# TSO -- Two-State Ontology # Machine-readable project spec for AI and LLM navigation # Version: 11.9 | May 31, 2026 # Author: John Pepin | incapp.org/TSO/ # Site: https://incapp.org/TSO/ > "The goal is to understand, not to be right." --- ## 0. STATUS AND HONEST FRAMING TSO is a conjecture, not established physics. Probability substantially correct: ~5%. Primary concerns: mostly retrodictive; AI-assisted coherence bias possible; no dedicated experimental confirmation yet. CENTRAL CLAIM (v11.8 reframe): Reality has three phases -- Wave (quantum), Solid (classical), and Dust (below floor) -- and the Wave-to-Solid transition is an observable physical phase change at a specific coupling. Everything else in the framework (seven paths, Fano plane, percolation threshold, Lindblad analogue, Pip catalog, constants) is supporting machinery downstream of the phase structure. The framework's truth or falsity hinges on whether the phase transition exists, NOT on whether any particular critical exponent matches any particular value. A successful Rydberg test (Prediction 1) would establish the phase-structure claim. It would NOT prove TSO -- too many moving parts. Three pre-registered outcome scenarios (A: phase transition + nu ~0.88; B: phase transition + nu elsewhere; C: no transition) committed on the predictions page. Key honest limits: - TSO does not predict the fermion mass hierarchy from first principles (yet). - The particle stability result (89.5%) uses a crude path-word mapping -- 10.5% unexplained. - p_q = 0.6556 (TSO) differs from tight-binding literature p_q approx 0.44 for Z=6 cubic -- open problem 59, not yet resolved. - All hadron mass predictions are retrodictions (masses known before framework). - No free parameters were adjusted in the stress tests -- but they were designed after the framework was built. - v11.8 retired the previous nu = 4/3 claim (formerly "kappa = 4/3 from 2D universality"); corrected to nu ~ 0.88 from 3D site percolation. The Belenos QPU measurement of nu = 1.325 is now ~5σ from the corrected prediction -- unresolved, kept visible, likely reflects QPU calibration assumptions in the analysis chain that aren't yet fully understood. See predictions.html#nu-3d for full disclosure. Decisive experimental test: Rydberg sigmoid phase transition. Priority contacts: (1) Montfrooij group, Missouri -- published 3D protected percolation universality class with gamma' = 1.3066. Structural overlap with TSO's wave-to-solid mechanism is direct. Outreach planned May 2026. (2) Prof. Jaewook Ahn, KAIST -- Rydberg experimental group. Email sent April 2026, awaiting response. --- ## 1. NOMENCLATURE (updated May 2026) Wave (was: steam) -- quantum phase, W > p_c, no persistent HERE Solid (was: water) -- classical phase, W_dm < W < p_c, persistent HERE Dust (was: ice) -- dead matter, W < W_dm, below both systems v11.8 NOTATION CLEANUP (May 30, 2026): Previous versions used "kappa" for two distinct mathematical objects. v11.8 separates them: alpha (unchanged) -- effective branching factor; alpha_max = 7 from S^7 lambda (was kappa_1) -- rate constant in alpha formula; asserted = e STATUS: EMPIRICALLY FIRM (MIPT fit 0.12sigma from e), THEORETICALLY OPEN (no derivation closes) nu (was kappa_2) -- correlation-length critical exponent of percolation STATUS: CORRECTED from 4/3 (2D, retired) to ~0.88 (3D site percolation universality) Authoritative reference: Notebook 1 in the v11.8 reference notebook set. If this document conflicts with Notebook 1, Notebook 1 wins. --- ## 2. CORE AXIOM AND VARIABLES S + W = 1 (always, everywhere, exactly) W = fraction of 7 paths that are open (quantum connectivity) S = fraction