OPEN PROBLEMS

Roof — Master List

Version 11.6  |  Updated May 20, 2026

⚠️ Ongoing research project. This is the honest list of things TSO does not yet explain, cannot yet predict, or has no clean derivation for. Reading the open problems is often more informative than reading the results — it shows where the framework could most fruitfully be tested or refuted.

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NEW — JUNE 2026 (MASS-FROM-CLUSTERS + BARYON SHORTFALL SESSION)

Session summary. A sustained investigation into how mass arises from clusters, prompted by the realization that every baryon/cosmology test had been measuring "mass" as a node/site count, while the framework's own position is that mass = γ_o,stored = connectivity-stored tension (a proton is ~99% gluon/binding energy, ~1% quark/node mass). The work poured a foundation for the mass mechanism, unified two previously separate mass accounts, bracketed the long-standing baryon shortfall, and sharpened the central open problem into a single decidable question. Confidence framing unchanged throughout: the whole arc is consistency/structure work and does not move the framework's standing (~5% by the author's estimate; the decisive test remains the Rydberg sigmoid). Companion Colab notebooks: mass-from-clusters, baryon-factor, baryon-partition-sweep, two-p_q, melded-mass, mass-consistency/feedback, stored-tension-law, Fano-cycle-coefficient.

Result — the two mass stories unify (consistency check passed). TSO carried two accounts of mass that had never been checked against each other: the σ/Pip account (mass = N × E_Pip, N an integer Pip count) and the connectivity account (mass = stored tension, not a count). The decisive proton test shows N = 28 Pips matches the total/binding mass (total/E_Pip ≈ 27.95), not the node/quark reading (≈ 0.27). So a Pip is a quantum of connectivity-stored tension: σ sets the quantum size (E_Pip), connectivity sets the count (N). The two stories are one mechanism. (Unification, not independent derivation — the N values were originally mass-fit.)

66. The stored-tension law — how many Pips does a topology store? With mass established as connectivity-stored tension counted in Pips, the central open problem is now sharply stated: the exact rule for how much tension a given topology stores. It is bracketed — pure node-weighting gives a cosmic baryon fraction ~1.5× too low; pure degree/connectivity-weighting gives ~1.2× too high; the true law is a principled intermediate, closer to degree than to node count. Cycle/loop weighting overshoots, so the law is bond-degree-like, not topology-complexity-like. Triangulation against the proton 99/1 split and the cosmic baryon fraction shows a single one-parameter degree^α law cannot satisfy both (proton wants steep, cosmos wants nearly flat), so the law has interacting structure (a degree piece and a cycle piece), not one knob.

67. Does stored tension normalize by total cycles or tension-carrying cycles? The cosmic baryon fraction wants the cycle-term coefficient near 1/8 = 0.125 (a 0.4% match, and a real Fano count: the Fano complex has β₁ = 8 independent 1-cycles). But the framework's own torsion rule — active cycles carry the torsion, the three trivial cycles carry zero topological charge — forces the active-cycle normalization 1/5 = 0.20, which the fit disfavours. So 1/8 is structurally motivated yet in tension with the tension-carrier rule. This is decidable independent of the baryon fit: determine from the framework's torsion structure whether stored tension normalizes by total β₁ = 8 (gives 1/8, matches) or by the 5 active cycles (gives 1/5, fails). Resolving it would either derive the coefficient or expose it as a crowded-window coincidence (≈9 simple ratios live near the target, so proximity alone is not evidence).

Baryon shortfall — status upgraded from "34% low" to "bracketed." The ~1.54× under-prediction of the baryon fraction survived four attempted explanations, each eliminated cleanly: a clean structural factor (no forced candidate; ≈14/9 = 2Z/9 is seductive but the 9 is not forced and the window is crowded); a bond/node correction (gives 0.39, wrong); a two-threshold/frame-dependent-p_q partition (the splits decouple but the shortfall persists ~31% low — robust to partitioning); and finally the melded-mass weighting, which is the first survivor and brackets the answer between node and degree weighting. The shortfall is therefore not a partition/sorting problem but a mass-weighting problem — it lives in how much each baryon weighs, which is exactly the stored-tension law (problems 66–67).

