Original ledger status
AX.P2.01
g_car = 5 carrier interface (3+2) -- a DECLARED input but an OVER-DETERMINED bootstrap fixed point, not a free choice: forced three independent ways by the E8 closure (bootstrap mu^2-5mu+4=0, BOOT.01/v6), uniquely solved by the Pascal carrier condition 2^g=g^2+g+2 => g=5 (Lean-formalised, no sorry; FORM.LADDER.01), and the (g_car,N_fam)=(5,3) pair is the anchor moment data e2(a)=g_car (ARCH.CORE.01/v53; a=(1,1,2) the unique multiset with elem-symm (4,5,2)). Reduces with P1 to {a, pi}. SYNTHESIS NOTE (reduction state 2026-07-21; text consolidation, marker Axiom UNCHANGED): P1 + the four marks are [E]-anchored (v216); given the marks, g_car = 5 follows via the partition 4 = 2+1+1 plus the Deligne/Birkhoff-Grothendieck/stability typing (v491/v499, residual R1 [C]); the clock order, the Z8 tower, the deck class and the position half of the alignment bit are theorems (v506/v507/v510) -- the compiler's dimensionless inputs reduce to: four marks (derived from P1-side topology), ONE square-modulus datum (tau = i, equivalently: the clock / the CM-fixed half-period / the non-split extension class on the free seam circle / the flag-transitivity bit V4 -> D4, v512), and pi, plus the [C] identifications R1/R2 of v499. SYNTHESIS NOTE (2026-07-22, v512 -- marker UNCHANGED): the reduction state can equivalently be written 'four marks + one discrete symmetry-lift bit (flag transitivity <=> tau = i) + pi'. This describes the REDUCTION STATE; the axiom stays declared and QGEO.REALIZE.01 stays [C]/[O] [2026-08-02 XXXIX: the four-mark closure lands -- v624: under the D_{d+1}+A_{d-1} glue architecture three independent selectors (disc-group census, even-glue norm equation, Pythagorean (3,4,5)) force d = 4, with (1,1,2) the unique 3-part partition and c_3 = 1/(8 pi): the two-input presentation reduces to ONE boundary degree d = 4 plus pi, CONDITIONAL on the architecture; the axiom keeps its typing -- the residue moves to why the physical boundary realizes the minimal cyclically-glueable genus-0 divisor; see EXTREV.LATTICE.01.] SYNTHESIS NOTE (2026-08-28, v993 -- marker Axiom UNCHANGED): the architecture conditionality of v624 is lifted at the census level -- the FULL rank-8 ADE pair census with cyclic Z4 glue on BOTH factors selects (D5, A3) uniquely (D3 ≅ A3 aliases collapsed), so the D+A split is an OUTPUT of (rank 8 + cyclic Z4), not an INPUT. Cited-not-proved remain c_- = 8 and holomorphic uniqueness of (E8)_1. Axiom typing UNCHANGED. WAVE-6 (2026-08-30, v1005): relative pencil identities exact but CIRCULARITY-FLAGGED -- carrier 5 already sits in the column sums of Q_2 and C; NOT a P2 selector until Q, C, epsilon are derived from seam geometry independently. Axiom typing UNCHANGED. LATE EVENING (2026-08-30, v1014): W-bridge premise P-anch DERIVED (anchor chain: e1 = R^{-1}(1,1,2)^T uniquely via the winding/triple lock); P-dem narrowed to the character-blind determinant-response map -- same MMST/Quillen externalized leg as TEL-B/ALG-EXH/P1. Axiom typing UNCHANGED. MONDAY MORNING (2026-08-31, v1015): BOTH W-bridge premises now derived at finite level -- P-anch already (v1014 winding/triple lock); P-dem DERIVED (character-blind determinant response r=(1,1,1) exactly at collar sizes 12 and 16, democracy residual 0; mutants split (1,0,0) and (5/4,1,5/4)). The axiom-core remainder is ZERO modulo the externalized MMST identification. Axiom typing UNCHANGED (the finite derivations are shadows; the continuum identification is the same external leg).