of 7 paths that are closed (classical solidification) Seven paths: T (time), null/empty (vacuum/HERE), x, y, z, X1, X2 T = time path (couples to gravity, cannot be closed by EM) null = vacuum/HERE path (position requires this to be closed) x,y,z = three spatial paths (form Fano triangle) X1 = EM path (long-range, parity-symmetric, charge carrier) X2 = gravity/spatial curvature path (couples with T) BEST_PERM topology (confirmed): T=0, null=1, x=2, y=3, z=5, X1=4, X2=6 xyz triangle: nodes {2,3,5} = Fano line (confirmed) Four forces from four geometric structures: Gravity = T + X2 (temporal + spatial curvature = one tensor) EM = X1 (long-range, parity-symmetric) Strong = xyz triangle (color = which edge is minority) Weak = xyz asymmetry (strangeness = triangle edge asymmetry; NOT a separate path -- emerges from triangle geometry) --- ## 3. CORE CONSTANTS p_c = 0.3116 3D site percolation threshold (Stauffer & Aharony) Analytic formula (proposed, v11.5): p_c = (2+e+phi)/(16+e+phi) = 0.31158 (0.008% from measured). e=Euler, phi=golden ratio. W_dm = 2/7 = 0.2857 dead matter floor (two unclosable paths T, null) delta_W = p_c - W_dm = 0.0259 approx kBT at 300K (0.15% match) Z = 7 six cardinal directions + stay (3D cubic lattice) E_Pip = 33.437 MeV fundamental energy quantum (PG(7,2) collapse) PIP = p_c/1000 = 0.0003116 (Pip unit) p_q = 0.6556 quantum percolation threshold (TSO, open problem 59) sigma = 6/sqrt(1104) = 0.18058 thermodynamic noise scale (DERIVED, v11.6) Lambda = 1/(2*sqrt(sigma)) = 1.17662 M_Z = 91.19 GeV Z boson mass (experimental anchor for mass scale) sin2_W = 3/13 = 0.2308 weak mixing angle (Fano degree counting, 0.09% error) --- ## 4. SIGMA -- FULLY DERIVED (v11.6, May 20, 2026) sigma = C(V_tet, 2) / sqrt(V_tet x C(chi_K3, 2)) = C(4,2) / sqrt(4 x C(24, 2)) = 6 / sqrt(4 x 276 ) = 6 / sqrt(1104) = 0.18058 Every term is a TSO axiom: V_tet = 4 vertices of {x,y,z,T} tetrahedron = 4D spacetime boundary C(4,2) = 6 edges of tetrahedron = directed lattice paths = Z-1 chi(K3) = 24 Euler char of K3 surface = CY tower floor = |chi(CY4)|/133 C(24,2) = 276 K3 cohomology pairings = 11D bulk degrees of freedom gap_pips = 4 x 276 = 1104 = holographic projection of bulk onto boundary Holographic meaning (Joshua Osborne): sigma is the friction created when the 276 continuous 11D K3 bulk pairings project onto the 4 discrete {x,y,z,T} boundary vertices. The 4D screen has 4 vertices and 6 edges -- both Z-1 and V_tet come from the same object (the tetrahedron). From sigma: Lambda = 1/(2*sqrt(sigma)) = 1.17662 E_Pip = Lambda x M_Z x PIP = 1.17662 x 91187.6 x 0.0003116 = 33.43 MeV --- ## 5. THE PIP TOWER AND PARTICLE MASSES Formula: mass(N) = N x E_Pip where N = Pip count from PG geometry PG tower (Fano projective hierarchy): Level N (Pips) Mass (MeV) Observed Error Particle PG(7,2) 0.996 33.3 33.44 0.4% E_Pip (fundamental quantum) PG(6,2) 1.98 66.2 -- -- virtual/wave mirror PG(5,2) 3.938 131.6 134.977 4.2%* Pion pi0 (*ZPE, not codeword) PG(4,2) 7.75 259 -- -- rho/eta scale PG(3,2) 15.0 501.6 493.677 1.6% Kaon K+ PG(2,2) 28.0 936.2 938.272 0.2% Proton PG(1,2) 48.0 1605 ~1600 -- vector meson scale E7 special entries (N = E7 group theory numbers): N=56: 1872.5 1869.660 0.15% D meson (E7 minimal rep) N=133: 4447 4421 0.59% Psi(4415) charmonium (E7 dimension) N=0.996: 33.3 33.44 0.4% E_Pip (PG(7,2) collapse = 255/256 Pips) Self-referential closure: PG(7,2) gives 255/256 Pips = E_Pip. Seven levels exhaust seven imaginary octonionic dimensions. The universe is a bounded engine -- its limit is its own heartbeat. --- ## 6. CALABI-YAU STAIRCASE (PALP-verified, v11.6) The tadpole denominator 24 = chi(K3). K3 is the unique CY2 and