Original ledger status
FR.KOIDE.07
OPERATOR ORIGIN OF THE KOIDE SOURCE->POLE FACTOR 53/54 (external-review proposal 2026-06-14, validated; upgrades the FR.KOIDE.03 conjecture from a bare arithmetic guess 1-1/(2 N_fam^3) to an exact operator identity on the carrier): u_pole/u_source = a^T (R+Q) 1 / (2 * 1^T R a) = 53/(2*27) = 53/54. (1) THE CUBIC FAMILY BLOCK [I]: 1^T R a = 27, the E6xA2 flavor-shadow split 248 = dim E6 + det R + 2(1^T R a)N_fam = 78 + 8 + 2*27*3, so 2*27 = 54 is the sheet-doubled denominator. (2) THE MISSING CORNER [I]: the Sheet Diamond has present corners R=M(0,0), K=M(1,-1), L=M(2,0) and the ABSENT corner F=R+Q=M(1,1) with anchor-block determinant det B_F = 52 = dim F4 (FLAV.PENCIL.02/v80); its anchor response a^T(R+Q)1 = 53 = 52+1 (F4 shadow + singlet). (3) THE RATIO [I]: a^T(R+Q)1/(2*1^T R a) = 53/54 = 1-1/(2 N_fam^3) exactly (54 = 2 N_fam^3 = 2*27), so the two readings coincide but this one is structural, not fitted. (4) NEGATIVE CONTROL [I]: only the missing corner F gives 53 -- a^T M 1 for M in {R,Q,K,L} = {32,21,35,56}, none = 53 (specific, not generic). PHYSICAL STATUS [C]: the FACTOR is now sourced exactly; the MECHANISM (the leptonic pole-mass transfer evaluates the F corner) stays a conjecture, an F_transfer special case (F_pole: source->pole). Koide thus moves from 'near miss + conjecture' to 'operator-sourced source->pole transfer'; the prediction itself stays [C]. Cross-ref HOR.TRISECT.01 (the same Sheet-Diamond double-cover grammar carries the gravity clock, exponent ratio |Z2|)
Recorded status: Identity [I] (exact operator factor + negative control) + Physical [C] (the transfer mechanism)
Dependencies, status detail and source
Canonical status: Identity [I]: 53/54 = a^T(R+Q)1/(2*1^T R a) sourced from the missing Sheet-Diamond corner F (det B_F=52); mechanism stays [C]
Dependencies: FR.KOIDE.03; FLAV.PENCIL.02; FLAV.PLUCKER.02; v80_operator_pencil_geometry.py
Scripts: v183_koide_f_corner_transfer.py
Location: tfpt_4_frontier
Original CSV, line 178Original ledger status
GATE.UWALL.06
TORSION NORMAL FORM + THE DELTA = 1/2 THEOREM (executes the GATE.UWALL.05 'genericity future work'; the distinguished lepton transport value delta = 1/2 stops being a point observation): (1) FLATNESS = mu4 TORSION [I, symbolic generic M] - prod_k U^k M U^{-k} = (MU)^4 exactly, so the Z4-family flatness constraint of the (U_wall) bundle IS the torsion statement 'T = MU is a fourth root of unity': the mu_4 atom appears as the ORDER of the twisted cusp generator. (2) DELTA = 1/2 THEOREM [I, both directions]: on the involutive branch (T^2 = 1) T is a Hermitian reflection 2vv^dag - 1 and the cusp trace condition 2v^dag U^{-1}v = 1 splits exactly into |v1|^2 = 1/2 (real part) + |v2| = |v3| (imaginary part), forcing diag M = (0, i/2, -i/2) with spec M = {1, w, w^2} AUTOMATIC (unitary + tr 0 + det 1 => char poly lam^3 - 1): delta = |M_22| = 1/2 EXACTLY AND CONSTANTLY on the whole 2-parameter branch - the value v20 used by hand and v40/v41 observed at the explicit point is a mu4-torsion identity. (3) REFLECTION LEMMA [I]: the D4 reflection forces diag M = (r, z, zbar) with r real and Re z = -r/2 - the D4 diagonal freedom is ONE real parameter, delta = 1/2 <=> r = 0. (4) BRANCH CENSUS [N, seeded scipy sampling, Python-only]: the full D4-fixed flat cusp locus realises only tr(MU) in {1, -1}; the involutive branch has diagonal CONSTANT (0, 1/2, 1/2) to 1e-15 across all samples; the {1, i, -i} branch has d1 varying over [0, 1] and the explicit v33/v40 point sits in its d1 = 0 slice - the same delta value. (5) RESIDUE [P] (recorded): whether the anchor splitting type O(-2)+O(-1)^2 (Mehta-Seshadri side) forces the d1 = 0 slice or selects the involutive branch is the remaining question; delta = 1/2 itself is no longer open
Recorded status: Identity [I] (symbolic theorems) + Numerical [N] (branch census) + Physical [P] (residue)
Dependencies, status detail and source
Canonical status: Theorem: delta = 1/2 is a mu4-torsion identity on the involutive branch; flatness = (MU)^4 = 1 normal form; residue = bundle-side branch selection
Dependencies: GATE.UWALL.04; GATE.UWALL.05; FLAV.DELTA.01; v20; v30; v33
Scripts: v114_torsion_delta.py