Recorded status: Axiom (declared input; over-determined bootstrap fixed point, Lean-forced)
Dependencies, status detail and source
Canonical status: Axiom (declared) but bootstrap-forced (3 ways) + Pascal-unique (Lean): g=5 is not a free knob; reduction state 2026-07-22: four marks + one discrete symmetry-lift bit (flag transitivity <=> tau = i) + pi (v491/v499/v506/v507/v510/v512), marker unchanged | 2026-08-28 v993: v624 architecture conditionality lifted at the census level (D5, A3 unique in full rank-8 ADE); axiom typing UNCHANGED | WAVE-6 (2026-08-30 v1005): pencil circularity-flagged (5 already in Q_2/C column sums); NOT a P2 selector; axiom typing UNCHANGED | AFTERNOON (2026-08-30 v1010): pencil selector rehabilitated: column sums forced by prior constructions (ladder c=2 + n=3 force Q sums (9,5,1); C's 5 inherited from R col 3 -- non-circular); W-shift conditionally unique given democratic-image + carrier-anchor-kernel (1078 -> 1); remaining obligation = seam-geometric derivation of those premises; axiom typing UNCHANGED | LATE EVENING (2026-08-30 v1014): W-bridge premise P-anch derived (anchor chain); P-dem narrowed to the character-blind determinant-response map -- same MMST/Quillen externalized leg as TEL-B/ALG-EXH/P1. Axiom typing UNCHANGED. | MONDAY MORNING (2026-08-31 v1015): BOTH W-bridge premises derived at finite level (P-anch v1014; P-dem r=(1,1,1)); remainder 0 modulo MMST. Axiom typing UNCHANGED.
Dependencies: BOOT.01; ARCH.CORE.01; v491; v499; v510; v512; v993
Scripts: v1005_relative_pencil_bridges.py, v1010_simplicity_bridge_census.py, v1014_bridge_refinements.py, v1015_axiom_core_closure.py
Location: tfpt_1
Original CSV, line 3Original ledger status
E8.GLU.01
E8 = (D5 (+) A3) + mu4 glue: explicit lattice certificate (240 roots norm^2=2; even; unimodular Gram det=1; glue index 4=|mu4|); disc=Z4; q(D5)+q(A3)=5/4+3/4=2
Recorded status: Lattice
Dependencies, status detail and source
Canonical status: Lattice
Dependencies: D5; A3; Z4
Scripts: v1_e8_glue.py
Location: tfpt_1;tfpt_3
Original CSV, line 5Original ledger status
BOOT.CLASS.01
D5(+)A3 is the UNIQUE familyful cyclic-glue decomposition of E8 (16-dim half-spinor + 3-family A3); glue Z4=|mu4|
Recorded status: Lattice
Dependencies, status detail and source
Canonical status: Lattice
Dependencies: E8.GLU.01; even-unimodular rank-8 uniqueness
Scripts: v15_bootstrap_classification.py
Location: tfpt_1;tfpt_3
Original CSV, line 10Original ledger status
FLAV.SOLAR.02
solar coefficient is the A3 glue-norm: eps=q(A3)*phi0=(3/4)phi0, q(A3)=3/4 the same norm in q(D5)+q(A3)=2; leading term = c3 exact; sin^2 th12=1/3-phi0/2=0.30675. Product rule 32/9=2^gcar/Nfam^2 interpreted (full Clifford dim/Nfam^2); sum L_lepton=16=dim S+. Quark non-extension: cusp-leg law gives c_c/c_s=1/7 vs actual 0.724
Recorded status: Identity
Dependencies, status detail and source
Canonical status: Identity
Dependencies: FLAV.SOLAR.01; FLAV.LEPTONC.01; E8 glue norms
Scripts: v21_solar_product_quark.py
Location: tfpt_2
Original CSV, line 23Original 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)
Dependencies, status detail and source
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
SEL.THM.01
Boundary Carrier Selection Theorem (Theorem A): admissible boundary-carrier data SELECT (D5+A3)+mu4=E8 uniquely. Boundary mu4->H1=Z^3->A3,N_fam=3; minimal 16-spinor->D5 (only n=5); disc(D5)=disc(A3)=Z4 cyclic anti-isometric, q(D5)+q(A3)=5/4+3/4=2=E8 root norm, glue index 4=|mu4|, E8 unique even unimodular rank 8. Four simultaneous conditions (16-spinor, N_fam=3, cyclic Z4, q-sum 2) met ONLY by D5+A3; D8 (non-cyclic, no family), E7+A1 (1 fam), E6+A2 (2 fam, Z3), A4+A4 (Z5), A8 (single) excluded. Lattice facts [L]; physical selection (P1 seam + P2 carrier => these inputs) is [P]/[A] selection axiom, not zero-input derivation