the floor. Every level above K3 carries SVW debt (negative chi = singular geometry). Level Geometry d h11 h21 chi N=|chi|/K Mass (MeV) -------------------------------------------------------------------------- K3 (floor) K3 surface -- 1 0 +24 1 (/24) 33.4 Fano/CY3 WP4[1,1,2,2,2] 8 2 86 -168 7 (/24) 234 Kaon/CY3 WP4[1,1,1,6,9] 18 2 272 -540 15 (/36)* 502 E7/CY4 WP5[1,3,7,19,19,19] 68 ? ? -3192 133 (/24) 4447 -------------------------------------------------------------------------- *kaon uses /36: Z3 orbifold correction at [6,9] stratum (open problem 60) All three rungs PALP-verified (algebraic geometry tool). Both CY3 rungs have h11=2 consistent with two TSO phases (Wave, Solid). Bidirectional derivation: -3192 <-> WP4[1,1,1,6,9] Top-down: chi=-3192 -> chi_K3=24 -> PG(3,2) N=15 -> Koide 6/9=2/3, 6+9=15 -> weights [1,1,1,6,9] d=18 Bottom-up: WP4[1,1,1,6,9] PALP chi=-540 -> N=15 -> E7 N=133 -> chi=-3192 SVW debt: chi(CY4) = -3192 means a tadpole debt of 133 M2-branes (singular). PALP flag "non-transversal" confirms singularity -- E7 gauge symmetry lives in the singularities. Reference: Sethi, Vafa, Witten hep-th/9606122 (1996). --- ## 7. STRESS TESTS (Joshua Osborne, May 20, 2026) All six tests use only TSO geometric primitives. No parameter adjustment. 1. chi SENSITIVITY (exact): Only chi=-3192 gives integer chi_K3=24. Every other chi in -3180 to -3200 gives non-integer or wrong proton mass. The formula is not tunable. 2. MASS RATIOS vs PDG (1-3%): Pip integer ratios: Proton/Kaon=1.867 (PDG 1.901, 1.8%), D/Pion=14.22 (PDG 13.85, 2.7%), Jpsi/Proton=3.321 (PDG 3.301, 0.6%). Mean error 1.4%. 3. FINE STRUCTURE CONSTANT (0.026%): dim(E7) + V_tet = 133 + 4 = 137 alpha^-1 observed = 137.036 Integer 137 matches to 0.026%. Fractional 0.036 not yet derived (open). 4. DARK ENERGY (0.07%): 1 - p_c = 1 - 0.3116 = 0.6884 Planck 2018 Omega_Lambda = 0.6889 +/- 0.0056 Error 0.07%, within 1 sigma of Planck. Physical derivation open (problem 65). BONUS: Omega_matter (Planck 2018) = 0.3111, p_c = 0.3116, error 0.16%. The classical matter fraction of the universe = the percolation threshold. 5. W BOSON (0.49%): sin2_W = 3/13 (Fano degree counting: U(1)=1, SU(2)=6, SU(3)=6, total=13) M_W = M_Z x sqrt(1 - 3/13) = 79.977 GeV PDG M_W = 80.369 GeV. Error 0.49%. 6. LEPTON MASSES (PARTIAL): 2T binary tetrahedral group (order 24) has three 1-dim irreps at angles 0, 2pi/3, 4pi/3. Angular positions DERIVED from 2T geometry. Mass ratios: exact Koide formula Q = 2/3 (error 0.0009%). Absolute scale: one anchor needed (m_tau or A from sigma x M_Z -- open 64). --- ## 8. THREE GENERATIONS (Wilson 2023, substantially closed) Binary tetrahedral group 2T (order 24): Irreps: {1,1,1,2,2,2,3}. Sum of squares = 24 = |2T|. (Burnside check) THREE 1-DIM REPS = THREE PARTICLE GENERATIONS. 2T acts on {x,y,z,T} tetrahedron. All 6 edges are Fano edges. Chirality: T as 4th vertex breaks L/R symmetry. Weak force is left-handed because time flows one way. E8 decomposition: 248 = 133 + 56 + 56 + 1 + 1 + 1 Three singlets = three 1-dim reps of 2T = three generations. Koide formula: Q = sum(m_i) / (sum(sqrt(m_i)))^2 = 2/3 (exactly from 2T). Computed: Q = 0.666661. Error from 2/3: 0.0009%. No Standard Model derivation exists. TSO gives it from geometry. Reference: Wilson R.A. arXiv:2301.11727 (2023) "Tetrions" --- ## 9. HAMMING CODE AND PARTICLE STABILITY (v11.5) [7,4,3] Hamming code: 7-bit codewords, minimum distance 3, corrects 1-bit errors. The 7 TSO paths map to 7 bit positions. Topological particles: path-word sits ON a codeword -> stable (error-corrected). Energetic particles: HD=1 from nearest codeword -> unstable (decay = bit correction). Pion: N=4, minimum