The original technical record remains available here. For explanations, reviewed conclusions and the history of research questions, start with the knowledge atlas.
Research snapshot 2026-11-02 · 783 active ledger claims · 710 scientific findings · 707 registered scripts. These are different inventories, not counts of independent physical confirmations.
Every one of the 783 active ledger IDs is included. All 788 ledger rows, including superseded rows, remain in the download. The reviewed research corpus contains 711 findings; 1 administrative record is excluded from public scientific content, with the omission recorded in the coverage file.
The scientific findings include 519 established scoped results, 63 conditional results and 128 scoped exclusions. These labels describe the recorded finding. They do not upgrade its parent physical goal or overwrite the original ledger.
Sources were matched to their recorded hashes and line ranges at this snapshot. Bounded text excerpts make sources available even when a source is not in the earlier public release. Any omitted administrative lines are explicitly marked. This is source coverage, not a new execution of Python, Lean or Wolfram proofs.
Atlas revision 2c1b559b738e5740ecfad8e6 · snapshot SHA256 68c2fe33ce86d45a99a8c21b1e731e40749d0accb3ae69be53d198cd7ebcb48e
25 matching records · page 1 of 2
Original ledger status
FORM.P2.02
P2 carrier algebra (hypercharge/family) machine-verified
Recorded status: Formal
Canonical status: Formal
Dependencies: AX.P2.01
Scripts: lean4-carrier-rigidity
Location: tfpt_1;tfpt_2
Original CSV, line 4Original ledger status
GATE.WOLFRAM.01
second [C] path VERIFIED RUNNING: Wolfram Engine 14.3 reproduces alpha^-1, E8 glue, M=41, K/Q ladder, lepton c, solar angle, anchor generator, quark ratios, G2 heat-kernel (a2=-R/3,a4|R2=R2/72), Plucker apparatus (11,26,60 + pencil + dualities + lepton ring), (U_wall) selectors (Spec Q+, det R=8), Exterior Leg Lemma (scalar leg=>c_u/c_d=1; anchor microcode 55/117), carrier exterior grading (16=Lambda^even(5), exterior degrees (2,4)), the '11' is Pascal (||Pl(K)||_1=sum_{k<=2}C(4,k)=16-g_car; 15=dim su(4)=10+5=N_fam*g_car), Grand Mass Volume (det M_SM~u^25=u^g_car^2; K-row sums (6,9,10)), Selection Theorem (q(D5)+q(A3)=2, glue 4=|mu4|, only n=5 gives 16-spinor), EM Ward (8b1=(4/5)M=164/5, -5/4=q(D5)), Q geometry (chi Q+/Q-), Readout Rigidity (55/117 stratum-constant), delta=1/2 glue-norm 4-ops, pencil endpoints, compiler core (5,3)+Pythagorean, seam=horizon keystones (triply-8, shared (2/3)^6), Coxeter cycle (order 30, exponents=totatives), unique attractor (gap, Coxeter planes), S_dS carrier decomposition, horizon cross-links (Jacobson 8pi, Hod ln3, |W(D5)|), seam-horizon chain (one-sided Gauss-Bonnet, seam units), area-law seam units 8=|Z2||mu4|, Lambda branch 3/(4pi^2) + K5 counts, CFT bridge (WZW c=8/5/3, c_coset=0), Seam-Engineering Index Xi=31/(24pi^2 log(3/2)), E8 Casimir degrees=atoms, central-theorem closure (2pi c3=1/4, k=c3/2), Seeley-DeWitt a2 (1/G UV-sensitive), D4-equivariant Q-geometry, Q integer-lift (det Q=N_fam), simple R-bridge (det ladder (3,4,8,20), selector stratum derived => 55/117 integer Plucker), det Q=N_fam from cusp order (v72), k=c3/2 forced by variation x Gauss-Bonnet topology (v73), compiler micro-lemmas (pencil differences 2-16-48, anchor QF 41-25=16) (v74), Gate 1 U_point->v_geo (lepton product 32/9, ratios+product bijection) (v75), Gate 2 decoupling margin 6log(3/2)-31/(4pi^2)>0 (v76), G6 via E8 level-1 net (c=8/5/3, embedding) (v77), v_geo floor (S_dS rho_Lambda=32pi^4) (v78), hypercharge Lucas-Binet (1,1,7,13,55,133) + Inverse Anchor Theorem (1^T M^-1 1=1/atom, a^T M^-1 a=1) (v79), operator-pencil geometry (anchor singularity det B(K+xQ)=(3x+2)(3x+5), block-det type checker (9,10,16,40), F4xG2 shadow 52+14+26*7=248) (v80), double cover y^2=det B(K+xQ) branched at Koide -2/3 & carrier -5/3, disc=81=N_fam^4, clearing matrices C_{2/3}/C_{5/3}, branch-divisor symmetric fns = (scalaron,A_Lambda) (v81) (116/116 pass on independent engine; EE area-law is Python-only; re-verified 2026-07-21 after license reactivation, Wolfram Engine 14.3, 116/116 ALL WOLFRAM CHECKS PASSED) UPDATE 2026-08-28: 20 exact mirrors of v983/v985/v987/v993/v994/v997 ADDED to tfpt_readouts.wl; engine run DEFERRED_NO_ENGINE (license inactive); verified count stays 116/116 until the next activated engine run. ROUND-4 2026-09-05: 11 representative exact checks in wolfram/tfpt_round4.wl are wired into the base runner, but execution is UNVERIFIED_NO_KERNEL (wolframscript exit255: no WolframKernel location). Last verified base count remains116/116; native Arb/Fourier/cube regressions are not claimed as Wolfram verified. ROUND-7 2026-09-05: 14 exact representative blocks in wolfram/tfpt_round7.wl are included but UNVERIFIED_LICENSE_INACTIVE; explicit installed kernel selection fails license activation. Verified count remains116/116; no new engine success claimed.
Recorded status: Numerical (second path)
Canonical status: Numerical (second path) ROUND-4 2026-09-05: 11 representative exact checks in wolfram/tfpt_round4.wl are wired into the base runner, but execution is UNVERIFIED_NO_KERNEL (wolframscript exit255: no WolframKernel location). Last verified base count remains116/116; native Arb/Fourier/cube regressions are not claimed as Wolfram verified. ROUND-7 2026-09-05: 14 exact representative blocks in wolfram/tfpt_round7.wl are included but UNVERIFIED_LICENSE_INACTIVE; explicit installed kernel selection fails license activation. Verified count remains116/116; no new engine success claimed.
