NOTEBOOKS

WHAT THIS PAGE IS

Every numerical claim TSO makes — σ = 0.18058, p_c = 0.3116, 1−p_c = Ω_Λ to 0.07%, the Pip mass spectrum, sin²θ_W = 3/13, the Anderson localization gap, and the rest — comes out of a notebook that can be opened, run, and verified. This page is the index of those notebooks. They are organized by topic, with the most load-bearing results listed first.

Notebooks marked [load-bearing] support a claim referenced from the landing page, math cheat sheet, or house. Notebooks marked [exploratory] or [roof level] are speculative work in progress and should be treated accordingly. Notebooks marked [superseded] are kept for the historical record; newer notebooks above them carry the current result.

The framework's policy: anything claimed in prose has a notebook behind it. If a notebook below conflicts with prose elsewhere on the site, the notebook wins — please report the discrepancy.

v11.8 REFERENCE NOTEBOOKS — NOTATION CLEANUP

Three reference notebooks support the v11.8 disambiguation of κ into three distinct named quantities (α the branching factor, λ the rate constant, ν the correlation exponent). The first is the canonical reference for the renamed framework; the other two are the substantive investigations of λ = e and the corrected ν ≈ 0.88.

See retired Prediction 2 and Prediction 40 for the full retirement/replacement; Prediction 41 for the EMPIRICALLY FIRM status of λ = e; and the math page v11.8 notation update for the equations under the new names.

v11.9 NOTEBOOKS — DARK MATTER / EPI-MATTER (WORKING)

Six notebooks were produced during the May 31, 2026 dark matter session, which introduced the framework's identification of dark matter with epi-matter — substrate adjacent to matter in the V(W) landscape but distinct from it, occupying the protected percolation regime. Companion to Prediction 42.

The notebooks span: structural due diligence, quantitative cluster ratio test, σ₈ tension investigation, Euclid prediction package, finite-size scaling check, and Kibble-Zurek consistency test. They are listed in roughly the order they were produced during the session, which is also the order they should be read in. The framework does not yet commit to a single mechanism for the cluster ratio match; four candidate explanations are tracked.

Open Problem 60 (added v11.9): how is the cosmic L (where the cluster ratios get locked in) set? Three candidates: (a) Planck-scale cutoff at L ~ ℓ_Planck; (b) Kibble-Zurek-driven lock-in scale set by cosmic quench rate at percolation event; (c) cosmic correlation length at the moment of the percolation event. Resolution requires either deriving the lattice unit in physical length from framework axioms or specifying the cosmic dynamics during the early-universe percolation event. The Fayfar-Bretaña-Montfrooij group at Missouri (published protected percolation universality class with γ' = 1.3066, the closest condensed-matter analog) is the natural expert audience for this question; outreach planned.

See Prediction 42 for the consolidated dark matter / epi-matter prediction package on the predictions page.

1. CORE RESULTS — σ DERIVATION AND THE CY STAIRCASE

The thermodynamic noise scale σ = 6/√1104 = 0.18058 is the centerpiece of v11.6. It is a proposed closed form built from two TSO axiom integers (V_tet = 4, χ(K3) = 24), with provenance unverified: it reproduces 0.18058, but 6 and 1104 are not yet shown to be forced rather than selected to match the target, and the derivation chain has not been independently reconstructed. The Calabi-Yau staircase associated with it has been PALP-verified at three rungs.

2. STRESS TESTS AND FIXES — THE v11.6 / v11.7 COLLABORATION

Joshua Osborne's six stress tests subjected TSO's geometric primitives to independent checks against PDG masses, the fine-structure constant, dark energy density, the W boson mass, and lepton ratios. Five of six pass cleanly. The sixth (lepton absolute scale) became Fix 4, which has a candidate resolution via the Fano-Tetrahedron formula A = √E_Pip × (Z/V_tet)² — a 0.04% numerical match, though not truly parameter-free: E_Pip derives from σ = 6/√1104, whose provenance is unverified, and the (Z/V_tet)² factor and the squaring step are proposed, not derived. A genuine 0.04% match resting on a candidate σ, pending the squaring derivation.