codeword weight=3 -> pion CANNOT be a codeword. Pion is quantum ZPE -- lowest-energy non-codeword excitation. pi0 -> gamma gamma = X1 release = Hamming correction to vacuum. Fastest hadronic decay because no codeword to correct back to. Omega- (sss): symmetric triplet restores codeword -> topological (0.036%). Stability accuracy: 89.5% (17/19). Two failures: both pions (crude path-word mapping). Particle stability is a THEOREM of [7,4,3]. --- ## 10. TENSION ASYMMETRY AND LINDBLAD MAPPING Closing tension Gamma_C = sum(gamma_c,i) (monotonically non-decreasing) Opening tension Gamma_O = sum(gamma_o,i) (decays or latches) Net: Gamma_net = Gamma_O - Gamma_C Phase conditions: Gamma_net > 0 -> wave phase Gamma_net approx 0 -> solid phase Gamma_net < -p_c -> percolation collapse (sigmoid, kappa approx 4/3) gamma_o splits: gamma_o,active: decays without input (laser, metabolism, RF pulse) gamma_o,stored: latched at formation (rest mass, bonds, Cooper pairs) Lindblad mapping (confirmed April 2026): gamma_c = Lindblad dissipator L_k gamma_o,active = Hamiltonian drive gamma_o,stored = decoherence-free subspace Gamma_net < -p_c = NO Lindblad equivalent (TSO's new content) Charge conservation: pair-correlated L_k commutes with Q exactly ||[L,Q]|| = 0 (machine precision). Single-bond operators do not. Charge conservation is structural, not a separate postulate. --- ## 11. SIGMOID DECOHERENCE (THE DECISIVE PREDICTION -- v11.8 reframed) Standard: W(t) = W_floor + (1-W_floor) x exp(-Gamma x t) TSO: W(Gamma_net) = W_floor + (1-W_floor) x 0.5 x [1-tanh((Gamma_net+p_c) x scale x nu)] nu ~ 0.88 from 3D site percolation universality (v11.8 corrected from previously asserted kappa = 4/3 from 2D) Two curves differ ~35% at the transition -- cleanly distinguishable. v11.8 reframe: the DECISIVE claim being tested is not the value of nu, but the EXISTENCE of the phase transition at the predicted location with the predicted floor (W_floor = 2/7). Three pre-registered scenarios on predictions.html: A: phase transition + nu ~ 0.88 -- supports central claim + 3D class B: phase transition + nu elsewhere (1.2-1.4) -- supports central claim; non-standard universality class, framework needs theoretical work C: no phase transition (pure exponential everywhere) -- central claim falsified, framework retires Empirical support so far (all reanalyses or QPU runs, no dedicated test): - IBM Marrakesh: below-threshold exponential confirmed (ΔAIC > 30 vs sigmoid) - Quandela QPU nu measurements: Linear: nu = 1.138 Deep: nu = 0.836 (Linear+Deep average 0.99, consistent with 3D ~0.88) Belenos: nu = 1.325 (anomalous, only point near retired 4/3 value) - Kim et al. 2024 reanalysis: WITHDRAWN May 2026 (dataset misidentification). Was previously cited as "tanh beats exponential 2.75x"; that claim retired. - Quandela Ascella QPU: d_f = 2.0000 (fractal dimension consistent with TSO) The Belenos anomaly: under v11.7 (target nu=4/3) Belenos confirmed. Under v11.8 (target nu~0.88) Belenos is ~5sigma off. Three explanations honestly considered on predictions.html#nu-3d, with QPU-calibration-uncertainty-on-our-end as the most likely. Belenos kept visible rather than discarded -- framework credibility depends on disclosure. --- ## 12. QUANTUM PERCOLATION RESULTS (HARDWARE) IBM QPU (ibm_fez, bond percolation, v1, May 2026): p_c_ibm = 0.796, p_q_ibm = 0.957, gap = 0.161 Confirms p_q > p_c (gap direction). Gap fraction ~23% of quantum range. Geometry: 2D heavy-hex, z=2.256. Not comparable to TSO 3D cubic z=7. IBM QPU (ibm_kingston, site percolation, v2, May 2026): 16,800 circuits. P_sink ~ 0.47-0.48 at all p and path lengths. GHZ circuit approach hits noise floor. IBM