Original ledger status
CMNORM.DUAL.01
CM-NORM DUALITY (2026-06-16): the two exceptional CM moduli give two central TFPT integers as ideal NORMS. SQUARE seam (Gaussian Z[i], j=1728): N(g_car+i|mu4|)=5^2+4^2=41=10 b1 -- the EM index IS the Gaussian norm of the carrier-glue vector; N(3+2i)=13=Delta_Q. HEX partner (Eisenstein Z[omega], j=0): N(3+2 omega)=3^2-3*2+2^2=7=scalaron exponent. The (3,2)=(colour,weak) split generates (5,6,7,13)=(g_car,|R^+(A3)|,scalaron,Delta_Q) by sum/product/Eisenstein-norm/Gauss-norm; rings rigid (Eisenstein of (5,4)=21!=41, Gauss of (3,2)=13!=7).
Recorded status: Identity (exact ring arithmetic)
Dependencies, status detail and source
Canonical status: [E] 41=N_Zi(5,4)=10 b1, 13=N_Zi(3,2)=Delta_Q, 7=N_Zomega(3,2)=scalaron; (3,2)->(5,6,7,13); the square<->EM, hex<->scalaron architecture bridge [C]
Dependencies: ANCHOR.GEN.01; EM.B1.01; SEAM.KHALF.01
Scripts: v222_cm_norm_duality.py
Location: origin_theory
Original CSV, line 307Original ledger status
COX.CLOCK.01
COXETER TOTATIVE CLOCK (2026-06-16): the mu4 clock is the order-4 character of the E8 Coxeter cycle. (Z/30)^x={1,7,11,13,17,19,23,29}=the E8 exponents=live Coxeter phases; phi(30)=8=rank E8, 30=|Z2|*N_fam*g_car=2*3*5. (Z/30)^x ~ Z/4 x Z/2, order-4 generator 7 (7^2=19,7^4=1 mod 30): a literal mu4 clock <7>={1,7,13,19} on the exponents; conjugate pairs m+(30-m)=30 give |mu4|=4 invariant 2-planes the clock permutes. Only E8 has phi(h)=rank AND h=2*3*5. Complements MCKAY.E8.01 (McKay gives (2,3,5) from the finite group, this gives mu4 from the Coxeter cycle).
Recorded status: Identity (exact)
Dependencies, status detail and source
Canonical status: [E] (Z/30)^x = E8 exponents, order-4 element 7 = mu4 clock on the exponents, 4 invariant planes; seam-clock identification [C]
Dependencies: SEAM.COX.01; AX.P2.01
Scripts: v223_coxeter_totative_clock.py
Location: origin_theory
Original CSV, line 308Original 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
QGEO.RR.01
RIEMANN-ROCH INDEX GATE (2026-06-16): P2 as the mode space of a degree-4 seam divisor (bedrock LANGUAGE for P2, NOT a proof from nothing). deg D=4=|mu4| on P^1 => h0(O(D))=deg+1=5=g_car (Riemann-Roch, genus 0); rank H1(P^1 minus 4 marks)=4-1=3=N_fam; h0+rank H1=8=rank E8, h0-rank H1=2=|Z2|, (h0+rank H1)/2=4=|mu4|; Lambda^even(C^5)=1+10+5=16=dim S^+ (the D5 half-spinor, ARCH.RRCAR.02). Negative controls: deg 3->(4,2), deg 5->(6,4), colliding marks lower H1 and break N_fam. Relocates P2 from '5 slots' to 'the genus-0 mode count of a 4-mark divisor', conditional on the raw seam producing the degree-4 divisor (=QGEO.SYM.01).