Location: tfpt_research_contracts
Original CSV, line 198Original 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)
Dependencies, status detail and source
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
FLAV.H2.03
THE ADDRESS TABLE (the open FLAV.H2.02 item structured; exact arithmetic on FROZEN v18/v20 integers): (1) THE LEPTON WORDS ARE THE COMPILER ATOMS [I]: (L_e, L_mu, L_tau) = (8, 5, 3) = (rank E8, g_car, N_fam) = (p0+e2, e2, p0), in mass order (longest word = lightest lepton). (2) ADDRESSES = EUCLIDEAN DIVISION BY THE HEXAGON [I]: (r, w) = L divmod p2 with p2 = 6 = |R+(A3)| itself an atom: e -> (2,1), mu -> (5,0), tau -> (3,0); sum r = 10 = p3 = A_Lambda; sum L = 16 = dim S+ = 2^{g-1}. (3) SHEET PARITY [I] (the FLAV.H2.02 dictionary applied): e sits on the untwisted sheet (omega in spec M0), mu and tau on the twisted sheet (-omega, -1 in spec(-M0)); the anchor lepton tau occupies the unique REAL twisted eigenvalue -1 - exactly the site where v20's product rule replaces the resolvent. (4) QUARK SUM RULES [I] (frozen v18 words u,d,s,c,b,t = 7,7,5,3,2,0): up-type sum = 10 = p3; down-type sum = 14 = p1 + p3; ALL QUARKS = 24 = |W(A3)| (the flavor-wall monodromy group order, GATE.UWALL.09); ALL NINE CHARGED FERMIONS = 40 = p1 p3 = a^T R a (ARCH.TRIAD.01 bonus checksum); quark sum r = 12 = 2 p2, sum w = 2 = |Z2|; the top sits at the vacuum site (0,0) (zero word length, no suppression - the established ladder anchor). (5) RESIDUE [P] (recorded): five independent closures (16, 10, 14, 24, 40 - all anchor atoms or today's group orders) constrain the address map, but the per-fermion assignment remains the v18/v20 input; deriving it is the remaining H2 content. FIREWALL: all integers were frozen before today's readings - no degrees of freedom spent
Recorded status: Identity [I] (exact arithmetic on frozen integers) + Physical [P] (per-fermion derivation)
Dependencies, status detail and source
Canonical status: Identity: lepton words = (rank g N); addresses = divmod hexagon; quark sums = (p3 p1+p3 |W(A3)| p1p3); assignment derivation open
Dependencies: FLAV.H2.02; GATE.UWALL.09; ARCH.TRIAD.01; v18 (quark words); v20 (lepton words)
Scripts: v120_address_table.py
Location: tfpt_research_contracts
Original CSV, line 204Original ledger status
FLAV.H2.04
THE ADDRESS TABLE IS PINNED (the FLAV.H2.03 per-fermion item closed at the information level; exact census theorem): (1) THE WORD TABLE IS THE RESIDUE OPERATOR [I]: the established identity L = R + 2U (FLAV.DIAMOND.02, U = winding axis N_fam 1 e_1^T) says the word-length table IS L[sector][generation] with rows (up; down; lepton) = ((7,3,0); (7,5,2); (8,5,3)) = the v18/v20 word lengths verbatim; the addresses are R's entries plus one hexagon turn for generation 1, and R's first column is THE ANCHOR a = (1,1,2) - the first-generation residues are the anchor components. (2) THE MARGINS ARE ATOMS [I]: row sums of R = (4, 8, 10) = (e1, rank E8, p3); column sums = (4, 13, 5) = (e1, Delta_Q, g_car); total 22 = 2x11 (ARCH.TRIAD.01). (3) PINNING THEOREM [I, exact census]: among ALL 3x3 matrices with entries in the hexagon {0..5}, exactly 17 have the atom margins, and exactly ONE has det = 8 = rank E8 - and it is R (the same one is the unique one with SNF (1,1,8); all 17 determinants are distinct, 8 occurs once - control computed explicitly). The per-fermion assignment table carries ZERO residual information beyond the atom margins and the rank determinant. (4) within-sector assignment = the established transport reading (m ~ lambda_Y^L, longer word = lighter fermion). (5) RESIDUE [P] (recorded): the open H2 item shrinks from 'derive 9 per-fermion integers' to 'derive the six atom margins + det = rank'. FIREWALL: R, L and all word lengths were frozen in v4/v18/v20/v71 long before today's census - no degrees of freedom spent
Recorded status: Identity [I] (exact census/uniqueness theorem on frozen operators) + Physical [P] (margins)
Dependencies, status detail and source
Canonical status: Theorem: R = unique hexagon matrix with atom margins + det 8; address table = R + first-generation winding; H2 residue = the margins
Dependencies: FLAV.H2.03; FLAV.DIAMOND.02 (L = R + 2U); FLAV.H2.01; ARCH.TRIAD.01; v18; v20; v71