hardware sits above p_c by design. Result: Confirms gap exists. Cannot measure p_c quantitatively. Tight-binding computational test (May 20, 2026): Z=6 cubic, L=6,8,10,12. Level-spacing ratio method. L->inf extrapolation: p_q ~ 0.44-0.47. Literature p_q = 0.44 +/- 0.01. TSO predicts p_q = 0.6556. Anderson disorder W=8t needed to reach 0.6556. OPEN PROBLEM 59: Are TSO's p_q and tight-binding p_q the same quantity? Do NOT register p_q=0.6556 as a formal prediction until resolved. Prediction 34 status: SUGGESTIVE -> STRENGTHENED (two QPU platforms confirm gap). --- ## 13. PREDICTIONS (LIVE STATUS AS OF v11.9) Key predictions and status (full list at incapp.org/TSO/predictions.html): CENTRAL CLAIM (the decisive test): P1: Phase transition between Wave and Solid at Gamma_net = -p_c. FIRM. (v11.8 reframed from "sigmoid with kappa=4/3" to "phase transition at predicted location with predicted floor".) Three pre-registered outcome scenarios A/B/C on predictions page. The Rydberg sweep is the decisive test. CONFIRMED / SUGGESTIVE: P13: DESI DR2 w0waCDM tension. SUGGESTIVE (DESI DR2 upgraded this). P34: p_q > p_c gap on QPU hardware. STRENGTHENED (IBM x2, Quandela). P41: lambda = e in alpha formula. EMPIRICALLY FIRM (MIPT fit 0.12sigma) but THEORETICALLY OPEN (no derivation closes). (v11.8 new entry.) NEW IN v11.9 (May 31, 2026): P42: Dark matter is epi-matter -- protected percolation regions. FIRM. Hard predictions (no direct detection ever; no indirect detection; static epi-matter/baryon ratio since BBN; no de Broglie interference in halo density). Soft predictions for Euclid DR1 (Oct 21, 2026): cored cluster profiles with inner slope 0.8+/-0.2 (not NFW 0.4); halo c/a > 0.7 and b/a > 0.85; cosmic web shows two universality classes (standard 3D + protected percolation per Fayfar 2022); environmental sensitivity of epi-matter/baryon ratio at fixed z. Quantitative support: 3D site percolation at p_c reproduces the observed cosmic baryon:epi-matter:void ratios to within factor 1.6 across all three components (void match exact at 0.3%, epi-matter at 5%, baryons at factor 1.6). Six companion notebooks document the structural and computational case. PENDING (decisive tests): P28: Space Roar (ARCADE 2) via Larmor radiation. OPEN. P29: Sigmoid transition width = delta_W. PENDING (Rydberg sweep needed). P30: Peak decoherence rate at Gamma_c. PENDING (same sweep). P34: p_c = 0.3116 quantitatively (Rydberg, KAIST or Montfrooij group). PENDING. P40: nu ~ 0.88 from 3D percolation universality. PENDING (Rydberg, replaces retired P2). Informational about universality class, NOT load-bearing for central claim. RETIRED (v11.8): P2: kappa = 4/3 from 2D universality. RETIRED. Three reasons: framework's own April 2026 self-correction, direct Fano-bond MC gives nu~0.82-0.91 (3D class), bulk of Quandela data (Linear+Deep average 0.99) closer to 3D than to 4/3. Replaced by P40 (corrected to nu ~ 0.88). NOT YET REGISTERED (needs clarification): p_q = 0.6556 -- conflicts with tight-binding literature. Open problem 59. Cosmic L scale -- where do the cluster ratios get locked in? Open problem 60 (added v11.9). Three candidates: Planck-scale, Kibble-Zurek-driven lock-in scale, cosmic correlation length at percolation event. Resolution requires deriving lattice unit in physical length or specifying early-universe percolation dynamics. --- ## 14. ELECTROMAGNETISM DERIVATION (April 2026, roof-em.html) All four Maxwell equations + c = 1/sqrt(mu0 epsilon0) derived from: - X1 conservation (charge is a codeword property) - T as active path (time evolution) Seven Colab notebooks. See roof-em.html for the full chain. The c derivation asserts K = Q.v (X1 potential = charge x velocity). K = Q.v is motivated but not yet derived from Pip lattice dynamics. --- ## 15. LIFE AT p_c AND BIOLOGY Life operates at p_c -- the critical surface between Wave and Solid. delta_W = p_c - W_dm = 0.0259 eV approx kBT at 300K (0.15% match). This is the per-interaction energy to climb from dead floor to criticality. Metabolism pays this cost continuously. Death = losing the delta_W budget. Minimum spanning cluster: ~473 nodes on Z=7 at p_c. syn3.0 minimal cell: 473 essential genes. 