattice of over hundred Rydberg atoms," Scientific Data 11, 111 (2024), DOI 10.1038/s41597-024-02926-9. A fresh audit on the correct dataset found that its data structure — 45 distinct experiments with three-parameter variation per experiment (t_Δ, Δᵢ, Δ_f) rather than a single-axis sweep — is not suited to the four-model AIC protocol as specified. None of the models in the protocol set fits the points well on the correct data. The Rydberg-evidence claim is in withdrawn status pending audit of a different dataset; Keesling 2019 or Ebadi 2021 are the natural candidates.
Current status
Removed from "Current evidence" in Prediction 1. Replaced with explicit withdrawal note.

P40 — Fano Fidelity Lock at σ = 0.18058 on IBM FALSIFIED

Pre-registered May 22, 2026 (Joshua Osborne proposal): FANO 7-qubit circuit infidelity (1−F) should lock at σ = 0.18058 ± 10% across IBM calibration cycles, with coefficient of variation at least 3× lower than NULL and RANDOM controls.

Falsified
May 24, 2026, ibm_marrakesh, 6 runs across calibration cycles, 4096 shots each
Result
FANO infidelity = 0.0895 ± 0.0078 (CV 0.087). Pre-registered band [0.163, 0.199]. Observed value at exactly σ/2 (ratio 0.4954). Sign ordering NULL (0.0084) < FANO (0.0895) < RANDOM (0.1191) preserved. CV ratios NULL/FANO = 1.39× and RANDOM/FANO = 1.99× — both below the 3× threshold.
Diagnostic confirmation
Cell-5 printout showed "2Q=0" — Joshua initially hypothesized the transpiler had stripped entangling gates (false negative). Post-hoc diagnostic confirmed the diagnostic counter checked only `cx` and `ecr` gates, missed the native `cz` gate of the Heron family. The cz gates ran (verified directly). The 10× separation between NULL and FANO infidelity is inconsistent with stripped circuits. The original result stands as a clean falsification.
Factor-of-2 analysis
The observed ratio of 0.4954 is suspiciously close to 0.5. Three candidate explanations were tested for internal consistency: (H1) classical-vs-quantum fidelity (~35% probability), (H2) bare-vs-pole dressing (~10%), (H3) rank-2-vs-rank-1 projection (~25%), with H0 coincidence at ~30%. No hypothesis was sufficiently derived to claim the σ/2 result supports rather than falsifies the prediction. The honest reading: the magnitude is wrong.
Surviving sub-result
FANO has the lowest coefficient of variation across calibration cycles (0.087, vs NULL 0.120 and RANDOM 0.172). Fano topology produces lower calibration-cycle infidelity variance than random or null on 7-qubit IBM circuits. Not a 3× effect, but a real ~30% to 50% effect. Worth tracking as a separate observation.

P41 — Three-FANO + matched-random replication at May 14 thresholds PARTIAL FALSIFIED

Pre-registered May 24, 2026: three independent 7-qubit FANO subgraphs on the same chip (single submission, same calibration cycle) should produce T3 patterns that agree with each other and beat a matched-edge-count random control at the May 14 thresholds (FANO/RANDOM >= 2.0, FANO/NULL >= 3.0).

Tested
May 24, 2026, ibm_kingston, 4 circuits × 32,768 shots = 131,072 total shots in one job (d89hbc9789is7393akug)
Result
Criterion A1 (sign matches across copies): PASS. The C_MA sign predictions replicated across three independent 7-qubit hardware regions.
Criterion A2 (within-Fano CV ≤ 30%): FAIL. RMS T3 magnitudes disagreed between the three FANO copies beyond the 30% threshold.
Criterion B1 (FANO/RANDOM ≥ 2.0): FAIL. Below May 14 threshold.
Criterion B2 (FANO/NULL ≥ 3.0): FAIL. Below May 14 threshold.
Criterion C (Steane improvement ≥ 1.2× per FANO copy): PASS literally, but counterintuitive direction. FANO improvement ratio = 3.99×, RANDOM improvement ratio = 16.4×. The Steane decoder improved RANDOM more than FANO — the opposite of what built-in error correction would produce. Most likely reading: the decoder is generically increasing T3 magnitudes regardless of topology, not specifically correcting Fano errors.
Verdict
Structural sign-pattern replication held. Magnitude separation that worked on May 14 did not hold on the calibration-controlled multi-copy version. Steane built-in EC hypothesis is not supported by the correction-ratio asymmetry.
Surviving sub-result
The sign-pattern replication across three independent hardware regions is real and worth preserving. C_MA sign predictions correctly match three-body correlations on Fano lines, on real superconducting hardware, replicable across qubit choice. The combinatorial Fano structure has hardware signature; the specific magnitudes do not. This is consistent with the v11.7 empirical scope finding.