Scripts: v121_address_pinning.py
Location: tfpt_research_contracts
Original CSV, line 205Original ledger status
SYNTH.INVENTORY.03
TERMINAL RESIDUAL INVENTORY (post premise-(A) closure; supersedes the CONTENTS of SYNTH.INVENTORY.02): after the (A)-chain (v160-v165) premise (A) is NO LONGER an independent structural class. (1) (A) CLOSED AS A CLASS - the four (A)-closure rows exist (GATE.METRIC.16 fixed-point theorem; .17 cone eliminated, cone gap = one-particle gap; .18 numbers forced by mu4-equivariance; .19 factors into A2 + GATE.QGEO + irreducible core). (2) THE FIVE v123 CLASSES COLLAPSE: R1 clock, R2 index-4 net and R5 Q-realisation all merge into ONE Tier-1 hinge (the seam=flavour=horizon identification = A2 net existence [assembly of established net constructions, GATE.METRIC.11/13] + GATE.QGEO [seam boundary = P^1 minus mu4; cohomology b1=N_fam=3, cusp grading = A3 exponents]); R3 (EH step) folds into v_geo (SEAM.EHMODEL.03/v152: the normalisation IS the anchor); R4' (selectors) was already discharged. (3) TERMINAL STRUCTURE: Tier 0 = the irreducible core {pi, v_geo}, a THEOREM by the No-Unit Theorem (ANCHOR.VGEO.01/02), nothing to close; Tier 1 = ONE hinge; Tier 2 = folded (EH -> v_geo, ambient QG -> G_net via GATE.METRIC.02/v76, gap-decoupled); Tier 3 = F_transfer, ONE functor with four typed CONDITIONAL interfaces (Koide FR.KOIDE.05/06, eta_B FR.ETAB.01, m_p/m_e QCD.LAMBDA.01 [ratio stays open/not forced], RG-stable lepton mixing FLAV.RGSTAB.01; axion = scenario), eta_B carrying the most open computational room. (4) COMPLETENESS: the structural residual is now ONE hinge + ONE transfer functor + the {pi, v_geo} core; a sixth independent structural class - or a new irreducible - would FAIL this script. HONEST: a unification + re-typing, NOT an unconditional proof
Recorded status: Identity [I] (machine bookkeeping + typing contract; ledger-row membership)
Dependencies, status detail and source
Canonical status: Terminal inventory: (A) no longer a class; ONE hinge (A2+GATE.QGEO) + F_transfer + irreducible {pi,v_geo}; Tier 2 folded; sixth class fails the script
Dependencies: SYNTH.INVENTORY.02; GATE.METRIC.16; GATE.METRIC.17; GATE.METRIC.18; GATE.METRIC.19; ANCHOR.VGEO.02; FR.ETAB.01
Scripts: v167_inventory_post_closure.py
Location: origin_theory
Original CSV, line 208Original ledger status
FLAV.RGSTAB.01
F_TRANSFER SCALE-TAGGING (the lepton-mixing predictions are RG-STABLE outputs; the quark mass-ratio readouts carry a scale tag): (1) the PMNS angles run only through the charged-lepton Y_e Y_e^+ eigenvalue gap y_tau^2 ~ 1.0e-4 [I] (the only mixing-ROTATING Yukawa term is (3/2) Y Y^+ Y, PyR@TE SM RGEs), so the one-loop running from the seam/scalaron scale (M_scal = c3^{7/2} Mbar ~ 3e13 GeV) down to M_Z is kappa_tau = y_tau^2/(16 pi^2) ln(M_scal/M_Z) ~ 1.8e-5; (2) hence |Delta sin^2 theta_ij| <~ 1e-4 (normal ordering / hierarchical => O(1) spectrum factor, no quasi-degenerate enhancement) is two-three orders below current precision (sin^2 th12 +-0.013, sin^2 th13 +-0.0007) => the seeds sin^2 th12 = 1/3 - phi0/2 = 0.3067 and sin^2 th13 = phi0 e^{-5/6} = 0.0231 are SCALE-INDEPENDENT F_transfer outputs (seam value = measured value) [I]; (3) the up-quark sector runs through y_t^2 ~ 0.9, kappa_t ~ 0.15 = O(10-15%), so the m_t/m_b ~ 41 readout carries a scale tag (EW/M_Z), unlike the lepton angles [I]; (4) F_transfer TYPING [P]: the lepton-mixing transfer is trivial (no scale ambiguity), the quark-mass transfer is a genuine running map -- both the PyR@TE-confirmed SM Yukawa betas. Python-only (y^2-suppression magnitude bound, not a precision PMNS evolution; ref Antusch et al. 2005)
Recorded status: Identity [I] (y^2-suppression bound) + [P] (F_transfer typing)
Dependencies, status detail and source
Canonical status: Identity [I]: lepton angles RG-stable (y_tau^2-suppressed), quark ratios scale-tagged; F_transfer lepton sector trivial
Dependencies: EM.BUDGET.02; CAR.SM.01; v16_solar_dual_anchor.py; v21_solar_product_quark.py
Scripts: v163_rg_stability_flavor.py
Location: tfpt_2
Original CSV, line 249Original ledger status
E8.CHAN.01