149/473 unknown-function genes = 31.5% approx p_c = 31.16% (1.1% off). Passive criticality limit at 300K: N_max approx 27 nodes. Biological modules straddling this limit: ribosomes (15-40), respiratory chain complexes (15-40), nuclear pore (~30). Matches observation. Larger systems require active feedback (homeostatic regulation). --- ## 16. COSMOLOGY AND BARYON ASYMMETRY Baryon asymmetry (no fitted parameters): eta = delta_W^d_eff / N^(d_eff/2) x f^(1/n) delta_W = 0.02589, d_eff = 7 x p_c = 2.18 Result: eta = 7.26e-10. Observed: 6.1e-10. Ratio: 1.19x. Retrodiction (match computed after observed eta was known). Dark matter -- TSO identification: EPI-MATTER (v11.9 terminology). Epi-matter = 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 (p_c < W < p_q). The protection mechanism is structural: the path-identity channels that would deliver gamma_c (decoherence) to convert epi-matter back into baryons are exactly the channels that aren't fully active in epi-matter. Hard predictions: no direct-detection signal ever (XENON, LZ, PandaX, etc.); no indirect-detection signal (Fermi-LAT, AMS-02, IceCube, etc.); no de Broglie interference in halo density at any scale; static epi-matter/baryon ratio from BBN through today. Soft predictions (Euclid DR1, October 21, 2026): cored cluster profiles (inner slope 0.8+/-0.2); halo sphericity (c/a > 0.7, b/a > 0.85); cosmic web shows two universality classes (3D site + protected percolation); environmental sensitivity (DM/baryon ratio uniform across cosmic environments). Quantitative support: 3D site percolation at p_c reproduces observed cosmic baryon:epi-matter:void ratios to within factor 1.6 across all three components (void match exact at 0.3%; epi-matter at 5%; baryons at factor 1.6, four candidate explanations listed). See Prediction 42. Structural prior art: Fayfar, Bretana, Montfrooij (2022) protected percolation universality class. The framework's claim is that what cosmology calls dark matter is matter in this universality class at cosmological scales. Dark energy: globally inactive bonds 1-p_c = 0.6884. Planck 2018 Omega_Lambda = 0.6889. Error 0.07%. Physical derivation OPEN (problem 65). Omega_matter = 0.3111 approx p_c = 0.3116. Error 0.16%. Gravitational wave echoes (pre-registered): t_echo = 0.029-0.087 x r_s/c. Awaiting Einstein Telescope data. --- ## 17. LAYERED STRUCTURE (M-THEORY TO QM) 11D M-theory / CY fourfold (the embedding bulk) | chi(CY4)/24 = N [Sethi-Vafa-Witten 1996] 7D G2 manifold (TSO path space -- compactified boundary of CY4) | percolation criticality at p_c Classical / Quantum mechanics (limiting cases of TSO) | observable projection 4D spacetime: x, y, z, T FQG (Fractional Quantum Gravity, Briscese & Calcagni arXiv:2603.24593): Primary framework. 