Cosmology cross-check (2025 FRB data). The astronomical "missing baryon" problem is resolved: late-universe FRB dispersion gives total Ω_b ≈ 0.049–0.051, matching CMB+BBN, with ~76% of baryons in the diffuse intergalactic medium and ~24% halo-bound. TSO's target is the complete census, so there are no uncounted baryons to recover. A bonus consistency result: at the axis-aware (x,y,z) connectivity threshold the lattice reproduces both the ~76/24 IGM/halo split and the void fraction (0.688) jointly from one principled rule (consistent within the FRB ±0.10 error bars, not a unique fit). This does not explain the 1.54 shortfall, confirming again that the shortfall is a weighting, not a partition, issue.

Two-frames hypothesis (proposed, one supporting case). A conjecture that TSO gets direction/structure right but magnitude wrong because structure is the frame-invariant bridge while magnitude is frame-dependent. One genuine supporting case: the Pip's energy scales with system size by ~10¹¹ (a clean multiplicative scale factor — the connectivity-quantum count is frame-invariant, its size E_Pip is frame-dependent). A dedicated magnitude-error audit was under-powered (most TSO magnitude errors are sub-percent, where multiplicative and additive errors are mathematically indistinguishable) and mildly negative on the one clean statistic. Status: proposed, one case, not established.

Higgs = ∅/HERE (proposed, refined). The pre-existing identification of the Higgs with the ∅ (HERE) path was sharpened with a field-vs-excitation distinction: the ∅/HERE field is always on (the mass mechanism, low-energy), while the Higgs boson is a transient high-energy excitation of that field. The dimensionless Higgs VEV ratio m_H/v = 0.5087 was compared to p_q; it lands near the minimal-pinning value (0.53, ~4%) but the principled transition midpoint is further (0.55, ~8%), and zero of five dimensionless transition features land within 5%. Verdict: "similar but different" — m_H/v (a ripple-to-field ratio) and p_q (a threshold location) are different kinds of quantity that both sit near ½, a near-half coincidence that needs the Higgs = ∅ mechanism to mean anything. A genuine refinement from this work: p_q is not a single number but a sparse discrete ladder of axis-direction protection rules (0.53, 0.55, 0.58, 0.66), since the six neighbours are three axes × two directions and principled 3D-pinning has sub-variants between the integer-k rungs.

On the record-keeping: some specific numbers in earlier sessions above and on sibling pages (for example the original "factor 1.6 / 34% low" framing of the baryon match, or treatments that counted mass by nodes) are superseded by the connectivity-mass picture established here. They are deliberately left in place rather than deleted — the open-problems log and the session history exist partly to preserve the timeline of how the theory developed, including the steps that were later corrected. Where a claim has been superseded, the newer entry states so; the older text is kept as the dated record of what was believed when.

NEW — MAY 19–20, 2026 (CY STAIRCASE + σ DERIVATION SESSION)

Session summary. χ(CY4) = −3192 confirmed as PALP-verified Euler characteristic of WP5[1,3,7,19,19,19]. CY staircase verified at three rungs (K3, Fano/CY3, Kaon/CY3, E₇/CY4). SVW debt framing: negative χ = singular geometry = gauge symmetry in singularities. σ = C(4,2)/√(4×C(24,2)) fully derived from {x,y,z,T} tetrahedron + K3 cohomology. Six stress tests passed. IBM QPU v2 run (site percolation); tight-binding p_q test completed. New open problems #59–65 below.

59. Reconcile TSO's p_q = 0.6556 with tight-binding literature. The tight-binding quantum percolation threshold for 3D Z=6 cubic site percolation is p_q ≈ 0.44 (Soukoulis & Grest 1992). TSO's σ formula gives gap = 0.344 → p_q = 0.6556. Computational test (May 20, 2026) finds L→∞ extrapolation heading toward 0.44–0.47, not 0.6556. Anderson disorder W ≈ 8t is needed to reach the TSO value. These may measure different physical quantities. Required: identify what physical mechanism makes TSO's p_q = 0.6556 rather than 0.44, OR compute a Z=7 lattice at L→∞ to confirm or deny. Do not register as Prediction 38 until resolved.

60. Kaon tadpole denominator /36 vs /24. The Fano and E₇ levels use N = |χ|/24, but the kaon-level CY3 WP4[1,1,1,6,9] gives N = |χ|/36 = 15. The extra factor of 12 likely comes from the Z₃ orbifold correction at the [6,9] stratum (gcd=3, 3|18). Formal derivation of the orbifold contribution needed.