DEGREE/EXPONENT CHANNEL SPLIT (2026-06-16): 248=120+128 as a magnitude/phase channel typing (replaces the over-strong 'S^- is dark matter'). E8 exponents {1,7,11,13,17,19,23,29} sum=120=|R^+(E8)| (MAGNITUDE channel: positive roots/root transitions); E8 degrees {2,8,12,14,18,20,24,30} sum=128=2^(rank-1)=rank*dim S^+ (PHASE/GLUE channel); 248=120+128=adj(D8)+spinor(D8); sum(deg)-sum(exp)=rank=8. The (ratios,product) magnitude bijection (Target D) lives in the 120 channel, the un-covered CP phases in the 128 phase/glue channel; whether 128 hosts a dark sector is Frontier (NOT asserted). STRENGTHENED on the fiber (2026-07-29, T177/v561): the channel typing has an EXACT hexagonal realisation -- sum_k rho^{d_k} = 4 rho (arg = pi/3 exactly) and sum_k rho^{m_k} = 4 (arg = 0 exactly) on the CM unit rho = e^{i pi/3} -- with a parity typing forced by integer parity: all degrees are EVEN (phase channel SHEET-EVEN under rho -> rho^4), all exponents ODD (magnitude channel SHEET-ODD). CONSEQUENCE: the phase-channel angle is sheet-blind -- it carries pi/3 but cannot distinguish quark from lepton (not the CP.MU6.01 sheet split). Honest caveat: reality of the exponent sum alone is not hexagon-specific; only the degree half (= 4 rho) is. The channel typing stays [C].
Recorded status: Identity (exact)
Dependencies, status detail and source
Canonical status: [E] 248=120+128, exponents sum 120=|R^+(E8)|, degrees sum 128=rank*dim S^+; magnitude channel 120 / phase channel 128 [C]; dark-sector reading [O]; exact hexagonal realisation sum rho^{d_k}=4rho (arg pi/3, sheet-even) vs sum rho^{m_k}=4 (arg 0, sheet-odd) [E] -- the phase-channel angle is sheet-blind (T177/v561)
Dependencies: E8.CAS.01; FLAV.CP.01
Scripts: v227_degree_exponent_channel_split.py, v561_cp_channel_identities.py
Location: tfpt_5_redteam
Original CSV, line 309Original ledger status
LEP.FROB.01
LEPTON ETALE FROBENIUS ALGEBRA (2026-06-16): the three charged-lepton coefficients form a genuine commutative Frobenius algebra over the mu6 resolvent. Exact coefficients (c_e,c_mu,c_tau)=(16/7,4/3,7/6), ring closure c_e c_tau=8/3=|Z2| c_mu, product c_e c_mu c_tau=32/9=2^g_car/N_fam^2. A=Q[t]/(m), m=(t-c_e)(t-c_mu)(t-c_tau): the trace-form Gram G_ij=Tr(t^i t^j) is nondegenerate, det G=discriminant(m)!=0 (A etale/separable) -- a commutative Frobenius algebra with a nondegenerate trace pairing. The C6 shift has characteristic polynomial t^6-1 (spectrum mu6=mu3 family x mu2 sheet). PMNS extension: Aut(A) permutes {e,mu,tau} (real part), the hexagonal CM point j=0 supplies the phase part.
Recorded status: Identity (exact algebra) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] (16/7,4/3,7/6), ring closure c_e c_tau=8/3=|Z2|c_mu, product 32/9; etale Frobenius algebra (det Gram=disc(m)!=0); mu6=mu3 x mu2 spectrum; PMNS extension [C]
Dependencies: FLAV.LEPTON.01; ARCH.HEXRES.01; CP.MOD.01
Scripts: v229_lepton_frobenius_algebra.py
Location: tfpt_2_standard_model
Original CSV, line 315Original ledger status
CP.MU6.01
CP PHASES AS MU6 POWERS (2026-06-17): both CP phases are mu6 powers of ONE hexagonal CM unit, split by the sheet -- a structural reduction of red-team Target D, sharper than v220/v225 (which only located the residual). With rho=e^{i pi/3} the primitive 6th root (j=0 Eisenstein CM, CP.MOD.01): (1) rho^6=1, rho^3=-1 (the Z2 sheet half-turn); (2) delta_CKM leading = arg(rho^1)=pi/3 (quark, FLAV.CP.01), delta_PMNS = arg(rho^4)=4 pi/3 (lepton, the tfpt_2 neutrino phase lattice); (3) rho^4=-rho => delta_PMNS = delta_CKM,lead + pi = (CM unit) x (Z2 sheet) -- the two CP phases are ONE hexagonal unit on the two sheets, NOT two independent inputs; (4) the C6/mu6 monodromy U6 has charpoly t^6-1 (spectrum mu6 carries rho); (5) the dual-normal-frame orientation (DUAL.FRAME.01) is sheet-flipped: Im det(1,d,rho^1 n)=+21 sin(pi/3) (quark), Im det(1,d,rho^4 n)=-21 sin(pi/3) (lepton); (6) NEG: mu3 (cube roots) has no -1, so it cannot relate the two phases by a half-turn (mu6=mu3 family x mu2 sheet required). REDUCTION: removes one of Target D's two phase inputs (the lepton phase is the quark phase x the sheet); the quark seam correction 3 lambda_C^2 stays the v88 misalignment, the deck stays Z/4 (QGEO.KILL.01). Does NOT close Target D.