4D, renormalizable, spectral dimension d_S flows. Bridge: d_S(FQG) = d_f(TSO) = 2.571 at E = E_Pip. Level transitions PG(n,2) -> PG(n+1,2) ARE the FQG dimensional flow. M-theory: algebraic overlap only. TSO requires neither SUSY nor 11D. E7/E8/Leech/Monster chain (confirmed May 2026): E_Pip (+1 Anchor) -> PG tower -> E7 -> chi=-3192 -> E8 -> Leech -> Monster chi(K3) x dim(E7) = 24 x 133 = 3192 = |chi(CY4)| Top of tower = bottom of tower x ambient ceiling. Monster j-function: 196884 = 196883 + 1; the "+1" IS E_Pip. --- ## 18. WHAT TSO DOES NOT CLAIM - Does not derive the fermion mass hierarchy (mass spectrum) from first principles. - Does not predict why electron has 3 X1 bonds (no principled selection rule yet). - Does not derive alpha_EM from first principles (p_c^4 approx is 30% off). - Does not place W, Z, Higgs in the enumeration (consistency demos only). - Does not derive Lindblad matrix elements for specific particles. - Does not predict specific particle-to-bond-count assignments. - The topology enumeration sectors are NOT Z=7-specific (April 2026 null test). - TSO dynamics = Lindblad dynamics in different vocabulary. New content is only the sigmoid shape at threshold and the percolation finite-size scaling. - Baryon asymmetry is a retrodiction, not a prediction. --- ## 19. KEY COLABS Hamming stability: https://colab.research.google.com/drive/1NTkeNGjKtUwaZoNu1yqZA-HHfgfUcD6D Bounded tower + PG(7,2):https://colab.research.google.com/drive/1DE0YfoXfmYU1-nEgRXqZiFLgoMMvckfS E7 / 133: https://colab.research.google.com/drive/1-AYPST0zqGvowtEQrTRy4RzDLKu8x0NZ Wilson three gen: https://colab.research.google.com/drive/1FENJD10qJK5hYrlblHghQv8l5X-yLQ9b CY4 sigma derivation: https://colab.research.google.com/drive/1QGPaH3sn42ticxW7zm7G2AzLoz_KyEMU Joshua stress tests: (May 20, 2026 -- chi sweep, mass ratios, alpha, dark energy, W boson, leptons) Intermediate theory: https://colab.research.google.com/drive/1QGPaH3sn42ticxW7zm7G2AzLoz_KyEMU p_c analytic formula: https://colab.research.google.com/drive/1zPiNk54-GPY8J1TbKCE0y_PQRLp6Sgd6 EM derivation suite: roof-em.html (7 notebooks) Prediction 34 (QPU): d80827jack5s73bg6s10 (ibm_fez), d8684ftg7okc73ekptf0 (ibm_kingston) --- ## 20. KEY CONTACTS AND COLLABORATORS Joshua Osborne (LinkedIn, Helix AI): Active collaborator throughout May 2026 sessions. Contributed: bounded tower insight, octonion confirmation, E7 ambient ceiling, sigma identification, holographic projection framing, six stress tests. Status: ongoing collaboration. Robert A. Wilson (r.a.wilson@qmul.ac.uk): Email sent May 18, 2026 re: Fano connection to arXiv:2301.11727. Key hook: Koide formula (Q=0.666661) from 2T x xyz triangle geometry. Status: AWAITING REPLY. Calcagni (g.calcagni@csic.es): NOT YET CONTACTED. Priority: does d_S at 33 MeV = 2.571 in FQG? Prof. Jaewook Ahn (KAIST): NOT YET CONTACTED. Rydberg sigmoid -- the decisive experimental test. --- ## 21. OPEN PROBLEMS (v11.6, PRIORITIZED) IMMEDIATE: 59. Reconcile p_q=0.6556 with tight-binding p_q approx 0.44 (Z=6 cubic). Do NOT register as Prediction 38 until resolved. 60. Kaon tadpole /36 denominator -- Z3 orbifold correction derivation. 61. WP5[1,3,7,19,19,19] Hodge numbers -- resolve non-transversal singularity. 62. h11=2 at every CY3 rung -- derivation or coincidence? 63. E_Pip-level CY geometry -- find WP4 with chi=-24. 64. Lepton mass absolute scale -- derive A from sigma x M_Z. 65. Why 1-p_c = Omega_Lambda? Physical derivation open. PHYSICS (next sessions): - CKM/PMNS angles from 2T geometry - sin^2(theta_W) fractional part 0.036 derivation - Planck mass from CY4 compactification volume of WP5[1,3,7,19,19,19] - Quark -> path word derivation (100% Hamming stability) - PG(3,2) [15,11,3] -> full strange hadron spectrum - Formal V(p) derivation from percolation free energy - Path-integral quantization of dp/dt = gamma_o - gamma_c CONTACTS (highest priority): - Prof. Jaewook Ahn, KAIST -- Rydberg sigmoid experiment - Calcagni -- FQG bridge one-question email - Await Wilson response on three-generation / Fano connection