Recorded status: Identity (exact index) [E]/[C]/[O]
Dependencies, status detail and source
Canonical status: [E] deg-4 divisor => (h0,rankH1)=(5,3)=(g_car,N_fam), sum 8=rank E8, even Clifford 16=dim S^+; mode-space reading [C], the seam->divisor step [O] (=QGEO.SYM.01)
Dependencies: ARCH.RR.01; ARCH.RRCAR.02; QGEO.SYM.01
Scripts: v228_rr_index_gate.py
Location: origin_theory
Original CSV, line 310Original ledger status
QEC.SEAM.01
SEAM FINITE RECOVERABILITY CODE (2026-06-16): the seam as a finite quantum-error-correction-style code with recovery rate (2/3)^6=64/729. Code dimension = dim S^+ = 16 = 2^(g_car-1); the gapped boundary transport T on the cusp-weight 3-space (deviation directions (1,-1,0) and the Nariai anchor (1,1,-2)) is symmetric, doubly stochastic (CPTP), with spectrum {1,(2/3)^6,(1/3)^6}; on the trace-zero deviation subspace ||T delta|| <= (2/3)^6 ||delta||, hence ||T^n delta|| <= (2/3)^{6n} ||delta|| (a Knill-Laflamme-type per-step recovery bound). A free ratio r != (2/3)^6 gives r^n (rate not generic); breaking mu4-equivariance destroys it. 'Finite recoverability code' FIRST, 'holographic code' SECOND.
Recorded status: Numerical (contraction bound) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] code dim 16, transport spectrum {1,(2/3)^6,(1/3)^6}, recovery bound ||T^n delta||<=(2/3)^{6n}||delta||; holographic/Petz reading [C] gated on the Seam-Horizon theorem
Dependencies: SEAM.ATTRACT.01; SEAM.TRANSFER.01; HOR.PAGE.01
Scripts: v221_seam_qecc.py
Location: origin_theory
Original CSV, line 311Original ledger status
CP.MOD.01
CP HEXAGONAL MODULUS (2026-06-16): CP lives in the HEXAGONAL phase fiber, not the square seam deck (a geometric sharpening of red-team Target D, the magnitude bijection misses the CP phases). The seam deck is the SQUARE modulus j(i)=1728, automorphism Z/4 (the mu4 clock); its exceptional partner is the HEX modulus j(rho)=0, rho=e^{i pi/3}, automorphism Z/6, CM by Z[omega], arg(rho)=pi/3. The frozen leading CKM reading delta=pi/3+3 lambda_C^2=68.654 deg (FLAV.CP.01, registry untouched) has leading term pi/3=arg(rho); the |Z2| alternative pi/3+2 lambda_C^2 is the frozen look-elsewhere trap. CRITICAL: the seam deck stays Z/4 (QGEO.KILL.01); CP is the Z/6 phase fiber OVER it. SCOPED (2026-07-29, T177/v561): the [C] is relative to a declared branch -- the invariant part of the reading is the leading term arg(rho) = pi/3; the full delta = pi/3 + 3 lambda_C^2 is a branch/frame-relative quantity (it has NO character under the parity/sector involution: a CP-even correction added to a CP-odd angle). The frozen reading itself is untouched (REG.FREEZE.01).
Recorded status: Identity/Numerical (modular) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] j(i)=1728 (Z/4) vs j(rho)=0 (Z/6, arg=pi/3); delta=pi/3+3 lam^2 leading term = the hex CM phase; deck stays Z/4, CP is the Z/6 fiber [C]. NOT a CP derivation; scope narrowed: the invariant part is the leading term pi/3, the full delta is branch/frame-relative (T177/v561)
Dependencies: FLAV.CP.01; QGEO.PILLOW.01; QGEO.KILL.01
Scripts: v220_cp_hexagonal_modulus.py, v561_cp_channel_identities.py
Location: tfpt_5_redteam
Original CSV, line 312Original ledger status
DUAL.FRAME.01
DUAL NORMAL FRAME (2026-06-16): the pair (d,n) is one canonical boundary compass for flavor and horizon, with CP as orientation. d=a^T R^{-1}=a^T L^{-1}=(-1/2,-1/2,1)=-1/2 (1,1,-2) (frame-independent; the Nariai/horizon normal; d.1=0, d.a=1); n=(5,-9,6) with n^T R=(det R,0,0)=(8,0,0), n^T L=(det L,0,0)=(20,0,0) (n annihilates the stable columns 2,3 -- the first-generation/torsion selector). Oriented volume det(1,d,n)=21=N_fam*scalaron=3*7. CP AS ORIENTATION: Im det(1,d,rho n)=21 sin(pi/3) for rho=e^{i pi/3} (the hexagonal CM unit) -- exactly where the magnitude bijection (Target D) fails. NARROWED, sharply (2026-07-29, T177/v561): the CP orientation READING is homogeneous of degree +1 in the frame normalisation, so the NUMBER 21 sin(pi/3) is frame data, not an invariant; dividing by the oriented volume removes the frame IDENTICALLY (Im(rho det)/det = Im rho exactly), so the invariant core is the FIBER datum Im(rho) = sin(pi/3) and the SIGN is a declared orientation. The raw functional is deck-invariant only because orientation reversal cancels fiber conjugation -- the deck cannot detect the CP sign.