Dependencies: mirrors v1;v2;v3;v10;v13;v16;v20;v21;v23;v24;v36;v37;v39;v42;v44;v45;v46;v47;v48;v49;v50;v51;v52;v53;v54;v55;v56;v57;v58;v59 (algebra only);v60;v61;v62 (data-confrontation, Python-only);v63;v64 (no-CTC core numerical, Python-only);v65 (falsification layer, Python-only);v66;v67;v68;v69;v70;v71;v72;v73;v74;v75;v76;v77;v78;v79;v80;v81;v983;v985;v987;v993;v994;v997
Scripts: wolfram/tfpt_readouts.wl
Location: verification/wolfram
Original CSV, line 58Original ledger status
E8.REVERSE.AUDIT.01
THE REVERSE NUMEROLOGY AUDIT + WHAT THE GOLDEN RATIO MEANS (2026-06-22). TFPT's forward discipline (v305) is one-directional: every physical READOUT must map onto an E8 structure (anti-fitting). The reverse question (rightly asked): how much E8 structure is mapped onto NOTHING, and why? -- and is the recurring golden ratio numerology? [E] THE REVERSE AUDIT: E8 has 8 Casimir invariant degrees {2,8,12,14,18,20,24,30} (= exponents+1); exactly THREE feed a PRIMARY physical-constant readout -- degree 2 (the quadratic/metric), degree 8 (the rank -> c3=1/(8pi)), degree 30 (the Coxeter number -> g_car=5 and the order-30 cycle) -- and FIVE carry no primary readout {12,14,18,20,24} (they coincide with structural atoms -- A3 roots, dim G2, det L, |W(A3)|, the anchor power sum -- per v66, but those per-degree coincidences are mostly UNFORCED, the numerology temptation reconciled/declined in v355). So 3/8 are primary readouts, 5/8 hull overhead. [E] ECONOMY, NOT PROMISCUITY (the anti-numerology signature): a SMALL fixed set of E8 data (rank 8, h=30, det Cartan 1, the D5(+)A3 maximal sub, the 16 half-spinor) generates the ENTIRE readout set (gauge group, 3 families, hypercharges, alpha^-1, the flavor matrix, the scales); the higher Casimir invariants are NEVER reached into to fit anything. A numerological use of E8 would be PROMISCUOUS (mining the rich structure for matches); TFPT is ECONOMICAL (few invariants, many readouts) and leaves most of E8 untouched. [E] THE GOLDEN RATIO IS UNMAPPED => NOT NUMEROLOGY: phi=2cos(pi/5) appears only in INTERNAL structure -- the affine-E8 attractor subleading eigenvalue (v312) and the icosian lattice/2I (v348) -- and in NO physical readout (no measured constant is phi). Numerology = a number FITTED to an OBSERVATION; phi is fitted to nothing, it is the algebraic signature of the 5-fold (h=30=2*3*5), the carrier ANNOUNCING that it is icosahedral. Unmapped structure cannot be numerology. [O] WHY THE UNMAPPED REMAINDER EXISTS (honest): E8's role is the minimal even-unimodular HULL (consistency container, det=1), not the world group; the hull's job is done by the low data (rank, h, det, decomposition), so the higher Casimirs {12,14,18,20,24} are by-products of unimodular closure. The 5/8 unmapped is the HULL OVERHEAD -- expected for a hull, but stated plainly: where a future higher-invariant readout could live, or genuine over-capacity. TFPT does not pretend E8 is fully used.
Recorded status: Reverse anti-numerology audit [E]/[O] (3/8 Casimir invariants mapped, 5/8 hull overhead; economy not promiscuity; phi is unmapped structure not numerology)
Canonical status: [E] the reverse audit (3/8 mapped, 5/8 unmapped), the economy signature (small fixed invariant set -> all readouts), and phi-as-unmapped-structure (so not numerology); [O] the honest reading of the unmapped remainder as hull overhead. A self-critical anti-numerology audit -- the reverse complement of v305; closes nothing, flags the hull overhead plainly.
Dependencies: WITNESS.INDEP.01; v305; v100; v312; v348; v54
Scripts: v354_e8_reverse_audit.py
Location: tfpt_5_redteam
Original CSV, line 96Original ledger status
ARCH.REVIEW.01
Four validated review identities (passed arithmetic AND the anti-numerology/admissible-invariant discipline) + one disciplined rejection: (1) HYPERCHARGE LUCAS-BINET: carrier charges (q+,q-)=(3,-2) [X^2-X-6=(X-3)(X+2), Lean unique_carrier_pair] generate D_n=(3^n-(-2)^n)/5=1,1,7,13,55,133 = (N_Phi, -, scalaron exp 7, Delta_Q 13, quark numerator 55, dim E7 133) in order; c_u/c_d=D_5/(N_fam^2 D_4)=55/117 (cleaner than Plucker 11). (2) INVERSE ANCHOR THEOREM: 1^T M^-1 1 = 1/atom (Q->1/3=1/N_fam, R=K->1/4=1/|mu4|, L->1/10=1/A_Lambda); anchor self-dual a^T R^-1 a=a^T K^-1 a=a^T L^-1 a=1 (a^T Q^-1 a=7/3, so self-duality is exactly residue/mass/transport, not the pure difference Q). (3) MACWILLIAMS: C^+=even-weight code [5,4,2], dual=repetition [5,1,5], weight enum (1,10,5)=Lambda^even(5) (makes the existing Hamming-scheme duality the named MacWilliams/UV-IR transform). (4) 6Y^2-Y-1=(2Y-1)(3Y+1)=(sY-1)(bY+1), roots 1/2 (SU2) and -1/3 (SU3). FIREWALL (recorded): m_p/m_e=1920-84+3lamC^2 (SU(9)=A_8 not in carrier; m_p is QCD confinement, no mechanism) and eta_B=(2/13)c3^6 (model-dependent leptogenesis output) are arithmetically close but REJECTED -> stay [A]/[P] frontier, NOT promoted to [I]
Recorded status: Identity/Lattice [I]/[L]
Canonical status: Identity/Lattice [I]/[L] (4 accepted; m_p/m_e + eta_B firewalled)
Dependencies: CAR.UNIQ.01; FLAV.KQ.01; FLAV.SOLAR.01; v44; FR.MPME.01; FR.ETAB.01
Scripts: v79_review_identities.py
Location: tfpt_1;tfpt_2;tfpt_4
Original CSV, line 146Original ledger status
ARCH.QUAD.01
EXTERNAL-REVIEW VALIDATION + the DEGREE-2 pattern named: (1) SEED NORMAL FORM [I] - phi0 = (|mu4|/N_fam) c3 + Omega_adm c3^|mu4| exactly: the seed is a linear seam term plus a topological fourth-order correction over all admissible fermion states (4/3 = |mu4|/N_fam, 48 = Omega_adm = N_fam dim S+, exponent 4 = |mu4|) - a structured anchor readout, not a fitted formula. (2) HYPERCHARGE SECOND MOMENT [I] computed from the explicit charge table: Tr X = 0, Tr X^2 = 120 = 5! (X = 6Y on one 16-state generation). (3) FACTORIAL SPINE [I] (named lemma): 5! = 120 = |R+(E8)| = sum of E8 exponents = Tr X^2; 240 = 2x120; 1920 = 2^4 x 5! = |W(D5)| - the same factorial moment in four projections (hypercharge, E8 roots, D5 Weyl group, Hawking-power fingerprint): an anti-numerology structure statement. (4) DEGREE-2 INVENTORY [I]: six exact degree-2 structures (Pascal closure truncates at K=2 with UNIQUE solution g=5 on 1..40; glue norms 5/4+3/4 = 2 = root norm; c3 = (1/2) x 1/(4pi) = variational half x 2d-slice Gauss-Bonnet; pair sector C(5,2) = 10 = A_Lambda; second moments; codimension-2 seam). NAMED HYPOTHESIS [P] (recorded, NOT claimed): QUADRATIC BOUNDARY LOCALITY - the seam supports only bilinear data, hence the compiler truncation K=2 is forced rather than chosen; if proven, the Pascal SELECTION (red-team Target B residual, REDTEAM.B.01/CAR.PASCAL.01, typed [A]/[P]) upgrades to [L] and the chain locality => K=2 => g=5 => 16 => D5 => E8 closes the carrier choice - the named reduction target for Target B. (5) AUDIT: 240 = 16x15 (even-code transition reading) exact but non-unique (240 = 16x5x3 established, v1), no bijection exhibited - recorded like the v91 graph reading. NOTES: 'reality compiler = {a, pi, v_geo}' is a restatement of v23+v78 (confirmed); the requested grammar-freeze rule is already implemented by v84 (pre-data freeze) + v100 (declared-grammar census)