61. WP5[1,3,7,19,19,19] Hodge numbers. PALP returned M:581 27 F:14 non-transversal. The non-transversal flag means the generic hypersurface is singular — Hodge numbers h^{p,q} were not extracted. Required: resolve singularities or use a smooth deformation to get h^{1,1}, h^{1,2}, h^{1,3}, h^{2,2} and verify χ = 6 + 2h^{1,1} − 2h^{1,2} + 2h^{1,3} + h^{2,2} = −3192.

62. h₁₁ = 2 at every CY3 rung — derivation. Both confirmed CY3 geometries have h₁₁ = 2 (WP4[1,1,2,2,2] and WP4[1,1,1,6,9]). Two Kähler moduli = two TSO phases. Is this provable from the weight structure, or coincidence?

63. E_Pip-level CY geometry. The tower predicts a CY3 with χ = −24 (N=1) at the E_Pip level. This would have h₂₁ − h₁₁ = 12. Find the WP4 geometry and verify h₁₁ = 2 if the pattern holds.

64. Lepton mass absolute scale from σ. The 2T phase rotation matrix gives exact lepton mass RATIOS via the Koide formula (Q = 2/3 from equal angular spacing). The absolute scale requires A = mean(√m_i) to be derivable from σ × M_Z × PIP or equivalent. Currently one lepton mass is needed as anchor. Close this to make the lepton sector fully ab initio.

65. Physical derivation of 1 − p_c = Ω_Λ. Numerically: 1 − 0.3116 = 0.6884, Planck 2018 Ω_Λ = 0.6889, error 0.07%. Bonus: Ω_matter = 0.3111 ≈ p_c = 0.3116 (0.16%). Physical interpretation: inactive bonds (below classical percolation threshold) = dark energy / cosmological constant; active bonds = classical matter. Formal derivation of why the geometric bond fraction maps to the cosmological energy fractions is entirely open.

NEW — MAY 11, 2026 (THERMODYNAMIC DYNAMICS SESSION)

Session summary. γ_o and γ_c identified as forces on a potential energy landscape V(p). Equation of motion dp/dt = γ_o(p, stored) − γ_c(p, interactions) is the RG beta function with mechanical interpretation. V(p) minimum at Wdm = 2/7, saddle at p_c. IBM Anderson localization gap = 0.161 confirmed on ibm_marrakesh. sin²θ_W = 3/13 from Fano degree counting formally recorded (0.09%). Four new open problems added (#11–14). Open problem #2 (Hamiltonian specification) partially resolved.

Open Problem #2 — PARTIALLY RESOLVED

The dynamical equation dp/dt = γ_o − γ_c is now established as the equation of motion. The potential energy landscape V(p) is constructed phenomenologically with the correct boundary conditions. What remains: (a) formal derivation of V(p) from TSO axioms (open problem #11 below), (b) path-integral quantization of the equation of motion (open problem #13), and (c) Lindblad matrix elements for specific particles (still unresolved).

Four new open problems (v11.5)

49. Formal derivation of V(p) from TSO axioms. The potential energy landscape is currently constructed phenomenologically — it satisfies the required boundary conditions (minimum at Wdm, saddle at p_c, rising wave phase) but is not derived from the percolation free energy. The Sykes-Essam theorem guarantees a non-analytic feature at p_c in the free energy; TSO's V(p) should follow from that free energy by differentiation. Closing this would promote V(p) from phenomenological to derived.

50. Bridge γ_o/γ_c ratio to sin²θ_W = 3/13. Two v11.5 results exist independently: the equation of motion with γ_o/γ_c as force ratio, and the Fano degree counting giving 3/13. Both involve the same Fano geometry but no formal bridge connects them. Joshua Osborne's observation ("the answer is already in the structure") and the NB2 Colab confirm the normalization step IS the counting — but this is assertion, not derivation. The formal bridge would show that the γ_o/γ_c force ratio at p_c is exactly 3/13 from the G2 normalization of the path coupling geometry.

51. Quantize the equation of motion (path integral form). dp/dt = γ_o − γ_c is a classical dynamical equation on the potential V(p). The quantum version — a path integral over p-trajectories weighted by exp(iS/ℏ) where S = ∫[T − V(p)]dt — should recover standard QM in the wave-phase limit and classical behavior in the solid-phase limit. The quantization would also clarify the relationship between dp/dt and the Lindblad master equation (which is already a quantum dynamical equation). This is the deepest remaining theoretical task.