P42 — Hexagon-with-∅-at-center + path role differentiation QUEUED, awaiting IBM allocation reset

Pre-registered May 24, 2026: addressing the path-blank concern (P40 and P41 treated all 7 qubits as identical) and the routing-noise concern (BFS-grown subgraphs forced SWAP gates). Stage 1: ∅ at the maximum-degree node of the heavy-hex chip (closest available to "hexagon center" — heavy-hex max degree is 3, not 6); T idled via Delay instructions instead of being driven; x, y, z, X₁, X₂ as standard rotated perimeter qubits. Stage 2 (gated on Stage 1 passing): X₂ as Bell-pair endpoint (non-locality), ∅ as X-basis measurement (superposition). Three structural criteria (S1A, S1B, S1C); two Stage 2 criteria (S2A, S2B). No magnitude criteria — magnitudes deliberately omitted from pre-registration following the P40/P41 pattern.

Status
Job submitted to ibm_marrakesh as d89k5eas46sc73fao4o0 on May 24, 2026 at 1:26 PM. IBM free-tier allocation exhausted before job execution; "TSO v10.1 N-Qubit Crossover Experiment" instance showed 0s remaining. Job sits in pending queue. Will run when next-month allocation resets or via paid IBM plan.
Honest framing
This is the first hardware test in the cluster that explicitly attempts to give different TSO paths different hardware roles. Whatever it produces, it will be informative: signs replicate (consistent with v11.7 empirical scope), or signs and structure-differentiation both replicate (extends the scope finding), or signs fail (informative in a different way). Result, when it arrives, will be registered here as either a new prediction entry or a retirement.

HOW TO REPORT A FALSIFICATION

If any of the predictions on this page turns out to be wrong, please report it. The framework improves through honest testing and public failure. Several of the retirements above came from exactly this kind of feedback.

Contact: [email protected]

Please include the prediction number, the specific result that contradicts it, and the reference to the data source. Notebooks and replication code are welcome. The response will be public — either an acknowledgement and retirement entry added to this page, or a specific defense of why the result does not apply. Both outcomes advance the framework.

EDIT HISTORY

May 31, 2026 (v11.9) — Epi-matter terminology and Prediction 42 (the dark matter package) — The framework's central new claim was added: what cosmology calls dark matter is epi-matter — substrate adjacent to matter in the V(W) landscape but distinct from it, occupying the protected percolation regime between pc and pq. The terminology "epi-matter" (prefix epi- as in epigenetics, epiphenomenon, epitope: alongside, of the same level, distinct) was chosen over "pre-matter" and "meta-matter" for technical precision and to avoid the metamaterials collision. Prediction 42 added at FIRM status, consolidating the dark matter package: hard predictions (no direct detection in principle; no indirect detection in principle; static epi-matter/baryon ratio from BBN through today; no de Broglie interference in halo density at any scale) and soft predictions (Euclid DR1 should reveal cored cluster profiles with inner slope 0.8±0.2, halo sphericity bounds c/a>0.7 and b/a>0.85, two distinct universality classes in the cosmic web statistics, and environmental sensitivity of the epi-matter/baryon ratio). Quantitative support: two parameter-free matches on simple-cubic site percolation (voids = 1 − pc, 0.3%; total matter = pc, 0.9%), plus the baryon : epi-matter freeze located at the protected percolation threshold (pc,protected ≈ 0.3423), established by two independent routes (stopping-point convergence to 0.3421 as L → 130, and the broken-path density at the freeze). The session also tested a candidate equivalence-principle-violation for the σ₈ tension (simplest Fano-line counting gave 13σ disagreement, asymmetry parked) and added companion notebooks. Open Problem 60 (reframed): why does the freeze halt at the protected threshold — i.e. what pins the observed 0.157 : 0.843 baryon : dark-matter ratio? A protection fraction f ≈ 0.90 reproduces it (stable across lattice size) but is read off the data, not derived; collaborator geometric proposals (f = 9/10; dim(E7) = 133) are candidates pending an independent derivation. Note: the earlier "factor 1.6 at L=24 / 3-of-3 PASS" framing and the "Kibble-Zurek one e-fold (e ≈ 2.72)" claim have been superseded — the L=24 match was not asymptotic and the e-fold proximity was coincidental. Outreach to the Fayfar-Bretaña-Montfrooij group on the basis of the published protected-percolation universality class connection.