Recorded status: Identity (exact) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] delta_CKM,lead=arg(rho)=pi/3, delta_PMNS=arg(rho^4)=4pi/3, rho^4=-rho so the two CP phases = one hexagonal unit x the Z2 sheet; sheet-flipped Jarlskog orientations; reduces Target D's CP inputs from 2 to 1, physical derivation [C]
Dependencies: CP.MOD.01; DUAL.FRAME.01; FLAV.CP.01
Scripts: v231_cp_mu6_phases.py
Location: tfpt_5_redteam
Original CSV, line 317Original ledger status
CP.TRIALITY.01
CP = THE UNIVERSAL TRIALITY PHASE, SHEET-SPLIT (2026-06-17): one step past CP.MU6.01/v231 in the canonical mu6 = mu3 (family/triality) x mu2 (sheet) factorisation. (1) mu6=mu3 x mu2 (gcd(3,2)=1): the Z3 triality centre {1,omega,omega^2} = the cusp weights {0,1/3,2/3} x 2pi, the sheet is mu2={1,-1}; the hexagonal CM unit factors as rho = omega^2 * (-1). (2) SAME FAMILY CLASS: rho^4 = rho^1 * rho^3 with rho^3 in mu2, so the quark (rho^1) and lepton (rho^4) CP phases have the SAME image in the family quotient mu6/mu2 ~ mu3 (the same triality-centre element) and OPPOSITE sheet ((-1)^1 vs (-1)^4). (3) so the CP phase IS the universal triality phase omega^2 (the 2/3 cusp-weight Z3 centre), read on the two sheets -- NOT a free choice of mu6 power; the power choice from v231 is removed. (4) omega is the mu3 factor of the order-30 (2,3,5) Milnor/Coxeter monodromy that builds E8 (TOPO.E8.01/v232), so CP lives inside the same cycle as the hull. (5) NEG: mu2-only carries no triality, mu3-only carries no sheet; only the full mu6 gives one triality phase on two sheets. Reduces red-team Target D from 'one hexagonal unit + sheet' to 'the universal triality phase + sheet'; the physical CP derivation stays [C] (the quark seam correction 3 lambda_C^2 is the v88 misalignment).
Recorded status: Identity (exact) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] mu6=mu3 x mu2; quark rho^1 and lepton rho^4 share the family triality class omega^2 (the 2/3 cusp centre), opposite sheet; CP = universal triality phase + sheet, power choice removed; physical derivation [C]
Dependencies: CP.MU6.01; FLAV.CP.01; TOPO.E8.01
Scripts: v233_cp_triality_phase.py
Location: tfpt_5_redteam
Original CSV, line 319Original 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]
Dependencies, status detail and source
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]
Dependencies, status detail and source
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.DIRAC.02
FULL 96-DIM FINITE SPECTRAL TRIPLE BUILT + NCG AXIOMS VERIFIED (2026-06-17): advances CONTRACT.QFT4D.DIRAC.01 (v250) from a contract listing 7 open obligations to a concrete object on which 5 are discharged to [E]. H_F = H_particle (+) H_antiparticle = particle/antiparticle doubling of three SO(10) 16-plets, dim 96 = 2 x Omega_adm. One generation = nu_L,nu_R,e_L,e_R (colour singlets) + (u,d)x(L,R)x3 colours = 16. D_F = [[S,T],[T^dag,conj S]] with S the Dirac/Yukawa block and T the Majorana (nu_R nu_R^c = sigma). J = (particle<->antiparticle swap).conj; gamma = chirality (flipped on antiparticles). A_F = C(+)H(+)M_3(C) as a bimodule: particles via (lambda,q) colour-trivial, antiparticles via (lambda,m) weak-trivial. (1) [E] dim 96. (2) [E] D_F=D_F^dag and D_F gamma=-gamma D_F. (3) [E] reality J^2=+1, JD=DJ. (4) [E] gamma^2=1, [gamma,pi(a)]=0, J gamma=-gamma J. (5) [E] KO-dimension 6 mod 8 (Chamseddine-Connes-Marcolli). (6) [E] order-zero [pi(a),J pi(b) J^-1]=0 for the SM algebra. (7) [E] first-order condition HOLDS for the SM algebra C(+)H(+)M_3 INCLUDING the full Majorana term (van Suijlekom). (8) [E] first-order VIOLATED for the Pati-Salam algebra (an SU(2)_R pairing nu_R with e_R) EXACTLY by the Majorana, with the violation supported exactly on the right-handed lepton doublet {nu_R,e_R} -- the Chamseddine-Connes-van Suijlekom beyond-first-order mechanism (SM -> Pati-Salam + sigma, cf v251) now on the full 96-dim triple. (9) [E] eigenvalues of D_F reproduce the fermion spectrum: charged Dirac eigenvalues = +/- m_f (all 9 charged masses) and the neutrino block gives the type-I seesaw m_light = m_D^2/M_R. (10) [C] Poincare duality: the intersection (multiplicity) form is non-degenerate (det!=0). (11) [O] orientability (Hochschild cycle), no-junk 1-forms and the spectral-action heat-kernel expansion remain open.