52. Derive particle masses from oscillation frequencies near Wdm. Small oscillations around the potential minimum at Wdm = 2/7 give harmonic oscillator modes with frequency ω = √(V′′(Wdm)/m_eff). In quantum mechanics, the ground state energy ℏω/2 of each mode is a candidate rest mass. If the effective mass m_eff and V′′ can be derived from the lattice geometry, this would give a first-principles mass spectrum. The electron, muon, tau mass ratio should correspond to three distinct oscillation modes — matching the three fermion generations that already appear in the topology enumeration.

NEW — MAY 2026 (ADDITIONAL G2 NOTEBOOKS)

Weak mixing angle sin²θW = 3/13 — Colab

Pure Fano degree counting. Surviving path degrees: U(1)=1, SU(2)=6, SU(3)=6, Higgs=2. Total gauge (non-Higgs) = 13. sin²θW = (dSU2/2)/13 = 3/13 = 0.2308. Measured: 0.231. Difference: 0.1%. Higgs decoupling encoded in degree structure. Tadpole N=15 connects directly to the mixing angle.

TSO State of the Framework v11.4 — Colab

Complete single-notebook summary. Derivation chain with honest status labels. Exact results (K5 eigenvalues, p1=30, N=15, sin²θW=3/13). Nine proposed results with evidence and gaps. Ten open problems ranked by importance. Four falsification conditions. Independent convergences (Hope, Osborne, Clayworth). Confidence assessment per result. The single notebook to hand someone asking "what is TSO and where does it stand?"

NEW FROM APRIL 23, 2026 SESSION — EM DERIVATION AND X2 ENTANGLEMENT

Electromagnetism complete (roof-em.html). All four Maxwell equations plus c = 1/√(μ₀ε₀) derived from X₁ conservation and T as active path. Seven Colab notebooks. See roof-em for the full chain. Remaining open problems from this work listed below.

From the EM derivation

X2 = Entanglement Path — New Proposal (Colab: X₂ entanglement | Colab: Lindblad consistency)

X₂ has been relabelled from "superposition path" to "entanglement path." Superposition is no longer assigned to a path — it is cluster projection geometry onto the {x,y,z} window. This resolves the Bell paradox without mystery: two entangled particles are adjacent in W-space (they share an X₂ wall) regardless of their spatial separation. Bell proved there are no local hidden variables in {x,y,z} — correct. The hidden variable (X₂ adjacency) is local in W-space.

[DOWNGRADED July 13, 2026.] The "X₂ = entanglement path" and "local hidden variable in W-space" framings are downgraded on two grounds from the July gauge/HERE session:

(1) Not a path. Fixing ∅/HERE decomposes the node's C⁴ as C¹⊕C³ — a direct sum (1+3, the SU(3) branching), not a two-qubit tensor product C²⊗C². Entanglement requires a tensor product, so it cannot be carried by a single intra-node path. It is an inter-node property, inherited via the tensor-product composition rule (same tier as "inherits Born via Gleason") — not derived, not a path. X₂ may label or track the bond, but the bond is the inter-node tensor structure, not a node-internal path.

(2) Not a hidden variable. The "hidden variable local in W-space" wording is self-undermining and is retracted: the notebook below reaches the Tsirelson bound (2√2), and Bell's theorem forbids any local hidden variable — in any space, W-space included — from reaching Tsirelson (a local hidden variable caps at 2). Reaching 2√2 is precisely the signature that it is not a hidden variable. The correct frame is a non-traversable ER=EPR-type bond: a shared quantum state that carries no signal (consistent with no-signaling because nothing traverses it), not a hidden variable.

The concurrence mapping, orbital-degeneracy (2l+1), shell-capacity, and Pauli-from-topology results below are independent of this framing and are unaffected; only "path = entanglement" and "local hidden variable" are downgraded. Full record on house.

Lindblad consistency verified — 4/4 checks, 4/4 null tests. X₂ bonds map onto concurrence C in the joint density matrix ρ_AB. The complete Lindblad picture of TSO is now: T → −i[H,ρ] coherent H term; γ_c → L dissipator; X₂ bonds → concurrence in ρ_AB; superposition → local ρ_A coherence (not a path). Superposition is operationally distinct from entanglement in Lindblad: decoherence on A destroys A's local coherence without affecting B; decoherence on A also destroys the X₂ bond and affects the joint state. Same Lindblad machinery, different parts of it.