Recorded status: Identity (exact) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] d=(-1/2,-1/2,1)=-1/2 Nariai, n=(5,-9,6) reads det on the first-gen column, det(1,d,n)=21=3*7; CP orientation READING Im det(1,d,rho n)=21 sin(pi/3) [C], narrowed: degree +1 in the frame normalisation (21 sin(pi/3) is frame data), invariant core = the fiber datum Im rho = sin(pi/3), sign a declared orientation (T177/v561)
Dependencies: HOR.DUALANCHOR.01; FLAV.SELECTOR.01; CP.MOD.01
Scripts: v225_dual_normal_frame.py, v561_cp_channel_identities.py
Location: tfpt_5_redteam
Original CSV, line 313Original ledger status
FTR.PATH.01
DIAMOND F_TRANSFER PATH (2026-06-16): F_transfer is ONE path on the Sheet Diamond, not four external interfaces. Family M(s,t)=R+Q diag(s,t,t): the transfer corners K=M(1,-1), C=M(1,0), F=M(1,1) lie on the SHEET axis (s=1). The sheet axis is CURVED det M(1,t)=4t^2+14t+14 (dets (K,C,F)=(4,14,32), 2nd diff 8=rank E8), the winding axis det M(s,0)=6s+8 is FLAT (slope 6=|R^+(A3)|); the Plucker ladder Pl(C)-Pl(K)=(1,8,10)=(N_Phi,rank E8,A_Lambda), Pl(F)-Pl(C)=(1,8,16)=(N_Phi,rank E8,dim S^+) (DIAMOND.PLUCKER.01). F_transfer = the K->C->F sheet geodesic, the Koide source->pole its 1-D Moebius projection; the external solver evaluates continuously ALONG the known discrete path. The diagonal cut t=s mixes the axes (negative control).
Recorded status: Identity (exact) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] M(s,t)=R+Q diag(s,t,t), K/C/F on the sheet axis, curved (2nd diff 8) vs flat winding (slope 6), Plucker steps (1,8,10),(1,8,16); F_transfer = the sheet geodesic, Koide its 1-D projection [C]
Dependencies: DIAMOND.PLUCKER.01; DIAMOND.AXIS.01; CONTRACT.F.01
Scripts: v224_diamond_ftransfer_path.py
Location: tfpt_2_standard_model
Original CSV, line 314Original 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
CENTER.NORM.01
CENTER BUDGET NORMS (2026-06-16): the Sheet-Diamond center budget (7,11,13) is the three LOCAL NORMS of the theory. C=R+Q diag(1,0,0), row sums (7,11,13): 7=N_Z[omega](3+2 omega) (Eisenstein/hexagonal CM norm = scalaron exponent), 13=N_Z[i](3+2 i) (Gaussian/square CM norm = Delta_Q), 11=C(4,0)+C(4,1)+C(4,2)=1+4+6 (QBL boundary Fock count on the |mu4|=4 corners = dim S^+ - g_car = 16-5). So C = (hex norm, boundary Fock count, square norm): the two CM rings (CMNORM.DUAL.01) and the seam boundary count meet in one operator center; the ring assignment is rigid.