3. THE DECISIVE TEST — RYDBERG SIGMOID

The Rydberg sigmoid experiment tests four independent predictions (P1 shape, P40 ν ≈ 0.88, P29 width, P30 peak location) from a single sweep. It is the experiment that confirms or falsifies TSO. The protocol notebook closes the open observability questions (Γ_net measurement, δW window, and the question of which Kim et al. dataset to audit). Outreach to KAIST (Ahn) and MPQ Munich (Gyger) is pending response. v11.8 update: the original P2 prediction (κ = 4/3 from 2D universality) has been retired and replaced by P40 (ν ≈ 0.88 from 3D universality) — see retired Prediction 2 and Prediction 40.

4. EXISTING HARDWARE TESTS — QUANDELA AND IBM

Quandela Belenos (photonic boson sampling) supplies the only anchored Pip calibration to date: γ_BS = 522 Pips. IBM heavy-hex hardware confirms the Anderson localization gap direction (p_q > p_c) but cannot resolve its position because the hardware sits above p_c by engineering. The Fano 7-qubit circuit is the most direct available test of G2 structure.

5. PARTICLE STRUCTURE — PIPS, CODEWORDS, AND THE FANO PLANE

Topological particles (proton N=28, D meson N=56, Omega⁻) sit ON [7,4,3] Hamming codewords; energetic particles (kaon N=15, Λ, Σ, Ξ) sit OFF codewords with HD=1 — decay is the universe correcting a bit error. The Pip mass spectrum (E_Pip = 33.437 MeV) anchors hadron masses to 0.2–1.6% across the table. Strangeness emerges as the 4th coordinate of PG(3,2) — non-strange particles live in the 2D Fano subplane.

6. STANDARD MODEL CONSTANTS

Specific numerical results for SM constants derivable from TSO geometric primitives. sin²θ_W = 3/13 from Fano degree counting (0.09% from measurement, zero free parameters — integer counting, no tuned values). [Caveat added July 13, 2026: sin²θ_W runs with energy (≈0.2312 at M_Z, ≈0.2386 at low Q), so a fixed integer ratio matches at most one scale — the 0.231 match implicitly selects M_Z, unexplained. Treat as the M_Z-scale value. The "13 gauge degrees" count is also downstream of the gauge-group reading corrected below.] All four Maxwell equations are recovered from X₁ conservation and T as active path (a derivation within the framework's assumptions). The cosmological constant Λ_TSO is obtained from Fano geometry and checked against four independent tests.

7. G2 GEOMETRY AND THE FANO STRUCTURE

The 7D G2 manifold is the compactified boundary of a Calabi-Yau fourfold. The Fano plane provides the irreducible 7-path structure that grounds Z=7. Octonion / Fano mapping produces an identity-best 74% match with carrier neutrality. [CORRECTED July 13, 2026] An earlier version stated "spontaneous G2 → SU(3)×SU(2)×U(1) symmetry breaking occurs at p_c — the transition IS the GUT symmetry breaking event." That is group-theoretically impossible (G2 is rank 2, the Standard Model group rank 4; a subgroup cannot exceed its parent's rank — computed: dim Der(𝕆)=14, rank 2) and is retracted. What survives is colour SU(3) only, as the stabilizer of ∅/HERE in G2; the electroweak factor needs a separate rank-≥4 structure (octonion left-action / triality), not G2, and is open. See house.

8. DYNAMICS — V(p), RG FLOW, AND LINDBLAD

The equation of motion dp/dt = γ_o(p, stored) − γ_c(p, interactions) IS the RG beta function with mechanical meaning. The wave phase is the high-energy state; γ_c lowers energy via interaction, γ_o raises it via stored configuration. TSO's γ events map onto Lindblad jump operators in the technical sense — pair-correlated operators commute with the charge operator exactly (‖[L, Q]‖ = 0), making charge conservation structural rather than postulated.