Results from the notebook that are clean and exact:

Open problems remaining from the X₂ proposal:

NEW FROM APRIL 4–5, 2026 SESSIONS

These are the freshest open problems, arising from the v11.1 / v11.2 adversarial testing and the Pip framework.

39. Pip universality across hardware platforms — currently the single most important open question for the Pip framework. Only γBS = 522 Pips from Quandela is anchored to an independent experimental measurement. To give the Pip unit real cross-platform predictive power, we need ≥3 independent calibrations from different hardware classes (superconducting transmons, trapped ions, NV centers, Rydberg arrays, non-Quandela photonics), each extracted by fitting that platform's own decoherence to a percolation sigmoid. If J/Pip values agree to within an order of magnitude, the Pip unit becomes a real dimensionless coupling quantity. If they disagree by many orders of magnitude, the Pip unit is per-platform bookkeeping and must be relabeled. IBM gate-depth sweep is the first attempt (prediction 19).

40. Z=7 class-structure null test — the April 5 topology null test showed that the SM charge spectrum match is generic across Z ∈ {5..10} once nspatial = 3 is fixed. The detailed class structure — three classes per charge (generations), 3-fold color multiplicity for |χspatial| = 1 classes, total of 17 fermion classes, proper sector assignment — has NOT yet been tested the same way. Whether Z = 7 survives there determines whether the particle-topology page survives in strong form or needs to be retired entirely. This is a weekend notebook build and should happen soon.

41. What does the Lindblad mapping reveal? — the April 5 tension null test showed TSO dynamics reproduce Lindblad (GKSL) dynamics exactly across four observables. This is a strength — sixty years of quantum-optics theorems are inherited for free — but it raises a new question: does the γc/γo vocabulary reveal structure in Lindblad dynamics that standard notation hides? The second law emerging from closing-tension monotonicity is one example. Are there others? Specifically, can a Lindblad system exhibit a genuinely new observable when viewed through the TSO asymmetry that it does not exhibit in standard notation? This is a theory problem, not an experimental one, and may be worth more serious thought than it has received.

42. Formal proof or retirement of the αEM residual — αEM ≈ pc4 is within 30% of the measured value. The residual is 6.83 Pips and the candidate correction α × pc = 7.30 Pips is within 7% of that gap. Either this is a genuine geometric relationship that can be derived from first principles, or it is a coincidence that should be explicitly retired from the framework. Currently it is in limbo.

43. Pre-registration of the Rydberg prediction — the Rydberg sigmoid prediction needs to be pre-registered with a timestamp before the experiment runs. Specifically: the exact κ value expected (4/3 = 1.333...), the exact Γnet location where the transition should center, the minimum ΔAIC vs exponential required to claim support, the minimum precision on κ required to distinguish TSO from a mundane sigmoid. This is process, not physics, but it matters for the credibility of whichever outcome the experiment produces.

44. Degrees-of-freedom audit of "zero parameters" — TSO has no fitted numerical parameters but it does have structural choices (Z=7, symmetry reductions, sector definitions, inclusion of specific sub-categories). These function like parameters in the sense that changing them changes the output. An explicit audit listing every structural choice and what the alternatives were, what motivated each choice, and which were actively rejected vs never explored, would defuse the "hidden parameters" critique and may reveal choices that were not noticed as choices at the time.

45. Human review outside the AI collaboration loop — this is a process problem, not a physics problem, but it is real. TSO has been developed in extended conversations with AI models which are trained to find connections and to say "yes, and." This accumulates bias silently. Specific action: post a tightly-scoped technical question on Physics Stack Exchange (one specific claim, not "evaluate the whole framework"); email 2–3 specific researchers whose published work overlaps with one specific TSO claim; submit a short paper on the topology enumeration with the April 5 null result included to a preprint server. None of this has happened yet.

PARTICLE TOPOLOGY & STANDARD MODEL (page)

27. Derive Q = χspatial/3 from first principles — the charge formula is observed from the output, not derived independently. Even after the April 5 null test showed the charge spectrum is generic, the /3 itself is forced by SO(3) on 3 paths, which is a starting point rather than a final derivation.