May 30, 2026 (v11.8) — Notation cleanup, ν correction, Belenos disclosure, λ tagged EMPIRICALLY FIRM, AND Prediction 1 reframed around the phase-transition central claim — The previously-overloaded symbol κ was separated into three named quantities: α (the effective branching factor, unchanged), λ (the rate constant in the α formula, formerly κ1), and ν (the correlation-length critical exponent of percolation, formerly κ2). Prediction 2 (κ = 4/3 from 2D universality) retired with full disclosure: three converging reasons (April 2026 self-correction, direct MC of Fano-bond in Notebook 3, bulk of empirical data) put the universality class in 3D rather than 2D. Prediction 40 added as the corrected replacement: ν ≈ 0.88 from 3D percolation universality, with full disclosure of the Belenos anomaly (Belenos QPU's ν = 1.325 is now ~5σ from the corrected prediction, kept visible as unresolved, likely reflecting QPU calibration assumptions we don't yet fully understand). Prediction 41 added at the new EMPIRICALLY FIRM status tier: λ = e in the α formula, MIPT fit at 0.12σ from e, but no derivation argument survives scrutiny. Two new status tiers introduced (EMPIRICALLY FIRM, CORRECTED). Prediction 1 (Rydberg test) reframed around the phase-transition central claim: the experiment tests for the existence of the phase transition between Wave and Solid, not for the value of any specific critical exponent. Signatures reordered into three tiers (Tier 1: existence/location/floor — load-bearing; Tier 2: universality class identification — informative; Tier 3: TSO-specific multi-observable signatures — bonus). Three pre-registered outcome scenarios (A, B, C) added with explicit interpretations. A new "Central Claim" callout box at the top of the page makes the phase-structure framing visible. Three reference notebooks accompany the update: Notebook 1 (canonical reference), Notebook 2 (λ investigation), Notebook 3 (ν correction via Fano-bond MC).

May 24, 2026 (v11.7) — Empirical scope finding registered — Across four pre-registered hardware tests (Fix 4 in April, P40/P41/P42 in May 2026) a consistent pattern emerged: TSO's structural predictions (sign patterns, ordering relations, combinatorial structure on Fano lines) replicate on real quantum hardware; TSO's specific-magnitude predictions on quantum hardware do not. A new section, "Empirical Scope Finding," was added near the top of this page documenting the four tests, the platform constraint (IBM and Quandela are both engineered to one side of p_c and therefore cannot test sigmoid crossing through it), and the narrowed scope claim: on quantum hardware, TSO predicts the structure of Fano correlations, not the specific magnitudes of friction. The decisive sigmoid magnitude test requires a Rydberg array. Three new retirement entries added: P40 FALSIFIED on magnitude (factor of 2 off, signs preserved); P41 PARTIAL FALSIFIED (signs replicated, magnitude separation failed, Steane built-in-EC hypothesis not supported); P42 QUEUED at IBM free-tier exhaustion, will run when allocation resets. None of these are retirements of TSO axioms; they are narrowings of where magnitude claims can legitimately be tested. The structural-level predictions on quantum hardware (Fano sign patterns, three-body Fano-line correlations distinct from random topologies) remain supported and replicable.