Recorded status: Identity [I] (seed NF, moment, spine, inventory) + [P] (named locality hypothesis) + audit
Canonical status: Identity: seed NF + factorial spine + degree-2 inventory; locality hypothesis [P] named
Dependencies: ARCH.CORE.01 (anchor); CAR.PASCAL.01 / REDTEAM.B.01 (the residual it names); FLAV.MASSVOL.01; HOR.01 (1920); REG.FREEZE.01; v100
Scripts: v106_review_validation.py
Location: tfpt_1;introduction
Original CSV, line 189Original ledger status
FLAV.H2.02
THE HEXAGON IS THE SIGN-TWISTED FAMILY SPECTRUM (first exact piece of the H2 dictionary; the v20 lepton coefficients are resolvent determinants of the exact W(A3) monodromy GATE.UWALL.09): (1) SIGN-TWIST LEMMA [I]: -M0 has order 6 ((-M0)^3 = -1) and spec(M0) u spec(-M0) = mu_6 - the 6-site hypercharge hexagon spectrum IS the family monodromy spectrum together with its sheet twist, Z6 = Z2 x Z3 realised as (-1) x <M0>; the v20 hexagon denominators 5/4 - cos(r pi/3) equal |1 - zeta_6^r/2|^2, the eigen-denominators of the two family resolvents (1 -+ M0/2)^{-1}. (2) CYCLOTOMIC DETERMINANT [I]: det(1 - t M0) = 1 - t^3 = (1-t) Phi_3(t) (the N_fam cyclotomic) => det(1 - M0/2) = 7/8 and det(1 + M0/2) = 9/8. (3) LEPTON COEFFICIENTS = RESOLVENT DETERMINANTS [I]: c_e = |mu_4|/(2 det-) = 16/7, c_mu = N_fam/(2 det+) = 4/3, c_tau = |mu_4| det-/N_fam = 7/6, and v20's product rule = |mu_4|/det+ = 32/9 - the lepton denominators 7 and 9 ARE the two family-resolvent determinants (x 2^3), and delta = 1/2 = |(M0)_22| is supplied by the monodromy matrix itself; the e/mu/tau LEG assignment (residues r, windings w) remains v20's established input - nothing re-fished. (4) SHEET-EXTENDED GROUP [I]: <U, M0, -1> has order 48 = Omega_adm = N_fam x dim S+ (the seed quartic coefficient, ARCH.QUAD.01) = |S4 x Z2| (exact enumeration; audit cross-link). (5) RESIDUE [P] (recorded): the dictionary's VALUES are exact; its ADDRESS TABLE (which hexagon site each fermion occupies; the quark-sector composition) remains open
Recorded status: Identity [I] (exact spectral + determinant identities + group enumeration) + Physical [P] (address table)
Canonical status: Identity: hexagon = spec(M0) u spec(-M0); lepton 7 and 9 = det(1 -+ M0/2) x 8; product rule = mu4/det+; H2 values exact - address table open
Dependencies: GATE.UWALL.09; FLAV.H2.01; v20 (leg assignment); ARCH.QUAD.01 (Omega_adm); E8.GLU.01
Scripts: v118_hexagon_family_dictionary.py
Location: tfpt_research_contracts; tfpt_2
Original CSV, line 202Original ledger status
EM.BUDGET.02
PYRATE GAUGE CROSS-CHECK (independent third-party confirmation of EM.BUDGET.01/CAR.SM.01 and an F_transfer gauge-input check): the carrier/SM field content gives, by the textbook one-loop formula in GUT normalisation, (b1,b2,b3)=(41/10,-19/6,-7) [I]; (1) THREE INDEPENDENT PATHS to b1=41/10 - carrier algebra 10 b1 = g_car 2^{g_car-2}+1 = 41 (CAR.SM.01), the SM U(1) hypercharge index sum (3/5)Y^2 over the content, and the RGE generator PyR@TE 3 (arXiv:2007.12700) which writes beta_g1 = (41/10) g1^3 verbatim - all agree; (2) the M=41 decomposition 10 b1 = 40 (fermion U(1) index = sum_{f,j} L_{f,j}) + 1 (one Higgs doublet N_Phi) reproduces tfpt_2 Gate 1 exactly [I]; (3) PyR@TE also writes beta_g2 = -19/6 g2^3, beta_g3 = -7 g3^3 and the full standard 2-loop SM gauge matrix (evidence verification/pyrate/sm_gauge_betas.txt, regenerated by verification/pyrate/reproduce.sh) [I]. SCOPE [P]: confirms the gauge sector of the F_transfer functor (its running inputs are not free knobs but follow from the carrier content); PyR@TE is the right external tool for the transfer/RGE gates (gauge running, and - with a seesaw model - the neutrino-Yukawa running behind eta_B), NOT for premise (A) (a 2d boundary-CFT question)
Recorded status: Identity [I] (one-loop coefficients exact) + [P] (F_transfer gauge inputs)
Canonical status: Identity [I]: carrier content -> (41/10,-19/6,-7); PyR@TE 3 (external) reproduces them verbatim; F_transfer gauge inputs confirmed
Dependencies: EM.BUDGET.01; CAR.SM.01; v2_carrier_pascal.py; v13_open_gates.py
Scripts: v159_pyrate_gauge_crosscheck.py
Location: tfpt_2
Original CSV, line 248Original ledger status
QFT4D.MATTER.01
SPECTRAL-ACTION MATTER CONTENT (2026-06-17): the computable core of CONTRACT.QFT4D.01 (v244) -- the NCG matter representation, discharging the representation-theory + tree-relation core to [E] and leaving only the seam->Dirac realisation and the measured-coupling reproduction as the open residual. The carrier half-spinor is the SO(10) 16 (dim S^+ = 2^(g_car-1) = 16). One generation = SO(10) 16 = SU(5)(10+5bar+1) = SM: Q=(3,2)_{1/6}, u^c=(3bar,1)_{-2/3}, e^c=(1,1)_{1}, L=(1,2)_{-1/2}, d^c=(3bar,1)_{1/3}, nu^c=(1,1)_{0}. (1) [E] 16 = one generation: SM multiplet dims sum to 6+3+1+2+3+1 = 16 = dim S^+, N_fam=3 (15 SM Weyl fermions + a right-handed neutrino). (2) [E] electric charges Q=T3+Y are exactly the SM values (quarks +2/3,-1/3; anti-quarks -2/3,+1/3; leptons 0,-1; e^c +1; nu^c 0) -- the hypercharges are forced by the SO(10) embedding. (3) [E] anomaly-free: all four gauge anomalies cancel exactly over the 16: sum Y = 0, sum Y^3 = 0, [SU(2)]^2 U(1) = 0, [SU(3)]^2 U(1) = 0. (4) [E] spectral-action unification: sin^2 th_W = (sum T3^2)/(sum Q^2) = 3/8 at the spectral scale, i.e. g3=g2=sqrt(5/3)g1 (Chamseddine-Connes-Marcolli). (5) [E] Higgs = the (1,2)_{1/2} off-diagonal part of the finite Dirac operator (inner fluctuation), one SM doublet. (6) [O] residual: (i) the seam induces the Dirac operator D and (iii) the spectral action reproduces the MEASURED couplings after RG running -- still a contract, now with its rep-theory core verified
Recorded status: Numerical (exact rep theory) [E]/[O]
Canonical status: [E] SO(10) 16 = one anomaly-free SM generation with correct hypercharges/charges; sin^2 th_W = 3/8 (g3=g2=sqrt(5/3)g1); Higgs = (1,2)_{1/2} inner fluctuation. [O] the seam->Dirac realisation + measured-coupling reproduction stay the open contract
Dependencies: CONTRACT.QFT4D.01; FORM.P2.02
Scripts: v245_spectral_matter_content.py
Location: tfpt_research_contracts
Original CSV, line 331Original ledger status
PS.ALGEBRA.01
PATI-SALAM NCG ALGEBRA + EXACT SM MATCHING (2026-06-17): the finite algebra A_F = H_L (+) H_R (+) M_4(C) and its consequences (Reviewer-A Theorem 2). (1) [E] unimodular gauge group SU(2)_L x SU(2)_R x SU(4)_c (ranks 1+1+3=5=rank SO(10), dims 3+3+15=21). (2) [E] one generation 16 = (4,2,1)+(4bar,1,2) = 8+8. (3) [E] Y = T_3R + (B-L)/2 reproduces the EXACT SM hypercharges for all six multiplets (Q,u^c,d^c,L,e^c,nu^c), and Q = T_3L + Y the exact electric charges {2/3,-1/3,0,-1,1,0}; B-L is the SU(4)_c generator (lepton = 4th colour). (4) [E] coupling matching a1^-1=(3/5)a2R^-1+(2/5)a4^-1 (coeffs sum to 1, so a1=a_GUT at the SO(10) point), sin^2 thetaW=3/8 (=v245). (5) [O] that A_F is the UNIQUE real even algebra generated by seam+sheet-Z2+mu4 (so 'carrier gauged' is a theorem, not a fork). (6) [O] CAVEAT: the PS colour SU(4)_c sits inside SO(10)=D5; it is NOT the carrier factor A3=SU(4) (= family structure, N_fam=3=rank A3) -- a precision the reviews blur.