28. Mass hierarchy from topology — why is the electron lighter than the muon? The three generations have different quantum chirality assignments but no mass calculation exists.

29. W±, Z bosons, and Higgs placement — massive gauge bosons don't fit neatly into Sector A or B. Where do they live in the lattice topology?

30. Color dynamics (SU(3) action) — the 3-fold color degeneracy is validated structurally but the gauge dynamics (gluon exchange, confinement as topology) need formal derivation.

31. Sector B pruning — 9 classes in Sector B is more than needed for the SM. A stability or energy criterion should identify which classes are physical and which are artifacts.

32. Enumerate 3-closed sector — do configurations with 3/5 paths closed (W = 4/7) correspond to any known physics? W/Z transients? Virtual particles? Resonances?

ANTIMATTER & BARYON ASYMMETRY (page)

33. Derive baryon asymmetry from first principles — the current calculation is a retrodiction using metallurgical mathematics applied to TSO parameters. A first-principles derivation that commits to the formula before the observation is an open problem.

34. Connect β (CMB birefringence) to η quantitatively — the claim that both come from the same chirality-breaking event needs a formula, not just a narrative.

35. mc²/δW pattern across particles — is there a combinatorial formula for the number of degrees of freedom in each topology that determines the stored γo mass?

PATH ROTATION & QM (page)

1. Natural angular unit of S⁷ — octonion associator angle for β conversion.

7. Dimensional hypothesis validation — re-fit CDT data with tanh vs rational function.

8. Destruction testing — subject path rotation model to systematic falsification.

10. Path-space metric derivation — the g = +1/−1/0 assignment to paths is motivated but not derived.

21. X1 and X2 identity — genuinely non-local paths or compactified extra dimensions?

22. Sigmoid validation — tanh predicted from percolation, not fitted. Rydberg decisive test pending; IBM gate-depth test runs later today (April 5, 2026).

23. Two-window model Born rule — unifying existence/observability windows with path rotation cos²(θ).

2-3-2 STRUCTURE (page)

9. Bottom 2-floor geometric proof — the causal argument explains WHY T and ∅ resist EM coupling, but doesn't formally prove the ceiling is exactly 2/7.

11. QPU ceiling data — get IBM/Google/IonQ calibration data. Look for platform-independent purity deficit. (Connects to problem 39 — Pip universality.)

15. 3 contested = 3 spatial — proof or coincidence?

THREE-PHASE MODEL & COSMOLOGY (page, page)

2. Gravity derivation — can Gμν = 8πGTμν emerge from S/W dynamics?

4. QFT embedding — S/W-field in quantum field theory.

5. Time emergence — exact form of dτ/dt = f(W, Γ).

12. RETIRED: "Origin of 11 in 77 = 7 × 11" — the 2/77 approximation for δW was retired in v11.0; there is no physical 11. Use δW = pc − 2/7.

13. Dust-phase dynamics — transition function analogous to tanh?

14. Chemistry quantitative predictions — can spanning cluster model predict bond energies? (Connects to problem 39 via γo,stored in chemical bonds.)

16. W(r) inside a black hole — what functional form?

17. GW echo prediction (pre-registered) — techo = 0.029–0.087 × rs/c. Awaiting Einstein Telescope.

18. NN+NNN+4N exact threshold — is pc = 0.2885 exactly 2/7?

19. Gravity from W-gradient — Gμν from phase boundary dynamics?

20. Jaiswal ν = 0.88 vs TSO exponent — coincidence or structural?

DARK MATTER & EUCLID (preserved from v9.2)

46. Derive cored DM profile slopes from wave-state matter — TSO predicts inner slopes 0.8–1.2 from quantum pressure resisting collapse, but the specific shape and scatter across galaxy masses is not derived from first principles. Euclid data (October 2026) will test the range; the theory should be tightened before then.

47. Halo triaxiality prediction — spherical halos from no-classical-rotation is a qualitative prediction. A quantitative prediction of the allowed oblateness would sharpen the Euclid test.

BIOLOGY (page, foundation)

3. α(scale) — why α runs from 0.93 to 2.175.

6. W-maintenance quantification — map γo,active (metabolism) and γo,stored (structural proteins) to measured biological coherence times.

24. Minimum spanning cluster formal proof — derive analytically that the minimum cluster at pc on Z=7 contains ~473 nodes.