9. BLACK HOLES AND COSMOLOGY

Black hole resonance derived from Bell + Itô SDE formulations. Vacuum closing tension γ_c connects to dark energy as undepleted stored γ_o. The cosmological match 1 − p_c = Ω_Λ at 0.07% (Planck 2018) is one of the framework's tightest results. Boundary flux injection produces p₁ = 30 and the tadpole condition N = 15 as exact integers.

10. FRACTIONAL QUANTUM GRAVITY (FQG) BRIDGE

The primary theoretical framework for TSO is Fractional Quantum Gravity (Calcagni 2021, Class. Quant. Grav. 38, 165006, arXiv:2102.03363; recent perturbative-unitarity work Calcagni & Briscese 2026, arXiv:2603.25709). The bridge equation d_S(FQG) = d_f(TSO) = 2.571 at E = E_Pip connects the two frameworks at the Pip scale. The PG(n,2) → PG(n+1,2) level transitions in the projective hierarchy ARE the FQG dimensional flow.

11. PIP LATTICE AND FIRST-PRINCIPLES MATRIX WORK

The Pip lattice underlies the quantitative mass spectrum. First-principles matrix elements come from a Hamiltonian built directly from the function-identity structure. Monte Carlo on the Pip lattice addresses Open Problems 7 and 8 (couplings, K = Q × v).

12. SPECIAL-PURPOSE NOTEBOOKS

Notebooks supporting specific structural claims that don't fit neatly into the categories above. The Two Basins notebook formalizes the System 1 (Solid) / System 2 (Wave) interaction at the W_dm floor. The ∅-as-Higgs notebook proposes the ∅ path as the vacuum direction field that drives electroweak symmetry breaking. K = (e + φ)/2 derives the universal calibration constant from first principles.

13. META — STATE OF THE FRAMEWORK AND OPEN PROBLEMS

Notebooks that capture the framework as a whole. If you're new to TSO and want a single starting notebook, open tso_state first. The open-problems notebooks rank the unresolved questions — currently 68 open problems as of v11.7 candidate work.

HOW THE REST OF THE SITE LINKS HERE

This page is the single source of truth for notebook references. When other pages on the site cite computational evidence, they link to a specific anchor on this page rather than to the Colab URL directly. That way:

1. A notebook URL only needs to be updated in one place (here) if it changes.
2. The reader gets the surrounding context (which other notebooks are on the same topic, what status flag the notebook carries) instead of being dropped into a notebook cold.
3. Superseded notebooks remain accessible but flagged, rather than being silently broken.

Example link pattern for use on other pages:

Anchor reference for cross-page links: #core, #stress-tests, #rydberg, #quandela-ibm, #particles, #constants, #g2, #dynamics, #cosmology, #fqg, #lattice, #other, #meta.

STATUS LEGEND

[load-bearing] — supports a claim referenced from the landing page, math cheat sheet, or house. Should not be removed without updating dependent pages.

[v11.7 candidate] — produced during the v11.7 collaboration with Joshua Osborne (May 19–21, 2026). Pending derivation work before promotion to load-bearing.

[roof level] — exploratory or speculative work on the roof. Not load-bearing but worth keeping for the structural arguments.

[exploratory] — early-stage notebooks; results may be partial, untested, or pending revision.

[honest negative] — notebook that produced a result inconsistent with TSO's current prediction. Kept for transparency. See house page for the framework's response.

[superseded] — earlier version of a notebook that has been replaced by a newer version above it in the same table. Kept for historical record.

[partial] — notebook needs updating to reflect a newer version of TSO.

NOTEBOOK URL TABLE — TO BE FILLED

This page currently uses placeholder links (href="#") for each notebook. As Colab URLs are confirmed they will be filled in here. To verify a notebook before its URL is added, open the corresponding .ipynb file from the framework's Colab folder.

Suggested fill order: section 1 (core results) first — those are the load-bearing claims everyone wants to verify. Then sections 2–3 (stress tests + Rydberg). Then the rest can fill in over time as cross-references from other pages get added.