May 22, 2026 (v11.6) — Site audit, Kim withdrawal, v11.6/v11.7 predictions added — Site-wide audit applied to predictions page. Kim et al. 2024 "2.75×" reanalysis claim withdrawn after citation audit revealed misidentified dataset; correct Kim dataset (Sci. Data 11, 111) is structurally unsuited to the four-model AIC protocol. Predictions 3, 4, 5 reframed under the v11.3 bidirectional X1 bond formalism (replacing the retired Q = χ_spatial/3 chirality reading). Prediction 2 source attribution updated: κ = 4/3 derived in TSO from path-rotation projection, not inherited from standard 2D percolation universality. Notebooks navigation added; all Colab citations routed through the new notebooks page. DESI DR2 dates corrected (released March 19, 2025; Lodha et al. extended analysis October 2025). Two new entries added: Prediction 38 (Fano-Tetrahedron lepton scale candidate, CANDIDATE pending QED magnitude check and rank-2 tensor consistency on vector bosons) and Prediction 39 (sigmoid saturation edge p_q = (1+p_c)/2 = 0.6558 as candidate resolution to Open Problem 59, TESTABLE via extended Rydberg sweep). HTML structural bug fixed in Prediction 24 (orphaned card).

April 29, 2026 (v11.4) — Phase theory reframe and predictions 36–37 — Two new SPECULATIVE predictions added. Prediction 36: coupling constants run as power law (α ~ μ^−0.96 for strong) rather than logarithmically — diverges from SM at extreme scales, potentially testable at LHC. Prediction 37: position uncertainty grows linearly with Lorentz factor above γ_crit (Δx ~ γ × l_switch) — distinct from standard QM uncertainty, observable in principle at future colliders. Framework reframed as phase theory of matter: TSO describes phase structure (force hierarchy direction, symmetry breaking pattern, beta function signs); SM describes constituent details (exact masses, coupling magnitudes). Carrier neutrality derived: C = Q (carrier carries own charge) → non-Abelian → β < 0; C ≠ Q → Abelian → β > 0. All four force beta function signs from this rule alone. Color charge proposed as X₁-internal orientation in {x,y,z}: 3 colors, 8 gluons = 3×3−1. Three generations proposed as three spatial propagation orientations. Cluster identified as organizational structure of critical phase — not necessarily a particle. Striking convergence with anaesthesia research noted (same sigmoid, same non-locality, same component separability) but no claim to explain consciousness — additional path dimensions may be required.

April 26, 2026 (v11.4) — Quandela hardware test and P34 narrowing — P34 tested on Quandela Ascella photonic QPU using true single photons. Separable-circuit approximation (32×32 modes, outer product of two 1D circuits) run at N up to 10,000,000 shots. Result: d_f = 2.0000 flat across all N values. Standard QM confirmed. P34 (separable-circuit version) falsified. P34 narrowed rather than retired because the genuine 2D coupled free-space interference experiment was not performed — only a separable approximation. Prior for positive result in genuine test is low given all prior literature. X₂ entanglement path notebooks added (entanglement + orbital degeneracy; Lindblad consistency 4/4). ∅ as Higgs mechanism notebook added (4/4 null tests). Node switch rate and QGP frame-matching notebook added. Remaining gaps notebook added (K=Q·v closed geometrically; μ₀/ε₀ structure clear; X₂→spin consistent; ∅→Casimir consistent; parity partially closed). Superposition clarified as projection geometry — the car-behind-a-car analogy: two cars parked one behind the other appear in superposition from directly in front (same x,y window slot) but are clearly distinct from the side (different z position). The cluster is always definite in W-space; superposition is a projection aliasing artifact of the {x,y,z} window, not a real property of the cluster.

April 23, 2026 (v11.4) — Electromagnetic derivation and gradient loop EMF prediction — Prediction 35 added (SPECULATIVE): for a conductor loop spanning a gravitational gradient, TSO predicts ~17% larger induced EMF than GR+Maxwell. The difference arises because TSO applies δT = √(1−rs/r) as a spatial average over the entire loop (T conductance at every segment), while GR+Maxwell applies it only at the source point (gravitational redshift at emission). This is a direct consequence of the TSO electromagnetic derivation completed this session: all four Maxwell equations plus c = 1/√(μ₀ε₀) derived from X₁ conservation and T as active path with g = −1. No results imported from Maxwell or special relativity. Seven Colab notebooks. New sub-page: roof-em.html. δT derived from T direction asymmetry under G field (not borrowed from Schwarzschild). Lenz law = metric signature of T. EM waves = self-sustaining T-mediated X₁ oscillations.