25. 149/473 prediction test — track whether newly characterized unknowns are connectivity or metabolic.

26. δW ceiling across quantum biology — test whether quantum biology energy scales respect δW.

48. Extremophile biology Pip test — hyperthermophile enzymes (~395 K) should pay ~1.3× the γo per equivalent event compared to mesophiles (300 K) if the Pip framework is physical. Testable against published single-molecule kinetics data.

PREVIOUSLY NEW (MARCH 29 SESSION)

36. Z=7 as sufficient, not total — reframe 7 as the minimum for observable transitions. Higher paths may exist but don't couple to our instruments. Partially addressed in v11.2 with the 6 cardinal + stay geometric anchor.

37. Magnetic fields as X1 projections — B-fields don't do work, they connect. Test this interpretation.

38. Spanning cluster engineering — can the mapping from topology to γ coupling profile be formalized enough for materials science applications?

PROCESS PROBLEMS (as opposed to physics problems)

These are not about physics but about how the research program is run. They are on this page because they are real constraints on whether the framework can succeed.

• Engagement problem: LinkedIn views without responses. Cold email response rate 2–5% even for targeted outreach. Finding an endorser for arXiv is the specific bottleneck.

• Citation loss between sessions: good references were repeatedly found and then lost. Partially addressed by building references.html as a persistent bibliography, but the underlying issue (AI-assisted work is forgetful) persists.

• Prediction tracking: predictions made in different sessions were scattered. Addressed by building predictions.html as a live tracker, but older predictions may not all be migrated yet.

NEW OPEN PROBLEMS — MAY 15–17, 2026

49. Binary-to-real projection problem — TSO uses three incommensurable systems: GF(2)^7 (exact binary), real-valued percolation, and QFT (M_Z anchor). The ~1% mass errors may be partly projection artifacts. A deeper structure (2-adic, octonions, PG(n,2)) likely underlies all three.

50. Two-springs separation — the quantum spring (minimum at pion threshold p≈0.40) and the classical sink (drain at W_dm) are distinct. Classical V(p) requires 21D subspace projection onto {T,X₂} gravity bonds. BH QNM uses k_eff at p_c (the rim), not at W_dm (the drain).

51. Quark → path word derivation — the pion cannot be a Hamming codeword (minimum codeword weight = 3; pion N=4 ≠ 3×anything). The pion IS the quantum ZPE — lowest-energy non-codeword excitation. π⁰→γγ is X₁ release: Hamming correction to vacuum. Direct quark-content path word derivation needed for 100% stability accuracy.

52. PG(3,2) strange sector — strangeness = 4th coordinate of PG(3,2) = temporal asymmetry = CP violation (confirmed). The [15,11,3] Hamming code should yield the full strange hadron spectrum. The kaon (N=15 = full PG(3,2) activation at 1 Pip/point) confirmed at 1.6% error.

53. Bounded tower levels 1, 4, 6 — PG(1,2) at 1605 MeV (~vector meson), PG(4,2) at 259 MeV, PG(6,2) at 66 MeV (virtual/wave mirror) need particle identification or confirmation as virtual states.

54. E₇ ambient ceiling (Joshua Osborne challenge) — E₇ has 133 generators and minimal representation of dimension 56 (= D meson Pip count). 133 × E_Pip = 4448 MeV ≈ Ψ(4415) at 4421 MeV (0.6% off). Is E₇ the algebraic container for the 7-level bounded tower? Run the 133 notebook.

55. Particle oscillations as Hamming drift — neutrino oscillations, kaon mixing, B meson oscillations may be codeword drift in the wave state. Mixing angles (PMNS, CKM) may be derivable from Hamming distances between codewords.

56. Hawking radiation syndrome structure — identity stored in 21D codeword; gravity closes paths but cannot close algebra; Hawking radiation should carry H×radiation = 0 mod 2 correlations. Testable for near-critical PBHs at E = E_Pip by Fermi-LAT/AMEGO-X.

57. Contact Calcagni ([email protected]) — does d_S at E = 33 MeV in FQG equal 2.571? Single question that closes or opens the FQG bridge claim.

58. Rydberg sigmoid (Professor Jaewook Ahn, KAIST) — the decisive experimental test. Kim et al. 2024 dataset: tanh beats exponential 2.75× on 129,791 shots. Most important near-term action.