Recorded status: Numerical (NCG axioms) [E]/[C]/[O]
Dependencies, status detail and source
Canonical status: [E] dim 96 + Hermitian/odd + reality J + grading + KO-6 + order-zero + first-order holds(SM)/violated(PS, localized to nu_R,e_R) + spectrum=masses+seesaw; [C] Poincare duality; [O] orientability + no-junk + spectral action; discharges 5 of the 7 v250 obligations to [E]
Dependencies: CONTRACT.QFT4D.DIRAC.01; PS.DIRAC.01; PS.ALGEBRA.01
Scripts: v252_full_finite_triple.py
Location: tfpt_research_contracts
Original CSV, line 338Original ledger status
PS.NCG.FLUCT.01
INNER FLUCTUATIONS Omega^1_D -> SM HIGGS DOUBLET (no 126, no junk) + sigma (2026-06-17): closes the open obligation v250 #5 (Higgs content, NOT 126), the NO-JUNK obligation, and fixes the sigma quantum numbers (v250 #4 rep-theory half). Inner fluctuation D -> D + A + eps' J A J^-1 with A = sum pi(a)[D_F,pi(b)] in Omega^1_D = span{pi(a)[D_F,pi(b)]}. Because D_F is purely chirality-odd (Yukawa L<->R + Majorana), every 1-form is odd, so the FINITE fluctuations are SCALARS (gauge bosons come from the continuum [D_M,a]). (1) [E] Omega^1_{D_F} purely chirality-odd, gauge part 0. (2) [E] NO JUNK / NO 126: for the SM algebra C(+)H(+)M_3 every 1-form has support exactly inside the Higgs-doublet pattern (chirality-odd, colour-diagonal, no quark<->lepton mixing) = the single SM Higgs doublet (1,2)_{1/2}; no colour/weak triplet, no (10,1,3)/126-type scalar (0 junk entries, machine-checked). (3) [E] sigma NEEDS BEYOND FIRST ORDER: with the SM algebra the sigma (nu_R nu_R^c Majorana) direction is NOT generated by Omega^1_D (consistent with first order HOLDING, v252) but with the Pati-Salam algebra it IS generated -- sigma is precisely the Chamseddine-Connes-van Suijlekom beyond-first-order scalar (v251/v252). (4) [E] sigma quantum numbers: SM singlet (1,1,0) with B-L=2 (nu_R has B-L=-1, so sigma*(nu_R nu_R) is gauge invariant only for B-L(sigma)=+2), giving the nu_R Majorana mass and breaking B-L (the PS (4,1,2)->SM step). (5) [C] sigma=scalaron: sigma is a real SM-singlet scalar at the B-L/PS scale, consistent in quantum numbers and scale with the R+R^2 scalaron (M_PS=kappa M_s, v249/v253); the gravitational coupling proper remains [C]/[O].
Recorded status: Numerical (NCG inner fluctuations) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] finite fluctuations = SM Higgs doublet (no junk/no 126) + sigma beyond first order + sigma B-L=2 singlet; [C] sigma=scalaron; closes v250 #5 + no-junk obligation + sigma QN
Dependencies: PS.DIRAC.02; PS.DIRAC.01
Scripts: v254_inner_fluctuations.py
Location: tfpt_research_contracts
Original CSV, line 340Original ledger status
FLAV.PMNS.03
COMPLETE COMPLEX PMNS MATRIX + LEPTONIC JARLSKOG J_PMNS (CP STRENGTH) (2026-06-18): the four TFPT channels (sin^2 th12 = 1/3 - phi0/2 v9/v263, sin^2 th23 = 1/2 v9/v263, sin^2 th13 = phi0 e^{-5/6} v16/v268, delta = 4 pi/3 = 240 deg v231/v233) assemble into one exactly-unitary complex PMNS matrix U = R23 U13(delta) R12, from which the Jarlskog CP strength J_PMNS = Im(U_e1 U_mu2 U*_e2 U*_mu1) = s12 c12 s23 c23 s13 c13^2 sin(delta) = -0.02965 (J_max = 0.03424) is a DERIVED number (the leptonic analogue of the CKM J, v88). Data: J_max vs NuFIT 5.2 J_max 0.0332 (~3%), J vs best fit -0.026 (delta_data ~232 deg within ~1 sigma), the negative CP-violating sign reproduced. Closes the CP-STRENGTH readout; delta itself is the mu6/triality phase (assembled, not from M_nu/D_F) and the absolute neutrino-mass scale (Sigma m_nu, M_R) stays open.
Recorded status: Readout [C] (CP strength); [O] phase origin + absolute scale
Dependencies, status detail and source
Canonical status: [E] the three angle channels + the exact unitary assembly; [C] the derived Jarlskog CP strength + its NuFIT confrontation; [O] the phase's operator origin (delta = mu6/triality, not M_nu) + the absolute scale. A PMNS assembly + CP-strength readout, not a full operator closure.