Recorded status: Identity (exact) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] C row sums (7,11,13)=(hex norm, QBL Fock count, square norm)=(N_omega(3,2), 1+4+6, N_i(3,2)); the center collects the three local norms [C]
Dependencies: CMNORM.DUAL.01; DIAMOND.AXIS.01; ARCH.QBL.01
Scripts: v230_center_budget_norms.py
Location: tfpt_2_standard_model
Original CSV, line 316Original 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
TOPO.E8.01
THE SEAM AS THE E8 KLEINIAN SINGULARITY (2026-06-17): a canonical algebraic-geometric MODEL for the open seam-realisation premise QGEO.REALIZE.01, the du Val side of the McKay correspondence (MCKAY.E8.01/v219). (1) the McKay graph of 2I is affine E8 (9 nodes); dropping the unique trivial-rep node (the single Kac mark=1) leaves the FINITE E8 Dynkin on 8 nodes = the dual intersection graph of the 8 exceptional P^1's of the minimal resolution of C^2/2I (one trivalent node, arms of lengths 1,2,4). (2) the number of exceptional P^1's = 8 = rank E8 = g_car+N_fam = #nontrivial 2I irreps (9-1) -- a fourth reading of the '8' in c3=1/(8 pi). (3) the negated resolution intersection form is the E8 Cartan: even (each P^1 a (-2)-curve), unimodular det=1, positive definite -- the seam P^1's carry the E8 lattice as their intersection form. (4) 2I has exactly ONE degree-1 irrep (unique mark=1), so 2I is perfect (abelianisation trivial), hence H_1(S^3/2I)=0: the link is the Poincare homology 3-sphere, pi_1=2I order 120=|R^+(E8)|. (5) SEAM READING: the raw RP seam (a P^1 with marks) is canonically a component of this exceptional P^1-locus, so QGEO.REALIZE.01 gets an algebraic-geometric model (the seam P^1's ARE the E8 du Val curves) rather than a free postulate. Does NOT derive P2: it presupposes E8 (backward), so the carrier<->seam identification stays the open premise.
Recorded status: Lattice/Topology (exact) [E]/[C]
Dependencies, status detail and source
Canonical status: [E] McKay(2I)=affine E8; finite E8 = 8 exceptional P^1's intersection graph (det 1 Cartan); 2I perfect => link is the Poincare homology sphere pi1=2I order 120; [C] the seam is a du Val exceptional curve (model for QGEO.REALIZE.01, presupposes E8, bedrock [O])
Dependencies: MCKAY.E8.01; QGEO.SYM.01; E8.GLU.01
Scripts: v232_e8_kleinian_seam.py
Location: origin_theory
Original CSV, line 318Original 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
GATE.HOLO.01
SEAM-HOLOMORPHY SELECTION CERTIFICATE (2026-06-17): the entire structural residual of TFPT is ONE condition with THREE provably-equivalent faces, all forcing E8 -- so P2/G_net/Target A/QGEO are ONE gate, not four. THE CONDITION: 'the seam carries no nontrivial abelian sector.' Faces: (i) AQFT -- the boundary chiral net is HOLOMORPHIC (mu-index 1, single vacuum sector; Target A, v83/v154); (ii) geometry -- the seam link is a HOMOLOGY 3-sphere <=> the binary group Gamma is PERFECT <=> Gamma=2I (v232); (iii) rep theory -- exactly ONE 1-dim irrep (v219). All three are the SAME number: #(1-dim irreps)=|Gamma^ab|=|H_1(S^3/Gamma)|=#(mark-1 affine-Dynkin nodes), which equals 1 ONLY for affine E8 (A_n->n+1, D_n->4, E6->3, E7->2, E8->1). So 2I is the unique nontrivial perfect finite SU(2) subgroup and the Poincare sphere is the unique homology-sphere spherical space form. And holomorphic c=8=g_car+N_fam => the unique even unimodular rank-8 lattice = E8 (Gram even, det 1). THE CLOSING THEOREM (stated, NOT proved): RP + gap + chirality => quasi-free bulk (v160 fixed-point) => invertible bulk => holomorphic boundary net (no abelian sector) => E8; the single residual analytic step is 'free bulk => holomorphic boundary', after which P2/QGEO/G_net all follow. This certifies that the three faces coincide and force E8; it does NOT prove the analytic step.