Recorded status: Lattice [L] + selection [P]
Dependencies, status detail and source
Canonical status: Lattice [L] + selection [P]
Dependencies: E8.GLU.01; BOOT.CLASS.01; v1; v15
Scripts: v47_selection_theorem.py
Location: tfpt_1
Original CSV, line 69Original ledger status
SEAM.S3.LATTICE.01
Track 1 (2026-06-23): the EXPLICIT lattice realisation of the S3 input -- a concrete gapped chiral-Majorana (p+ip) lattice model whose edge is the 16-Majorana SO(16)_1 carrier, mu4-condensed to (E8)_1. Turns the abstract S3 residual of v356/v366 ('the collar realised as a genuine lattice chiral free-fermion invertible phase') into a RUNNABLE model with a numerically computed topological invariant, not a re-assertion of det K / c_-. [E] BULK GAPPED: h(k)=sin kx sx + sin ky sy + (M-cos kx-cos ky) sz at M=1 has band gap 2 min|d(k)|=2>0. [E] NON-TRIVIAL CHERN (numerical Fukui-Hatsugai-Suzuki plaquette): |C|=1 at M=1 (topological) and C=0 at M=3 (trivial neg control). [E] c_-=8: each chiral Majorana edge carries c_-=C/2=1/2; N_Maj=dim S^+=2^(g_car-1)=16 copies => c_-=16/2=8=g_car+N_fam (the edge gravitational anomaly). [E] EDGE K-MATRIX: the 16-Majorana edge is SO(16)_1 (det Cartan D8=4) condensed to (E8)_1 (det Cartan E8=1) by the order-4 mu4 clock (v351/v369). [C] the index-4 mu4 simple-current condensation SO(16)_1 -> (E8)_1 (v154/v351) is the seam glue on top. [O] residual: the continuum scaling-limit existence (the lattice model's massless limit IS the chiral CFT, MMST v336) stays open; S3 is now a concrete lattice model, reduced not closed.
Recorded status: S3 realised as an explicit gapped chiral-Majorana lattice model (numerical Chern |C|=1, c_-=8, det K 4->1) [E]/[C]/[O]
Dependencies, status detail and source
Canonical status: [E] the gapped Chern model + the c_-=8 counting + the det K discriminators (numerical Chern + lattice arithmetic); [C] the mu4 condensation to (E8)_1; [O] the continuum scaling limit. Reduces S3 to a runnable lattice model; does NOT close SEAM.EQUIV.01.
Dependencies: SEAM.EQUIV.01; v356; v366; v351; v369; v301; v302; v154
Scripts: v367_seam_s3_lattice.py
Location: tfpt_research_contracts
Original CSV, line 81Original ledger status
SEAM.S3.MODULAR.01
S3 closure stack (2026-06-23): the GENUS-1 discriminator -- the torus ground-state degeneracy of the seam net is 1 (holomorphic = (E8)_1), via the KLM index condensation and the modular invariance of the single (E8)_1 character. This is exactly the 'hard part' v344 flagged: the genus-0 arguments (a unique plane vacuum) are necessary but NOT sufficient (a plane vacuum is always 1, v87); det K=1 is the torus (genus-1) statement. [E] KLM mu-additivity: the carrier A=(D5)_1 x (A3)_1 has mu(A)=det Cartan(D5)*det Cartan(A3)=4*4=16; the order-4 mu4 glue (|L|=|mu4|=4) gives mu(E8)=16/4^2=1 (torus GSD=1); the index-2 glue gives the rival mu(SO16)=16/2^2=4. [E] |det Cartan(E8)|=1 (one primary), |det Cartan(D8)|=4 (four primaries). [E] the single (E8)_1 character has modular T-eigenvalue e^{2 pi i(h-c/24)}=e^{-2 pi i/3} (h=0,c=8), consistent with v377's q^{-1/3}; a holomorphic theory has a 1-dim modular S,T rep => exactly one character => torus GSD=1. [O] the abstract continuum EXISTENCE (v336).
Recorded status: torus GSD=1 / modular uniqueness -- the genus-1 holomorphy discriminator closes the v344 hard part [E]
Dependencies, status detail and source
Canonical status: [E] the KLM condensation 16->1, the det-Cartan #primaries (1 vs 4), the modular T-eigenvalue / 1-dim rep, and the genus-0-vs-genus-1 distinction; [O] the continuum existence (v336). Pins the net at genus-1; does NOT close SEAM.EQUIV.01.