Dependencies: FLAV.TH12.01; FLAV.PMNS.02; FLAV.TH13.01; CP.MU6.01; CP.TRIALITY.01
Scripts: v270_pmns_jarlskog_assembly.py
Location: tfpt_2_standard_model
Original CSV, line 363Original ledger status
PRED.LIVE.01
LIVE KILL-TEST SCORECARD OF THE RECENT ROUND'S COMPUTABLE PREDICTIONS (2026-06-18): a data-confrontation consolidation (confronts, does not add physics), each row tagged with the decisive near-term experiment. [N] PMNS angles: sin^2 th12=1/3-phi0/2=0.30675 vs NuFIT 0.303(12) [+0.31 sigma]; sin^2 th13=phi0 e^{-5/6}=0.02311 vs 0.02225(59) [+1.45 sigma]; sin^2 th23=0.5 maximal (octant-ambiguous) -- decisive JUNO/Daya-Bay/DUNE. [C] leptonic CP: J_PMNS=-0.0297 (J_max 0.0342 vs NuFIT 0.0332 ~3%), delta=240 vs NuFIT ~232(30) -- decisive DUNE/Hyper-K. [X] Sigma m_nu NO floor=0.0586 eV vs Planck+BAO<0.12, DESI~<0.072 (consistent at the edge; Sigma<0.0586 excludes the NO m1~0 spectrum) -- decisive DESI/CMB-S4. [X] proton decay tau_p(p->e+pi0)=1.55e35 yr for the E8-allowed +(15,1,1) content vs Super-K>2.4e34 (safe); minimal 16-Higgs 4.4e33 EXCLUDED -- decisive Hyper-Kamiokande (reach ~1.4e35). [N] closed readouts alpha^-1=137.0359992 (1.9 sigma known offset), Omega_b=(1-1/4pi)phi0=0.04894, birefringence beta=phi0/(4pi)=0.2424 deg -- decisive CMB birefringence. [N] all confronted rows consistent < 2 sigma; 2 sharp near-term kill tests (Sigma m_nu floor, proton decay).
Recorded status: Data confrontation [N]/[C] + [X] (two near-term kill tests)
Dependencies, status detail and source
Canonical status: [N]/[C] data confrontation (pulls vs current bounds) + [X] the two sharp near-term kill tests. A consolidation/scorecard, not new physics.
Dependencies: FLAV.TH13.01; FLAV.PMNS.03; FLAV.NUSCALE.01; PS.PROTON.02; EM.FP.01
Scripts: v283_live_killtest_scorecard.py
Location: tfpt_4_frontier
Original CSV, line 378Original ledger status
SEED.LEPTONMASS.01
SIXTH SEED CHANNEL, NEW MEASUREMENT SECTOR (2026-07-01, v466): the charged-lepton mass ratio m_e/m_mu=(12/7)phi0^2 is a sixth independent readout of the ONE axiom seed phi0=1/(6pi)+48 c3^4, extending the empirical over-determination (SEED.CROSSVAL.01/v306, SEED.CROSSSECTOR.01/v465) from three measurement sectors to five. [E] plumbing: axiom phi0 reproduces the frozen m_e/m_mu=(12/7)phi0^2=0.00484673 to 1e-9. [N] NEW SECTOR: back-solving phi0 from the measured POLE ratio m_e/m_mu=0.004836 (PDG 2024) gives phi0=0.053113, only -0.11% from the axiom -- a charged-lepton MASS reading (Penning-trap masses), a 4th measurement sector beyond {neutrino mix, CMB, quark mix}. [C] TRANSPORT: the formula is the SOURCE ratio, the datum the POLE ratio; the source->pole shift is the seam-gapped class (bound (2/3)^6=8.78%, CORRECTIONS.NUMERIC.01/v393) but largely cancels for m_e/m_mu, so the 0.11% residual sits far inside the band -- a CONSISTENT new sector, not a sharper pin. [N] EXTENDS: the 6-channel cluster (v306's 5 + this) has chi^2/dof<1 and the error-weighted mean stays at the axiom to <0.1%; with the corroborating heavy-quark m_t/m_b (-0.23%) it is a 7-channel, FIVE-sector agreement. [N] NEG/POWER: a data<->formula shuffle explodes the cluster chi^2 by >100x; m_c/m_s=(34/47)/phi0 is scheme-ambiguous (FLAG 11-14), a WEAK channel deliberately not counted. [C] HONEST: still the ONE seed (WITNESS.ECON.01/v305 multiplicity 1) -- an EMPIRICAL strengthening, NOT theoretical independence; phi0 is FIXED by the axioms, so it upgrades NO prediction and closes NO gate.
Recorded status: Numerical [N]/[C] (new-sector seed consistency statistic; source->pole transport-conditional)
Dependencies, status detail and source
Canonical status: [N] the charged-lepton m_e/m_mu back-solve to the axiom seed (-0.11%) + the 6/7-channel chi^2/dof<1 five-sector cluster + the shuffle power control; [C] the source->pole transport band and the one-seed honesty. A consistency statistic; does NOT upgrade any prediction or close any gate.