Recorded status: Numerical (exact rep theory) [E]/[O]
Canonical status: [E] A_F -> SU(2)xSU(2)xSU(4) PS group, 16=(4,2,1)+(4bar,1,2), exact hypercharges/charges, matching a1^-1=(3/5)a2R^-1+(2/5)a4^-1, sin^2=3/8; [O] seam-reconstruction + the colour/family distinction
Dependencies: QFT4D.MATTER.01; PS.E8BRANCH.01
Scripts: v248_ps_algebra.py
Location: tfpt_research_contracts
Original CSV, line 334Original ledger status
PS.NCG.ORIENT.01
ORIENTABILITY + POINCARE DUALITY -- HONEST STRUCTURAL TREATMENT (2026-06-17): the two NCG obligations of v250 that do NOT close to a clean [E] on the simplified v252 representation. NO faked proof. KO-dimension 6 forces the intersection form cap(p,q)=Tr(gamma pi(p) J pi(q) J^-1) to be ANTISYMMETRIC (from J gamma=-gamma J + order-zero + reality), so a skew form on the SM K-theory K_0(C(+)H(+)M_3)=Z^3 (odd rank) is necessarily degenerate -- a genuine structural fact. (1) [E] skew intersection form forced by KO-6, verified numerically on the explicit triple (v252). (2) [E] rank/corank: rank 2, corank 1, null direction ~ (1,1,-1) in (C,H,M_3). (3) [E] orientability local condition [gamma_F,pi(a)]=0 (v252); orientability proper is a degree-4 Hochschild cycle on the PRODUCT geometry M x F (metric dim 4), the finite factor (metric dim 0) only contributing gamma_F -- not a finite-only check. (4) [C] for the full hypercharge-faithful SM/PS spectral triple orientability and Poincare duality DO hold (van Suijlekom 'NCG and Particle Physics'; Chamseddine-Connes-Marcolli) -- the corank-1 of the naive skew form is resolved on the physical sublattice / proper K-theory pairing; established in the literature, not re-derived. (5) [O] a fully self-contained machine proof needs the COMPLETE hypercharge-faithful canonical bimodule; the v252 simplified rep faithfully verifies the five substantive axioms (reality, grading, KO-6, order-zero, first-order) but not these two skew/degree-4 conditions. Honestly open.
Recorded status: Numerical (NCG; honest status) [E]/[C]/[O]
Canonical status: [E] KO-6 skew intersection form + rank2/corank1/null(1,1,-1) + orientability local condition; [C] canonical triple satisfies both (literature); [O] self-contained machine proof needs full canonical bimodule -- no faked closure
Dependencies: PS.DIRAC.02
Scripts: v256_orientability_poincare.py
Location: tfpt_research_contracts
Original CSV, line 342Original ledger status
FLAV.TH13.01
REACTOR ANGLE EXPONENT = CARRIER HYPERCHARGE TRACE (2026-06-18): the theta_13 value sin^2 theta_13 = phi0 e^{-5/6} = 0.0231 (v16) has its EXPONENT origin closed exactly -- gamma = tr_E Y^2 = 5/6 over the 5-slot carrier hypercharge Y=diag(-1/3,-1/3,-1/3,1/2,1/2) (anomaly-free roots of 6Y^2-Y-1=0), complement 1/6 the neutrino ratio. theta_13 is confirmed a SEPARATE carrier-trace channel: the mu-tau-breaking eps=3phi0/4 (which gives theta_12) induces only ~1.6e-3 << 0.023, correcting the tempting 'theta_13 from M_nu' route (v263). CP magnitude (delta_PMNS=240 deg, mu6/triality) and absolute nu-mass scale (M_R) remain the open PMNS items.
Recorded status: Numerical/identity (flavor readout) [E]/[C]/[O]
Canonical status: [E] gamma=5/6=tr_E Y^2 (exponent origin) + own-channel separation (eps^2 ~ 1.6e-3 != 0.023); [C] value 0.0231 vs ~0.0222; [O] CP magnitude + absolute scale open. Closes the theta_13 exponent origin, not full PMNS dynamics.
Dependencies: FLAV.TH12.01; FLAV.SOLAR.01; FLAV.PMNS.02; CAR.SM.01
Scripts: v268_theta13_carrier_trace.py
Location: tfpt_2_standard_model
Original CSV, line 361Original ledger status
FLAV.TH13.PRESSURE.01
THE theta13 PRESSURE POINT -- THE HONEST WEAK SPOT, QUANTIFIED AND PRE-REGISTERED (2026-06-22). [N] TENSION: sin^2 theta13 = phi0 e^{-5/6} = 0.023108 vs NuFIT 6.0 NO (0.02195 +- 0.00058) is +2.0 sigma -- the most-tensioned CORE prediction (v62/v307). [E] SEPARATE CHANNEL: theta13 is the carrier hypercharge trace (exponent gamma=tr_E Y^2=5/6 EXACT, v268), NOT the seesaw mu-tau breaking that sets theta12 (eps=3 phi0/4 induces only ~1.6e-3 << 0.023) -- distinct channels, a theta13 pull does not move theta12. [N] NO CHEAP RELIEF: phi0(theta13)=e^{5/6} sin^2 theta13_exp=0.0505 is ~5% below the axiom 0.05317; PMNS theta13 RG running is <1% (NO) so cannot close a 5% gap, and the exponent 5/6 is exact -- no freeze-respecting sub-leading correction relieves it; prediction stays frozen (REG.FREEZE.01). [X] PRE-REGISTERED KILL: a stable sin^2 theta13 away from 0.023108 at >3 sigma (JUNO/global) flags the carrier-trace/seed-grammar reading. [E] SEED-HYPERPLANE CONSISTENCY: exactly the v306 leave-one-out outlier (theta13 the single ~2 sigma channel, others ~1 sigma) -- one honest pressure point, not a pattern.
Recorded status: Numerical/data [N]/[X] (theta13 pressure point)
Canonical status: [N] the precise +2.0 sigma tension + the no-relief audit; [E] the separate-channel structure (v268) + the seed-hyperplane consistency; [X] the pre-registered kill. Names and quantifies the honest weak point; no new claim, no freeze change.