Recorded status: Lattice/AQFT selection (exact) [E]/[O]
Dependencies, status detail and source
Canonical status: [E] #mark-1 = |Gamma^ab| = |H1(link)|; only E8->1 (2I unique perfect, Poincare unique homology sphere); holomorphic c=8 unique E8; the three faces (holomorphy/homology-sphere/one-1dim-irrep) are one E8-selector => Target A/G_net/P2/QGEO are ONE gate; closing theorem 'free bulk => holomorphic boundary' stated [O]
Dependencies: E8.GLU.01; MCKAY.E8.01; TOPO.E8.01; GATE.METRIC.06
Scripts: v234_seam_holomorphy_selection.py
Location: tfpt_research_contracts
Original CSV, line 320Original ledger status
GATE.HOLO.02
SEAM CHERN-SIMONS REALISATION (2026-06-17): the closing step of GATE.HOLO.01 realised in standard abelian Chern-Simons / quantum-Hall language, where 'holomorphic <=> det K = 1' is a THEOREM -- a genuine reduction of the analytic step into anyon condensation, NOT a closure. A free gapped BOSONIC 2+1d bulk = an even integer K-matrix; #anyons (torus degeneracy) = |det K|, edge chiral central charge c = signature(K), and the edge chiral net is holomorphic (single sector) <=> |det K| = 1. So the v234 condition 'no nontrivial abelian sector' = exactly |det K| = 1. The TFPT extension tower (v92/GATE.METRIC.07) IS the anyon-condensation tower read by determinant: carrier D5(+)A3 (even, det 16, c=8, 16 anyons, mu=16) -> SO(16)_1=D8 (det 4, 4 anyons, mu=4) -> (E8)_1 (det 1, 1 anyon, mu=1, HOLOMORPHIC); all rank 8 with c = signature = 8 = g_car+N_fam. Holomorphic <=> det 1 <=> E8 = the unique even unimodular rank-8 K-matrix = the Kitaev E8 quantum-Hall state (edge (E8)_1). CONDENSATION: a Lagrangian (maximal isotropic) glue of order sqrt(16)=|mu4|=4 takes det 16->16/4^2=1 (carrier->E8); an order-2 isotropic only ->16/2^2=4 (D8). So 'holomorphic' = 'condense the order-|mu4| Lagrangian glue', not a partial. NEG: D8 (det 4) is free+bosonic yet has 4 anyons (not holomorphic, the SO(16)_1 rival); an odd-diagonal K is fermionic (spin-CS) -- 'free+bosonic' does NOT imply holomorphic, det=1 is the extra physical condition. RESIDUAL [O]: the closing step = 'the free RP gapped seam condenses the order-|mu4| Lagrangian glue (det->1), not a partial isotropic (det->4)' -- the same sheet/mu4 selection as GATE.QGEO, now with holomorphy<=>det1 a theorem and the residual a single integer condition.