Dependencies: SEED.CROSSVAL.01; SEED.CROSSSECTOR.01; REG.FREEZE.01; CORRECTIONS.NUMERIC.01
Scripts: v466_seed_leptonmass_channel.py
Location: tfpt_5_redteam
Original CSV, line 404Original ledger status
GALOIS.CP.PREDICT.01
A NEW FALSIFIABLE PREDICTION FROM THE GALOIS STRUCTURE: THE TWO CP PHASES ARE LOCKED, delta_PMNS = delta_CKM,lead + pi (2026-06-22, the v316 follow-up turned testable). [E] ONE UNIT TWO POWERS: both CP phases are powers of one hexagonal unit rho=zeta_6 in the family Galois factor (v316): delta_CKM,lead=arg(rho)=pi/3 (60 deg), delta_PMNS=arg(rho^4)=4pi/3 (240 deg), rho^4=-rho. [E] FORCED RELATION: delta_PMNS-delta_CKM,lead=pi exactly (the Z2 sheet flip rho^3=-1), equivalently delta_PMNS=4*delta_CKM,lead -- the quark and lepton leading CP phases are NOT independent (one is fixed by the other). [C] PREDICTION OF RECORD: delta_PMNS,lead=240 deg, forced from delta_CKM,lead=60 deg + the sheet flip (180 deg) -- upgrades delta_PMNS from an assigned texture to a Galois-forced relation to the measured quark phase. [N] CURRENTLY COMPATIBLE: 240 deg lies within the broad current global-fit range for the PMNS Dirac phase (NuFIT 6.0, normal ordering); decisive test = DUNE/Hyper-K/JUNO. [X] KILL TEST: a measured delta_PMNS robustly incompatible with delta_CKM,lead+pi=240 deg (beyond the sub-leading budget, at >3 sigma) falsifies the Galois-CP organization (v316/v317). A genuine NEW falsifiable cross-prediction from the v313-v319 arithmetic arc; the leading-order/holonomy reading is [C] like delta_CKM, the relation itself [E], the kill test [X]; does NOT derive the magnitudes.
Recorded status: Identity [E] (Galois relation) + [C] (prediction) + [X] (kill test)
Dependencies, status detail and source
Canonical status: [E] the exact Galois relation delta_PMNS=delta_CKM,lead+pi (rho^4=-rho, both powers of zeta_6) + the non-triviality; [C] the leading-order prediction delta_PMNS,lead=240 deg; [N] current compatibility; [X] the pre-registered kill test (DUNE/Hyper-K/JUNO). A NEW falsifiable cross-prediction from the Galois arc; does NOT derive magnitudes and does NOT upgrade the CP-phase typing beyond the relation.
Dependencies: GALOIS.READOUT.01; ARITH.CAPSTONE.01; v316; v231; v233
Scripts: v320_galois_cp_relation.py
Location: origin_theory
Original CSV, line 418Original ledger status
GALOIS.CP.SHARPEN.01
THE v320 CP-LOCK PREDICTION SHARPENED INTO A QUANTITATIVE PRE-REGISTERED KILL TEST (2026-06-22). [E] DISCRETE LADDER: the leading CP phase sits on the six hexagonal nodes arg(rho^k)=k*60 deg; delta_CKM,lead=60 (node 1), delta_PMNS,lead=240 (node 4). [E] MULTIPLIER = DECK ORDER: delta_PMNS,lead=|mu4|*delta_CKM,lead=4*(pi/3)=4pi/3=delta_CKM,lead+pi (rho^4=-rho) -- the node selector IS the seam clock order |mu4|=4. [C] SUB-LEADING BUDGET: delta_CKM,full=pi/3+3 lambda^2 (~68.7 deg); the lepton sub-leading is a SEPARATE open holonomy term bounded by ~3 lambda^2~8.7 deg => band 240 +- ~9 deg. [N] CURRENT TENSION: vs NuFIT 6.0 NO (delta_CP=212 +26/-41 deg) the leading 240 deg sits at +1.08 sigma, band lower edge ~231 deg at +0.74 sigma -- compatible today. [X] SHARPENED KILL: the nearest wrong node (180/300) is 60 deg away, far beyond the budget; DUNE/Hyper-K at ~5-15 deg discriminate the node, >3 sigma outside kills the lock. [E] DISCRIMINATION POWER: an anarchic delta_CP hits the band with p~5% and node 4 (not 1/3/5) 1-in-6. Sharpens v320; no magnitudes derived.
Recorded status: Identity [E] (node+multiplier) + [C] (budget) + [N] (tension) + [X] (kill test)
Dependencies, status detail and source
Canonical status: [E] the discrete hexagonal node + the |mu4| multiplier + the discrimination geometry; [C] the sub-leading budget (the lepton holonomy term is only bounded by the quark analog, not closed); [N] the +1.08 sigma current tension; [X] the sharpened pre-registered kill test (node discrimination). Sharpens v320; does NOT derive magnitudes or upgrade the CP typing.
Dependencies: GALOIS.CP.PREDICT.01; GALOIS.READOUT.01; v320; v316
Scripts: v322_cp_lock_sharpened.py
Location: origin_theory
Original CSV, line 420