Dependencies: FLAV.TH13.01; DATA.SCORECARD.01; SEED.CROSSVAL.01; v268; v62; v306; v307
Scripts: v328_theta13_pressure.py
Location: tfpt_2_standard_model
Original CSV, line 427Original ledger status
ALPHA.QUILLEN.PROGRESS.03
A THIRD HONEST step on the external target ALPHA.QUILLEN.EXACT.01 (2026-06-28, v434): it settles the status of the three residuals named after v433 and shows they are NOT three independent open problems -- the target stays [O], alpha^-1 stays [E]. [E] b1 IS THE U(1) a_4 HEAT-KERNEL COEFFICIENT (the beta-function = a_4 theorem, Vassilevich): computed from the carrier hypercharge content with the standard spin weights (2/3 per Weyl fermion, 1/3 per complex scalar), sum (2/3)Y_f^2 + (1/3)Y_s^2 = 41/6 (SM normalisation) and (3/5)*that = 41/10 = b1 (GUT) -- so the b1 in the counterterm 8 b1 c3^6 is the a_4 heat-kernel coefficient of the carrier U(1)_Y content (same number as the beta, v159/v246), the SAME KIND of object as the alpha^2 Calderon a_4 (v342), NOT a fitted multiplicity. [E] the geometry factors off: 8 b1 c3^6 = b1*(rank E8)*c3^6 (rank E8=8 the chi=2 seam boundary, v216; c3^6 the six boundary insertions, v342). [C] RESIDUAL (1) 'exact a_4 = 8 b1 c3^6 on the mu_4 seam moduli' == RESIDUAL (3) 'the seam F-normalisation': with b1 and the c3-powers heat-kernel-forced, the only freedom left in the exact a_4 value is how the gauge curvature couples to the boundary measure -- ONE [C] obligation, not two. [E] RESIDUAL (2) located (not closed): a^3 - 2 c3^3 a^2 = a^2 (a - 2 c3^3), with a^2 the Gilkey gauge-curvature (Quillen/Chern) density (v342), so the leading a^3 = a*a^2 is the first MOMENT of the Chern density -- a topological level at boundary order c3^0, not a Seeley-DeWitt curvature integral; its from-first-principles (Chern-Simons-type) origin stays [O]. [E] NET REDUCTION: the EM-Ward residual is ONE [C] (residuals 1&3) + ONE [O] (residual 2), not three independent problems. [O] NOT CLOSED: the alpha^3 Chern level + the from-first-principles proof are external math (type A, v384); the seam F-normalisation stays [C]; SEAM.EQUIV.01 continuum existence (MMST, v336) stays the other external [O]; alpha^-1 stays [E].
Recorded status: Third honest step / grounding+reduction [E]/[C]/[O] (b1 = the U(1) a_4 heat-kernel coefficient via beta=a_4; residuals 1&3 collapse to one seam F-normalisation [C]; residual 2 the alpha^3 Chern level located but [O]; the headline target stays OPEN)
Canonical status: [E] b1 = 41/6 (SM) = 41/10 (GUT) is the U(1)_Y a_4 heat-kernel coefficient of the carrier content (beta=a_4 theorem), grounding the counterterm's matter factor; the geometry factors as 8 b1 c3^6 = b1*(rank E8)*c3^6; the cubic factors as a^2(a-2c3^3) (a^3 = the first moment of the Chern density, a level). [C] residual (1) 'exact a_4 = 8 b1 c3^6' == residual (3) 'seam F-normalisation' (ONE obligation). [O] residual (2) the alpha^3 Chern level + ALPHA.QUILLEN.EXACT.01 stay open. A third honest step that grounds, reduces (3 residuals -> 1[C]+1[O]) and locates, it does not close; no new number, alpha^-1 stays [E].
Dependencies: ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.PROGRESS.01; ALPHA.QUILLEN.PROGRESS.02; EM.WARD.01; EM.WARD.02; v159; v216; v246; v341; v342; v382; v433
Scripts: v434_alpha_quillen_betafunction.py
Location: tfpt_1_architecture_e8
Original CSV, line 457Original ledger status
ALPHA.QUILLEN.INFLOW.01
THE ALPHA^3 LEVEL = THE COMPUTED BULK CHERN INVARIANT + THE SEAM F-NORMALISATION = THE AFFINE EMBEDDING INDEX (2026-07-02, closure-route round) -- upgrades BOTH residuals left after v433/v434/v435; does NOT close ALPHA.QUILLEN.EXACT.01. [E] TARGET RE-VERIFIED: alpha^-1 = 137.0359992168 unique root; Quillen split a^3 - 2 c3^3 a^2 = 8 b1 c3^6 ln(1/phi_seam) at the root < 1e-35 (v341/v382). [E] THE INVARIANT COMPUTED: FHS Chern C(M=1) = 1, C(M=3) = 0 -- the same integers as v367/v461, here read as the quantised U(1) response of the collar phase. [C] k0 = |C| = 1 UNDER THE EM1 READING: the a^3 coefficient EQUALS the computed bulk invariant of the SAME p+ip model that realises S3 -- 'why exactly 1' is answered by COMPUTATION plus the cited inflow identification (TKNN PRL 49 (1982) / Avron-Seiler-Simon PRL 51 (1983): integer quantisation of the U(1) response; Callan-Harvey NPB 250 (1985): boundary level = bulk response; APS 1975 / Alvarez-Gaume-Della Pietra-Moore Ann. Phys. 163 (1985) / Witten RMP 88 (2016): the metric-independent part of delta log det is the eta/CS level; Quillen 1985 / Bismut-Freed CMP 106 (1986): determinant-line curvature integrality) -- REPLACING v435's minimality assumption ('1 is the unit level') by a measurement on the model. [E] k_Y = 5/3 EXACT: tr_5bar(Y^2)/tr(T3^2) = (5/6)/(1/2) = 5/3 (Ginsparg PLB 197 (1987), the string-GUT hypercharge level); (3/5) x (41/6) = 41/10 = b1 -- the 'GUT 3/5' in the closure IS the inverse embedding index, not an imported convention; carrier decomposition 41/6 = 20/3 (3 generations x 16-content) + 1/6 (Higgs doublet). [C] F-NORMALISATION RETYPED: once the seam net is (E8)_1 at level 1 (SEAM.EQUIV.01), the U(1)_Y current sits inside a level-1 current algebra and <J(z)J(w)> = k/(z-w)^2 is FIXED by the embedding index -- level-1 current-algebra rigidity, no continuous dial; the v434 [C] ('how does the gauge curvature couple to the boundary measure') has ZERO independent content: it is a face of SEAM.EQUIV.01 (consistent with the v382 typing), its value the embedding index. [E] THE STRUCTURAL UNIFICATION: the two named targets share ONE object -- the collar phase carries TWO quantised responses, gravitational c_- = 16 x 1/2 x |C| = 8 = g_car + N_fam (feeds SEAM.EQUIV.01/S3, v456) and U(1) C = 1 (feeds the a^3 level, EM1); 'the one theorem and the one number' are two faces of the SAME invertible phase, and closing R1' (v469) feeds both residuals simultaneously. [O] NOT CLOSED: the bridge lemma 'delta log det_zeta(seam) = the inflow response' stays the named cited step; the EM1 reading stays [C]; ALPHA.QUILLEN.EXACT.01 stays [O]; alpha^-1 = 137.0359992 stays [E] regardless. UPDATED 2026-08-27 (v974): the inflow step 'boundary level = bulk response' is upgraded from cited to COMPUTED on the same model (probe laughlin_pump_em1_probe 20/20, PUMP_QUANTIZED_MATCHES_CHERN): Laughlin pump +1 per flux quantum (teleport bookkeeping with exact period closure), edge spectral flow -1/+1 antisymmetric as inflow demands, Streda dN/dPhi = C/(2 pi) exact integers over n_phi = 0..3 -- all equal to the FHS Chern, with the M = 3 controls all zero. The identification of the complex-copy U(1) with the physical Majorana collar stays part of the cited EM1 reading [C]; ALPHA.QUILLEN.EXACT.01 stays [O].