Recorded status: Lattice/CS realisation (exact) [E]/[O]
Dependencies, status detail and source
Canonical status: [E] free gapped bosonic bulk = K-matrix; #anyons=|det K|, c=signature, holomorphic<=>det 1; the v92 tower D5(+)A3(16)->D8(4)->E8(1) is the condensation tower; holomorphic=E8=Kitaev E8 state; residual = 'condense the |mu4| Lagrangian glue' = the sheet/QGEO selection [O]
Dependencies: GATE.HOLO.01; GATE.METRIC.07; TOPO.E8.01; QGEO.SYM.01
Scripts: v235_seam_chern_simons.py
Location: tfpt_research_contracts
Original CSV, line 321Original ledger status
TOPO.BRIESKORN.01
BRIESKORN CAPSTONE (2026-06-17): the (2,3,5) Brieskorn singularity x^2+y^3+z^5 is the ONE generator of the discrete skeleton -- the capstone of the icosahedral round (v55/v219/v223/v232/v233). Its three exponents ARE the atoms (|Z2|,N_fam,g_car)=(2,3,5). (1) MILNOR NUMBER = the '8': mu=(2-1)(3-1)(5-1)=(|Z2|-1)(N_fam-1)(g_car-1)=1*2*4=8=rank E8=#exceptional P^1 = the '8' in c3=1/(8 pi), a FIFTH independent origin (after geometry=2|mu4|, lattice=rank E8, gravity=8pi, Coxeter=phi(30)). (2) MONODROMY = the order-30 Coxeter cycle: the Milnor monodromy eigenvalues lambda=zeta_2^j1 zeta_3^j2 zeta_5^j3 (1<=ji<=ai-1) are the eight primitive 30th roots e^{2pi i m/30}, m in {1,7,11,13,17,19,23,29} = the E8 exponents; characteristic polynomial = Phi_30 (degree phi(30)=8=mu), so the Milnor monodromy IS the E8 Coxeter element of order 30=h(E8) (v55). (3) BOTH CLOCKS are facets of this one monodromy: the monodromy GROUP <h>=Z/30=Z/2(sheet)xZ/3(family/triality)xZ/5(carrier) carries the mu3 triality (the CP phase omega, v233) as the order-3 power h^10; the GALOIS group Gal(Q(zeta_30)/Q)=(Z/30)^x=Z/2xZ/4 carries the order-4 element (x7) = the mu4 clock acting on the spectrum (v223). (4) Milnor lattice=E8 (the resolution intersection form, v232/v234), link=Poincare homology sphere S^3/2I. (5) SYNTHESIS: one singularity x^2+y^3+z^5 generates the atoms (exponents), the 8 (Milnor number), E8 (Milnor lattice), the order-30 cycle (monodromy), both clocks (mu3 in <h>, mu4 in Galois) and the seam (link) -- not many numbers sharing {2,3,5} but one icosahedral singularity read several ways. Unifies the icosahedral round; does NOT close a gate.
Recorded status: Lattice/Topology (exact) [E]/[I]
Dependencies, status detail and source
Canonical status: [E] mu=(2-1)(3-1)(5-1)=8=rank E8 (5th origin of the '8'); Milnor monodromy eigenvalues = E8 exponents/30 = the order-30 Coxeter cycle (charpoly Phi_30); both clocks = mu3 in <h>=Z/30 (CP) + mu4 in Galois (Z/30)^x; one singularity generates the skeleton [I]
Dependencies: MCKAY.E8.01; COX.CLOCK.01; CP.TRIALITY.01; TOPO.E8.01; SEAM.COX.01
Scripts: v236_brieskorn_capstone.py
Location: origin_theory
Original CSV, line 322Original ledger status
GATE.HOLO.03
SEAM SRE CLOSURE (2026-06-17): the closing step of GATE.HOLO.01/02 recast as a PHYSICAL, falsifiable condition -- no topological ground-state degeneracy <=> det K=1 <=> the seam bulk is short-range-entangled (SRE/invertible). Sharpens the residual from definitional ('condense the Lagrangian glue', v235) to a yes/no statement about topological order. (1) the abelian K-matrix ground-state degeneracy on a genus-g surface is |det K|^g: carrier D5(+)A3->16, SO(16)_1=D8->4, (E8)_1->1 on the torus; so 'no topological degeneracy on ANY closed surface' <=> |det K|=1. (2) SRE <=> det 1 <=> E8: among rank-8 even positive-definite K (c=signature=8=g_car+N_fam) only E8 has det 1 -- THE unique nontrivial bosonic SRE 2+1d phase (Kitaev E8), edge (E8)_1 holomorphic; D8 and the carrier are long-range-entangled (topologically ordered). (3) PLANE vs TORUS: a unique ground state on the PLANE (RP+gap+cluster+OS, the established admissible-sector facts) is NECESSARY but not sufficient -- the plane has no non-contractible cycles and cannot see |det K|, the torus does; so the residual is exactly 'the seam unique-vacuum property extends to the torus' = SRE. (4) NEG: a topologically-ordered (LRE) bulk has |det K|>1 (D8: 4-fold torus degeneracy + a non-holomorphic boundary 1,v,s,c = SO(16)_1 rival). (5) SHARPENED RESIDUAL: the one open analytic step is now the physical statement 'the free RP gapped seam bulk is short-range-entangled (no topological ground-state degeneracy)' = det K=1 = the Kitaev E8 phase -- sharper than 'condense the Lagrangian glue' (v235) and than 'the seam is P^1 minus mu4' (QGEO.SYM.01). [E] the degeneracy=|det K|^g dictionary + SRE<=>det1<=>E8 selection; [O] the physical SRE premise. NOT a closure.