April 21, 2026 (v11.4) — Quantum geometry, cosmic structure, falsifiability boundary, and fractal dimension simulation — Two new predictions added following the scale-free percolation insight. Prediction 33 (TESTABLE): cosmic web cluster statistics should match 3D percolation universality class — Fischer exponent τ ≈ 2.18, void distribution, and filament fractal dimension df ≈ 2.52, all zero free parameters. Upgrades Prediction 10 from a single numerical coincidence to a full geometric constraint. Prediction 34 (CONDITIONAL): 3D volumetric single-particle accumulation using concentric annular slits should show fractal fine-structure in the probability density at high statistics, with d_f = 2.52. The theoretical gap for Prediction 34 was closed the same day by percolation simulation: M(L) ~ L^d_f scaling on the TSO 7-path lattice gives d_f = 2.4857 ± 0.0378 (consistent with literature value 2.5226 within 1.0σ); Fisher exponent τ = 2.097 ± 0.006 (consistent with 2.1875). Both confirm the TSO lattice percolates in the 3D universality class. New section: The Falsifiability Boundary.

April 19, 2026 (v11.4) — Projection falsification suite — Five new entries added following the projection falsification Colab suite (run April 18–19, 2026). All five derive from the same theoretical development: Heisenberg Uncertainty as a consequence of partial dimensional projection from finite probability fuel, rather than as an axiom. Prediction 28 (SUGGESTIVE): Space Roar as Larmor radiation from W-space bobbing — Larmor estimate within 2.2 orders of magnitude of ARCADE observed excess, no free parameters fitted. Prediction 29 (TESTABLE): sigmoid decoherence transition width = dW = 0.026 — same Rydberg sweep as Prediction 1, new observable. Prediction 30 (TESTABLE): peak decoherence rate |dV/dΓ| at Γ_c not before it — cleanly distinguishable from standard QM (separation 0.997 Γ_c in simulation). Prediction 31 (SPECULATIVE): THz spectral feature in QCP material Johnson noise at f = kT_c/2πℏ ≈ 6.3 THz at room temperature. Prediction 32 (SPECULATIVE): scattering anisotropy near decoherence threshold from 2D projection geometry. Predictions 29 and 30 are testable with no hardware beyond the planned Rydberg experiment.

April 18, 2026 (v11.3) — DESI DR2 update — Prediction 13 (dynamical dark energy) upgraded from TESTABLE to SUGGESTIVE following DESI DR2 results (released March 2025; extended analysis October 2025). BAO measurements from 14M+ galaxies show 2.8–4.2σ preference for evolving dark energy (w ≠ −1), consistent with TSO's Avrami crystallization prediction. Dataset tension caveat noted; full 5-year DESI results (2027) remain the decisive test. Prediction 10 (Ω_m ≈ p_c) updated with DESI DR2 CPL-model caveat: dynamical model fits prefer Ω_m ≈ 0.385, model-dependent but worth watching.

April 18, 2026 (v11.3) — Metamaterial prediction — Prediction 27 added: percolation-critical metamaterial with anomalous inertial and EM properties. A material engineered to Z_eff ≈ 7 connectivity and W ≈ p_c should show reduced effective inertia, anomalous EM transparency, and criticality amplification. The most TSO-specific test is a non-unity inertial-to-gravitational mass ratio at the quantum critical point — not predicted by standard condensed matter theory. Firmly Roof-level; derived from the three-phase model and criticality amplification argument, not from core axioms.

April 18, 2026 (v11.3) — Two new entries added. Prediction 25: LRD sublimation sigmoid — pre-registers the claim that LRD number density n(z) follows a sigmoid on the decline side (z ≈ 4.5 → 1.5), not an exponential, with the inflection at z ~ 2.5–3.5. Numerical test using Kocevski et al. 2025 and Ma et al. 2025 data showed sigmoid and exponential are indistinguishable with 4 decline-side data points (both R² = 0.9484); z = 1–2 data needed. Prediction 26: LEL cascade — recovers the Lower Entanglement Limit equation from TSO v6.3, formalizes the updated S-field with Heaviside step function Θ(ELEL − E), and pre-registers it as the mechanistic basis for the sigmoid shape in prediction 25. Both entries added before the z=1–2 data is in hand.

April 5, 2026 (v11.1) — Page created. Initial entries extracted from llms.txt v11.1, foundation.html, house.html, roof.html, and the DM analysis documents (TSO v6.1 and v9.2). Null hypothesis test results from April 5 incorporated as downgrades in the retired section.

Future updates will be logged here in reverse chronological order so that any revision of a prediction is traceable against the data that prompted it.