Recorded status: Inflow level + embedding rigidity [E]/[C]/[O]: the a^3 coefficient = the COMPUTED bulk Chern |C| = 1 of the v367 collar (TKNN/ASS quantisation + Callan-Harvey inflow + APS/Witten eta=CS), replacing v435's minimality; the seam F-normalisation = the affine embedding index k_Y = 5/3 (Ginsparg 1987, (3/5)(41/6) = 41/10 = b1) -- zero independent content, a face of SEAM.EQUIV.01; one phase, two responses (c_- = 8, C = 1) feeding both named targets; ALPHA.QUILLEN.EXACT.01 stays [O]
Canonical status: -
Dependencies: ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.PROGRESS.02; ALPHA.QUILLEN.PROGRESS.03; ALPHA.QUILLEN.PROGRESS.04; EM.WARD.01; SEAM.EQUIV.CROSSEDPRODUCT.01; v341; v367; v382; v433; v434; v435; v456; v461
Scripts: v470_alpha_inflow_level.py
Location: tfpt_1_architecture_e8
Original CSV, line 531Original ledger status
ARF.SPINORCOMPILER.01
The Arf/spinor compiler on V = L/(1+i)L = F2^4 -- Priority 1 of the Arf compiler programme, the exact finite-algebra layer (one module, 46 checks, ~2 s; discovery probe arf_spinor_compiler_probe.py 46/46, verdict ARF-SPINOR-EXACT, zero kills, both must-fail controls fire). THE COMPILER, EXACT END TO END: hbar rebuilt from the concrete v752 lattice (Gram J - I in the family/anchor basis, census 240 = 15 x 16, sigma symplectic; standard-doubled-model cross-check: chi coefficients (0,0,0,1), y0 = FSUM); brute force over all 2^16 functions: EXACTLY 16 quadratic refinements; Arf census 6 + 10 with |Sp(4,2)| = 720 (full 65536-matrix census) and a faithful+surjective S6 action on the six Arf-1 forms; the frozen selector (sigma-invariance census 4 -> q(A) = 1: 2 -> q(F_Sigma) = 0: 1) picks a UNIQUE q*; the parity lift iota: V ~ C_even(5) satisfies beta = hbar in all 256 cells (crosslink 1) and the weight form q_wt IS q* (offset 0; all 16 refinements = q* + hbar(., c) bijectively); Stab(q*) of order 120 acts as S5 with orbits {1, 5, 10} on refinements AND words: 16 = 1 + 5bar + 10 as Arf geometry; the K6 duad model v <-> D(v) is a bijection onto E(K6), Sp/sigma-equivariant, vertex split 15 = 5 + 10 at q*; B = I + A_KG(6,2) ENTRYWISE in all 225 cells, charpoly (x-7)(x-2)^9(x+2)^5, ovoid eigenvector B(1_O - (1/3)1) = -2(1_O - (1/3)1) EXACT (the six ovoid indicators span the (-2)-eigenspace, rank 5); all 6 fully isotropic spreads carry q*-signature (1, 2) per block; the hypercharge table X = (-2,-2,-2,3,3) reproduces the v310/v14 dictionary (values AND multiplicities); code polynomial moments (16, 0, 120, 0) with the chain 120/3 = 40, +1 = 41 = 10 b1, 2*120 = 240, +8 = 248 (the v2 master moment Tr X^2 = 120 = 5!); Pati--Salam 16 = 8 + 8 with the A bit as isospin index and B-L = 1 - 2 n_c/3 exact; chi_NSR = hbar(., F_Sigma) = the anchor bit on all 16 words. SEMANTIC SEPARATION (naming discipline, no physics claim): the SAME sigma acts as the family 3-cycle A3^Fam on the message bits AND as the 3+2 slot split A3^PS on the carrier legs -- two registers, never to be conflated. HONESTY FENCE (binding): the PHYSICAL code->matter reading is NOT claimed -- it is KILLED at root level by v775 (ROOTCLASS-MIXED), incl. the 'empty mailbox = right-handed neutrino' reading. Companion Lean module TfptCarrier/ArfSpinorCompiler.lean (23 kernel theorems, decide/norm_num only, no sorry, no native_decide, lake build green). No marker move, NO RH claim. NOTE (2026-08-05, v782/v784 -- marker UNCHANGED): the certified spread + q* selector become load-bearing in the transition-bus spread layer 240 = 5 x 3 x 16 (v782), and the q* parity acquires a sharp NEGATIVE boundary: the seam curve's canonical deck-invariant theta refinement is EVEN (Arf 0, decomposition 1+6+9) while q* is ODD (Arf 1, 1+5+10) -- the curve/code 2-torsion transport dies at exactly this layer alongside the syntheme-vs-duad sigma layer (v784, joint census 0 with positive control 6).
Recorded status: Exact [E] finite algebra (integer/Fraction/F2 arithmetic; Lean companion ArfSpinorCompiler.lean, 23 kernel theorems; Python-only per GATE.WOLFRAM.02); the physical code->matter reading FENCED (killed by v775/ARF.ROOTCLASS.01).
Canonical status: ARF-SPINOR-EXACT: unique sigma-selected Arf refinement q* (census 4 -> 2 -> 1; q_wt IS q*), parity lift iota ~ C_even(5) with beta = hbar exact, 16 = 1 + 5bar + 10 as Stab(q*) ~ S5 Arf geometry, K6 duad bijection, B = I + A_KG(6,2) with exact ovoid eigenvectors, spreads (1,2), hypercharge table -> v310/v14 dictionary, moments (16,0,120,0) with chain 40/41/240/248, Pati--Salam 8+8 with B-L exact, chi_NSR = anchor bit; A3^Fam != A3^PS discipline; matter reading fenced (v775); Lean companion 23 theorems; no RH statement.
Dependencies: E8.PROJHAMMING.01; PRIME.HECKEPOLARITY.01; CAR.SM.01; AX.P2.01; v752; v753; v2; v310; v14
Scripts: v774_arf_spinor_compiler.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 679Original ledger status
CARRIER.PETERSEN.RADIAL.01
CARRIER.PETERSEN.RADIAL.01 (+ TRANSPORT.SIXTHROOT.01): the K5 edge machine, the Petersen carrier geometry with the radial dynamics whose sixth power IS the deployed transport spectrum, + the bit-exact decider on the PSD sixth root, ONE module from two probes (19/19 + 16/16 checks, ~1 s; discovery probes carrier_petersen_radial_probe.py PETERSEN-RADIAL-EXACT and transport_sixthroot_probe.py SIXTHROOT-SPECTRAL-ONLY, both 2026-08-06). PART 1, THE K5 EDGE MACHINE (all exact integer/Fraction): X = (-2,-2,-2,3,3) is the UNIQUE primitive traceless block-constant charge for the F|W = 3+2 split (sign pinned by the certified v774 table); E(K5) = 10 pairs carry the charge census {-4: 3, +1: 6, +6: 1} = the SU(5) decuple 3_{-4} + 6_{+1} + 1_{+6}, every pair cross-checked against the certified v774 hypercharge table (classes u_c/Q_up/Q_dn/e_c); under disjointness the pairs form the PETERSEN graph SRG(10,3,0,1) (charpoly (x-3)(x-1)^5(x+2)^4 exact, girth 5, |Aut| = 120 by full backtracking census = the faithful S5); the distance shells around the W vertex are (1, 3, 6) and CHARGE-PURE (+6/-4/+1 = e^c/u^c/Q), and the distance-2 shell induces a C6 -- THE FLAVOR HEXAGON AS GRAPH GEOMETRY [E neu] (explicit cycle verified edge by edge; 6 = |R+(A3)| = the transfer exponent, v124); the shell partition is EQUITABLE with quotient [[0,3,0],[1,0,2],[0,1,2]] whose eigenvector (6,-4,1) -> -2 IS the hypercharge vector, and P = Q_Pet/3 has spec(P^6) = {1, 64/729, 1/729} == the deployed TFPT transport spectrum EXACTLY (v54/v56/v171/v317; v124 lambda_n = (1-n/3)^6; GATE.METRIC.18). THE PREDICTION [H neu]: the full 10-dim Petersen walk has spec(P10^6) = {1, (1/3)^6 x5, (2/3)^6 x4} -- fast mode multiplicity 5 = g_car, slow hypercharge mode 4 = |mu4| (trace crosscheck 990 = 729 + 5 + 256); NO corpus 10-dim operator exists (T is 3-dim on the cusp space) -- a prediction, not a verification. PART 2, THE SIXTH ROOT (exact Fractions): B = (1/18)[[13,1,4],[1,13,4],[4,4,10]] -- every entry a compiler number (18 = p4(anchor), 13 = N_fam^2 + |Z2|^2, 4 = |mu4|, 10 = A_Lambda, 1 = N_Phi) -- is the UNIQUE symmetric doubly stochastic PSD sixth root with the frozen corpus-basis eigen-assignment ((1,1,1) -> 1, (1,-1,0) -> 2/3, (1,1,-2) -> 1/3; spectral reconstruction entry-exact; exactly 2 assignments in the corpus basis, a 1-parameter circle without the pin); B^6 carries the deployed spectrum exactly BUT the decider lands SPECTRAL-ONLY: B^6 is GL(3,Q)-conjugate to v486's lazy-walk M^6 (exact rational W and orthogonal O conjugations verified) and to the cusp-diagonal canonical form, yet bit-equal to NEITHER -- the corpus freezes the SPECTRUM, not the basis; the stochastic types differ (doubly vs sub-stochastic with absorbing channel). Controls fire in both parts (wrong edge 4+1 kills the (1,3,6) structure; Johnson complement kills the hexagon; both matrix perturbations break the spectrum). Typed carrier representation geometry -- ROOTCLASS-MIXED (v775) cited, no particle semantics. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02. [2026-08-06 LXVI dated correction + addendum, v814: the sixth-root census missed the deployed v221 evaluation -- T_v221 (the exact spectral sum of v221's transfer (1-w)^6) == B^6 BIT-EXACTLY, so the TRANSPORT.SIXTHROOT.01 verdict upgrades from SPECTRAL-ONLY to BITEXACT-vs-v221 (the frozen SPECTRAL-ONLY stands as the probe's adjudication; ABEL-DEAD correction precedent); and the [H neu] 10-dim prediction now has a promotion-ready canonical PROPOSAL: T10 = P10^6 in the Lambda^2 basis passes all gates with the equitable v774 quotient == (Q_Pet/3)^6 bit-exact (TRANSPORT10-PROPOSED, no deploy claim), while the six-step composition is typed CLOCK-ONLY -- the deployed 6 is the clock exponent, every spatial route carries a typed obstruction.]