Recorded status: Lattice/topological-order (exact) [E]/[O]
Dependencies, status detail and source
Canonical status: [E] genus-g GSD=|det K|^g, no topological degeneracy <=> det K=1 <=> SRE; only E8 (det 1) is the bosonic SRE c=8 phase (Kitaev E8); plane unique-vacuum is necessary not sufficient (torus sees det K); residual = 'the seam is SRE' [O], a physical yes/no statement
Dependencies: GATE.HOLO.02; GATE.HOLO.01; QGEO.SYM.01
Scripts: v237_seam_sre_closure.py
Location: tfpt_research_contracts
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DYN.SEMIGROUP.01
STATIC->DYNAMIC FLIP (2026-06-17): the seam's modular flow (reversible) and its recovery channel read as a Markov/Lindblad generator (irreversible), with the dissipative gap EQUAL to the OS mass gap -- the point where the static compiler becomes a dynamics. Companion to v196/v198 (modular) and v221/v64 (recovery), which state the structure STATICALLY (a commutator, a contraction bound, a mass-gap number); this reads the SAME objects DYNAMICALLY. (1) [E] MODULAR FLOW = REVERSIBLE GENERATOR: sigma_t = e^{i t Lambda_Sigma} is a unitary one-parameter group (Tomita-Takesaki); the mu4 clock is conserved, rho sigma_t rho^{-1} = sigma_t for all t <=> [rho,Lambda_Sigma]=0 (the v198 state-invariance), so the static v198 commutator IS the conservation law of modular time. (2) [E] RECOVERY = DISSIPATIVE GENERATOR: L = log T is real-symmetric with off-diagonals >= 0 and zero row/column sums (a doubly-stochastic / CPTP-classical Markov generator); e^{L*1} = T reproduces the v221 channel and e^{L tau} -> the rank-1 democratic projector (the arrow of time, matching v64's T^n -> projector). (3) [E] KEYSTONE: the dissipative spectral gap = -log((2/3)^6) = 6 log(3/2) = the OS/RP mass gap Delta (v64) -- the STATIC recovery bound (2/3)^6 (v221) and the DYNAMICAL mass gap (v64) are ONE number, one exponentiated. (4) [E] GKSL split: G = i Lambda_Sigma + L has reversible (imaginary) + dissipative (real <= 0, gapped) spectrum. NEG: a mu4-breaking Lambda breaks conservation; a free rate r != (2/3)^6 breaks the gap identity. (5) [O] residual: geometric modular flow on the FULL seam algebra (Connes-Rovelli thermal time = physical time = QGEO.SYM.01, v198) and the continuum embedding beyond the finite block -- a target, not a closure
Recorded status: Numerical (finite-block) [E]/[O]
Dependencies, status detail and source
Canonical status: [E] finite block: modular flow = reversible unitary group with mu4 conserved <=> [rho,Lambda]=0; L = log T a doubly-stochastic generator with e^{L}=T; dissipative gap = -log((2/3)^6) = 6 log(3/2) = OS mass gap (v64); GKSL split. [O] geometric modular flow on the full seam algebra (= QGEO.SYM.01) and the continuum embedding -- a target, not a closure
Dependencies: QGEO.MODULAR.01; QEC.SEAM.01
Scripts: v238_modular_lindblad_dynamics.py
Location: tfpt_research_contracts
Original CSV, line 324Original ledger status
DYN.KMS.01
KMS / THERMAL TIME (2026-06-17): the modular flow of v238 makes the seam state a KMS (thermal) state at the canonical inverse temperature beta = 1, and the geometric (Unruh/Bisognano-Wichmann) normalisation fixes the physical seam temperature via the seam unit 2 pi = 1/(4 c3). Tomita-Takesaki: a cyclic-separating state is automatically KMS at beta = 1 for its own modular flow. (1) [E] KMS at beta=1: omega(A sigma_i(B)) = omega(B A) for random Hermitian A,B (omega(X)=Tr(rho X), rho=e^{-Lambda_Sigma}/Z), so modular time (v238) is a thermal time (Connes-Rovelli) and the seam state is the Gibbs state of the modular Hamiltonian. (2) [E] NEG: the same identity at beta=1/2 fails -- Tomita-Takesaki pins beta=1, no tunable knob. (3) [E] the seam unit: beta_phys = 2 pi = 1/(4 c3) exactly (v58; 1/4=1/|mu4|), so the modular KMS temperature is the horizon temperature T_H = kappa/(2 pi) = c3/M (v57/v208) -- thermal time = horizon time. (4) [E] one object with v238: the same Lambda_Sigma generates sigma_t and rho=e^{-Lambda_Sigma}/Z; the recovery generator L's stationary state is the beta->0 democratic point. (5) [O] residual: that this beta=1 flow is the geometric boost (T_H physical) is the QGEO.SYM.01/BW premise (HOR.BHTHERMO.01 [P]) -- a target, not a closure
Recorded status: Numerical (finite-block) [E]/[O]
Dependencies, status detail and source
Canonical status: [E] KMS at beta=1 (modular flow is thermal); seam unit 2 pi = 1/(4 c3) = horizon temperature T_H = c3/M; one object with v238. [O] the geometric-boost identification = QGEO.SYM.01 -- a target, not a closure
Dependencies: DYN.SEMIGROUP.01; HOR.BHTHERMO.01
Scripts: v239_kms_thermal_time.py
Location: tfpt_research_contracts
Original CSV, line 325Original ledger status
DYN.GNS.01
GNS / OS RECONSTRUCTION (2026-06-17, finite toy): from the discrete seam data (a *-algebra M + the state omega) one reconstructs a Hilbert space, a cyclic vector, the modular flow (v238/v239) AND a POSITIVE Hamiltonian -- so two QFT primitives (the Hilbert space and a positive Hamiltonian) are OUTPUTS of the seam data, not extra inputs. (1) [E] GNS: <A,B>=Tr(rho A^dag B) is Hermitian and positive-definite (rho>0), dim n^2; the identity is cyclic (pi(A)1 = A spans M) and separating. (2) [E] modular flow sigma_t(x)=rho^{it} x rho^{-it} is a state-preserving *-automorphism with generator i[log rho,.] = Lambda_Sigma (v238); the modular operator Delta:X|->rho X rho^{-1} is positive. (3) [E] OS Hamiltonian H_OS = -log T (T the v221 recovery transfer) is POSITIVE: eigenvalues {0, 6 log(3/2), 6 log 3} >= 0, ground state = the stationary mode, gap = 6 log(3/2) = the v64 mass gap -- OS reconstruction delivers v64's 'H >= 0 + mass gap'. (4) [E] H_OS = -L: the OS Hamiltonian is MINUS the v238 dissipative generator -- the recovery semigroup e^{L tau} IS the Euclidean evolution e^{-H_OS tau}; two Hamiltonians from one seam (modular thermal-time + OS positive-energy). (5) [O] residual: the geometric/operator-level identification = QGEO.SYM.01/BW and the full reconstruction = the standard OS theorem under the named RP/gap hypotheses (Layer 2) -- a target, not a closure
Recorded status: Numerical (finite-block) [E]/[O]
Dependencies, status detail and source
Canonical status: [E] GNS Hilbert space + cyclic/separating vector from (M,omega); modular flow = v238; OS Hamiltonian H_OS = -log T >= 0 with gap = v64 mass gap, and H_OS = -L. [O] the geometric/operator-level OS step = QGEO.SYM.01 + Layer-2 RP/gap -- a target, not a closure
Dependencies: DYN.SEMIGROUP.01; QEC.SEAM.01; QG.GAPDEC.01
Scripts: v240_gns_os_reconstruction.py
Location: tfpt_research_contracts
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