Recorded status: Exact [E neu] finite graph/matrix structure theorems (integer/Fraction; charpolys sympy-gated) behind the carrier-geometry fence; the 10-dim multiplicity prediction typed [H neu]; carries TRANSPORT.SIXTHROOT.01 (spectral-only decider)
Canonical status: PETERSEN-RADIAL-EXACT + SIXTHROOT-SPECTRAL-ONLY: charges (-4,+1,+6) = the SU(5) decuple against v774; Petersen SRG certified, |Aut| = 120 census; shells (1,3,6) charge-pure; the flavor hexagon = the distance-2 shell edge-by-edge; equitable quotient with hypercharge eigenvector (6,-4,1) -> -2; spec(P^6) = {1, 64/729, 1/729} = the deployed transport spectrum; 10-dim multiplicities (x5 = g_car fast, x4 = |mu4| slow) typed [H neu] -- no corpus 10-dim operator; B unique symmetric doubly stochastic PSD sixth root in the corpus basis, B^6 GL(3,Q)-conjugate to v486's M^6 and the cusp-diagonal form but bit-equal to neither -- the corpus freezes the spectrum, not the basis.
Dependencies: ARF.SPINORCOMPILER.01; v774; v54; v56; v124; v486; v327; v212; v397; v14; v700
Scripts: v808_petersen_sixthroot.py
Location: tfpt_2;tfpt_3
Original CSV, line 696Established within the stated premises
finding:partner-carrier-charges-and-state-types
epsilon1 epsilon4 produces u1∧u4 in the carrier: Y=1/6 and source charge change0. Root operator, spinor carrier vector and affine root-current state have different types. The exterior unit is the internal nu^c label, not the affine vacuum.
Scope: Original carrier plus supplied E8 charge dictionary; no physical field identification.
Given E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation.
premise:oriented-p2-exterior-carrierThe existing Weyl lift M, affine E8 module, Q'=2(H3+H6) and K_alpha=L0+delta_alpha.H0 with alpha=1/4,3/4 are held fixed for comparison. This representation is not derived from P1/P2; an unbroken SM time action is not assumed.
premise:fixed-e8-fold-quarter-dictionarySource SHA256: ff7c8dff8939e8380509bff5a34145f935407344a07bda1d65b7b25489a2677c
bounded-excerpt · current-at-snapshot
Established within the stated premises
finding:original-weak-current-coefficient-has-explicit-finite-oneform-consumer
The actual weak bar5 coefficient has an explicit quaternionic Higgs witness in the original finite algebra. Its evaluated one-form has LR=q(H)diag(Yup,Ydown), with correct SU2, hypercharge and grading and explicit nonzero lepton/quark entries. General sums retain a common2x2 matrix Q multiplying the already supplied Yukawas across generations and sectors. The separately evaluated central dz normal reader is finite-identity valued and does not create a family Hom matrix.
Scope: A genuine finite-slot coefficient witness, not a full geometric mu-to-current-to-Higgs identification. General complex-linear span gives Q in M2(C); quaternion conjugation constraints require an explicit real-algebra/reality contract and do not follow merely from self-adjoint completion. Preserve actual color projection and Pati-Salam scopes. Old v258 modular inversion is for a given covariance and records the physical seam compression as conditional, not an independently evaluated mu source. Next test the simultaneous common-Q times given-Y relation at the actual geometric sewing consumer. Crucial goal distinction: the QY test applies to inner fluctuations around a fixed supplied D_F, not to original generation of D_F and its Yukawa matrices themselves. Source reconstruction of the background may change those matrices and must neither be excluded by the fixed-background fluctuation class nor replaced by merely varying it. The reviewed further mandatory family-scalar mu-reader conclusion is unsupported. A bare C3 sum is not A4 invariant, and real D†D does not imply real full Pstr kernel with unchecked complex projectors.
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structuresGiven the full unchanged v252 constructor pi,J_F,gamma_F,D_F and its symbolic Yukawa/Majorana inputs. Compare real gauge lift U=pi(u)J_F pi(u)J_F^-1 on the connected unimodular branch lambda det(m)=1 with original oriented P2 carrier E3+E2,Y=(-1/3)^3+(1/2)^2. No full Spin10 source action is presumed. A cyclically fixed neutral family line is considered only with an expressly supplied sigma=(123) and eigenvalue1; its original physical selection is not assumed.
premise:actual-full-v252-unimodular-p2-gauge-liftUse the actual supplied level-one E8 current source C in1x4 and X inbar5x4, original cocycle and compact adjoints. The expressly restricted initial seed keeps only family labels1,2,3. Check current Lie words without presupposing geometric q/p access, a finite Phi coefficient or physical P1 source selection.
premise:given-original-e8-cx-current-cocycle-and-compact-adjointSource SHA256: e421b635bad88784b461c517f85d3b7c0ea90e2c673c92a9a979f1a14072fa06
bounded-sanitized-excerpt · current-at-snapshot · 12 administrative lines explicitly omitted
Source SHA256: 1727be5ccbaeaa31d9fa338412d7e13a9ff8741924c6a793afd397bb373282a8
bounded-excerpt · current-at-snapshot
Source SHA256: 820254440e178430422e50605067775656236602996307f67c9e69124ba5d163
bounded-excerpt · current-at-snapshot
Source SHA256: 820254440e178430422e50605067775656236602996307f67c9e69124ba5d163
bounded-excerpt · current-at-snapshot
Source SHA256: 7a1e93470b65dc8aa56106aa420392a986e8448816f5aa624b44600a696b642c
bounded-excerpt · current-at-snapshot
Source SHA256: 16c60e831dceba773f3629466895f1009654827286e5b760ae01bd755fd5c0b1
bounded-excerpt · current-at-snapshot
Source SHA256: 16c60e831dceba773f3629466895f1009654827286e5b760ae01bd755fd5c0b1
bounded-excerpt · current-at-snapshot
Source SHA256: be430e111469ab4f94478610626a0c0f4b4b7cf387075b876b00f0661a1acbcb
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Source SHA256: be430e111469ab4f94478610626a0c0f4b4b7cf387075b876b00f0661a1acbcb
bounded-excerpt · current-at-snapshot
Non-scientific attribution omitted from public display.
Established within the stated premises
finding:original-primitive-action-is-present-highpass-is-not-finite-selector
the reviewed source correctly quoted the original primitive relative-action formula and its bound reference/relative split. Do not reject it by substituting a different relative-trace convention. The actual primitive projector is seam-even times a spectral high-pass and retains infinitely many circle modes, so it does not by itself select finite Hcar or generate Yukawas. The displayed master variables and hypercharge Y are distinct from Yukawa matrices.
Scope: Preserve the original action and supplied full GNS/state/time source. Not an exclusion of every possible variation or renormalization; reuse existing coupled reference/reflection/gap/domain/projector/eta variation results. Old first-order-bound and D4 corrections are not rediscovered. This checks only the claim that primitive projection/stationarity already generated the finite background.
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structuresIn the existing Clifford chart on L2(S1,K) with finite K let h0=(-i∂theta+alpha)gamma,alpha=1/4 or3/4,gamma*=gamma,gamma²=I. Supply constant selfadjoint odd Phi,{gamma,Phi}=0,and V=-i gamma Phi,h=h0+V on common periodic H1. Compare given CAR sea projectors P_-(h0),P_-(h) and complete pure two-face projector G_ell(h),ell>0,including crossings. This is the existing source class with classical background, not physical selection from P1 or quantization of dynamic bosons.
premise:constant-odd-quarter-circle-source-sea-and-full-graphSource SHA256: b46a4cfb81b9126e495b2af431e15dae27ad70c4a9d76cf1702381ef0756527f
bounded-sanitized-excerpt · current-at-snapshot · 23 administrative lines explicitly omitted
Non-scientific attribution omitted from public display.
Established within the stated premises
finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion
For the actual nonzero Hardy coefficient and marked original weak P2 creators, the exact commutator gives a nonzero grading-odd color-neutral weak doublet of hypercharge+1/2, rank16 for each component in the declared whole-96 comparison. All45 D5 Clifford bilinears commute with the even Hardy projection. Adjoint completion alone has rank32 and fails finite reality. Full original KO6 completion has rank64, is selfadjoint, grading odd and J_F real, with D_KO^2=|kappa|^2(E00+E22) tensor I32. All four sectors retain the same family matrix but fixed quark/lepton signs and antiparticle conjugations; no Majorana block. Actual checker replays and independent root algebra pass. Crucially, original carrier008 already contains the primitive exterior-volume coupling. Its actual up-quark channel reads the new directed coefficient as+kappa; the fixed signed KO Hilbert convention gives-kappa because compact conjugation reverses the complementary wedge. No phase is fitted. The original weak carrier consumer is therefore present.
Scope: Exact operator and original carrier consumer under the declared family/96 P2 comparison. Original wedge contraction corrects the earlier overly broad claim that no original weak Clifford application exists; read the two earlier operator reports with this addendum. Original family coefficients are already prescribed by Hol(nablaF*)Kstr. It remains to compare the actual Hardy contribution with the relevant entry, actual variation or path summand, without imposing equality to the whole Ybr as a universal condition or treating original Y as arbitrary free v252 inputs. Keep mixed E8 family leg, fixed-background limits, C0 versus J_F, internal versus field CAR parity, and NS versus physical quarter time distinct. A correct finite block is not the complete physical source derivation. General addendum: identical familyM on all96slots yields S=M+M^T. Two directed edges give equal nonzero singular values, not unique polarCKM. Different bare doublet-component coefficients violate fixedSU2. Typed original sector-specific readers remain allowed.
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structuresGiven E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation.
premise:oriented-p2-exterior-carrierFor this explicitly alternative comparison identify actual G columns(L0,L2,L1) with supplied generation slots through whole signed P2 dictionary. D_E acts on gamma_F positive,barD_E on negative. Retain unchanged full_D with Y and symmetricMR,F5 structure,faces,graph state and given time. Do not silently replace earlier particlewise hypothesis. No P1 selection,global trivialization,new state/time or physicalE8gauge action assumed.
premise:declared-q-column-to-v252-chiral-slot-comparisonGiven the full unchanged v252 constructor pi,J_F,gamma_F,D_F and its symbolic Yukawa/Majorana inputs. Compare real gauge lift U=pi(u)J_F pi(u)J_F^-1 on the connected unimodular branch lambda det(m)=1 with original oriented P2 carrier E3+E2,Y=(-1/3)^3+(1/2)^2. No full Spin10 source action is presumed. A cyclically fixed neutral family line is considered only with an expressly supplied sigma=(123) and eigenvalue1; its original physical selection is not assumed.
premise:actual-full-v252-unimodular-p2-gauge-liftOriginal D5_1 x A3_1 base net and explicit P2 Clifford carrier supply full45-dimensional D5 operator action including20 non-U5 roots. Its zero modes act with the existing Chevalley cocycle on the supplied compact E8 currents; no primitive P1 preparation or history selecting a word is presumed.
premise:original-d5-base-current-action-on-given-p2-e8-sourceCompare holomorphic Hardy shifts M_z on S0 tensor L and the same degree-zero coefficient line L over the original pi:C→P1_z. Spin half-forms give boundary norm; Fredholm convention is det kernel tensor inverse det cokernel. Relative line is spin line tensor inverse reference line. This defines a mathematical sewing contract, not an established identification with physical D_rel/D_ref or state.
premise:relative-spin-scalar-hardy-cable-on-original-three-coverRead original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117.
premise:original-hard-holonomy-and-closed-triangle-readout-contractSource SHA256: f830ec1e84b614b175918fd7aad5659121c3f53d9f12693ab0bed602e4d4f87c
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Each research problem has its own scope. A resolved task does not close its whole physical parent. Historical tasks remain explicitly historical in the source record.
What is determined by complete future behavior, and what additional positive word-kernel source is needed to reconstruct a cyclic operator realization?
Outside the active mathematical research program since the user's23Oct2026 decision. Historical question: Do the original principles derive a common physical source together with its state, dynamical events, and physically observed fields?
Does the joint discrete theorem determine a concrete connection and a family coupling compatible with the determinant seam action?
Do the original reflection/projector structures determine the full physical time generator and required field transfer?
Which flavor quantity is fixed on the derived discrete stratum, and which requires the continuous holonomy anchor?
Where do the factors and closed alpha equation come from, which provenance steps are proved, and which precise physical EM identification remains open?
Do common matter-only observations derive geometric horizon flow and the area response from the original gravity source?
Which complete quadratic response can the actual clock images reconstruct?
How does the actual Gaussian J act on the complete marked source?
Which data separate sources with identical complete neutral vacuum response?
Can existing native charge fields produce the quarter-twist time response of the seam?
What does the complete phase search decide, and which additional state information prevents a false source solution?
Which charge, state type and time action belong to the root partner and original sheet pairing?
Which tools generate operator maps, learn counterexamples, and can search for the full positive source?
What does reverse selection of P1/P2 give for concrete local fields and multi-field responses, and which identification with the original P1 kernel has actually been proved?
Which operational conditions are independently required, which inequivalent models satisfy them, and which observable distinctions remain for selection?
Which carrier and glue statements are already present in the papers and Lean sources, and which physical selection does not follow?
Which marked seam/lattice transport geometries, lift classes and local-coefficient invariants arise from existing clock/reflection/quartic data? First complete case: sign lifts of fourJ representation on CP1 minusμ4.
Which previously separate data of the original TFPT core follow from a common clock and representation geometry, and which complete finite measurement classification follows without asserting physical source selection?
Which additional joint response actually follows from original source equations, and which entire finite process family remains undecided without it?