Dependencies: SEAM.EQUIV.01; v344; v154; v369; v83; v87
Scripts: v378_seam_s3_modular.py
Location: tfpt_research_contracts
Original CSV, line 90Original ledger status
E8.OTHERSIDE.AUDIT.01
THE 'OTHER SIDE OF THE SEAM' AUDITED AGAINST THE UNMAPPED E8 STRUCTURE (2026-06-27, v430): the sheet/deck complement of the reverse audit v354/v355. The reverse audit found FIVE Casimir degrees {12,14,18,20,24} with no primary readout ('hull overhead'); the double cover has an 'other side' (the one-sided Z2 collar / conjugate half-spinor S^-). Does that other side correlate with the unmapped E8 structure -- is the leftover where the second sheet lives? The answer is a disciplined NEGATIVE. [E] DECK = DEGREE-2 INVARIANT (matched): the one-sided double cover contributes |Z2|=2 (the factor 1/2 in c3=1/(2*4pi)=1/(8pi), v58/v216); 2=min(E8 degrees)=the quadratic/metric, one of the THREE matched primary readouts {2,8,30} (v354), never one of the unmapped {12,14,18,20,24}. [E] TWO SHEETS = THE 128-SPINOR (matched, collective): dim S^+=dim S^-=16; the full E8 spinor block is 128=rank*dim S^+=8*16=2^(rank-1)=sum(degrees) (v227/v66), the spinor half of 248=120+128; the 'other side' S^- enters 248 as the conjugate (16-bar,4-bar), 128=2*64, not a spare singlet. [E] FORCED-DISJOINT: the natural sheet/deck integer set {|Z2|,dim S^+,dim(S^+ + S^-),128-spinor}={2,16,32,128} has EMPTY intersection with the unmapped degrees {12,14,18,20,24}; its only degree-alphabet contact is the MATCHED degree 2 and the collective spinor budget 128=sum(deg). [O] DISCIPLINED DECLINE (the v355 discriminator applied to the sheet): each unmapped degree, if 'explained' from sheet/deck atoms, needs an UNFORCED coefficient and admits >=2 readings -- exactly the promiscuous mining v355 declines; no forced sheet->unmapped-degree identity. [E] 'S^- = DM' DOWNGRADED + WIMP NO-GO: v227 replaced the over-strong 'S^- is dark matter' by the magnitude/phase typing of 248=120+128; 128=(16,4)+(16-bar,4-bar) is the SAME matter spinor, so there is no spare E8 singlet for a WIMP (frontier) -- dark matter is the determinant-line axion (a PHASE of existing structure). [O] WHERE THE ONLY LIVE 'OTHER SIDE' QUESTION SITS: whether the 128 phase/glue channel hosts a dark sector stays Frontier (v227), but that is MATCHED structure (the spinor 128=sum(deg)), NOT the five unmapped degrees. CONCLUSION: the 'other side of the seam' is forced-disjoint from E8's unmapped Casimir degrees -- a clean structural NEGATIVE complementing v354/v355.
Recorded status: Sheet/deck reverse audit [E]/[O] (the double-cover 'other side' = degree-2 + the 128-spinor, forced-disjoint from the 5 unmapped degrees; the complement of v354/v355)
Dependencies, status detail and source
Canonical status: [E] the deck=degree-2 (matched) and two-sheets=128-spinor (matched, =sum(deg)) identities, and the forced-disjointness {2,16,32,128} cap {12,14,18,20,24}=empty; [O] the disciplined decline (no forced sheet->unmapped identity, v355 discriminator) and the honest residual (the 128 phase/glue dark-sector question concerns matched structure). The sheet/deck complement of v354/v355; closes nothing, records the structural negative.
Dependencies: E8.REVERSE.AUDIT.01; E8.UNMAPPED.BANDWIDTH.01; E8.CHAN.01; E8.CAS.01; v58; v109
Scripts: v430_other_side_reverse_audit.py
Location: tfpt_5_redteam
Original CSV, line 97Original ledger status
SEAM.EQUIV.BOOTSTRAP.01
THE HONEST CORRECTION OF v349's FRAMING (prompted by the right objection 'the inputs are not axioms -- they are back-determined by the theory', 2026-06-22). v349 concluded 'the raw seam does not carry the golden ratio (D5 has h=8 -> sqrt2)' and reduced the keystone to 'is g_car=5 a pentagon or a count?'. That framing was WRONG on two counts; this corrects it while keeping v349's true computations. [E] THE INPUTS ARE BOOTSTRAP-FORCED, NOT FREE AXIOMS (v6): g_car=5 is over-determined three ways -- rank-fill (g_car+N_fam=8=rank E8), Coxeter-match (g_car = max prime of h(E8)=30), Pascal/glue (2^4=C(5,0)+C(5,1)+C(5,2)=16). The objection is correct: the numerical inputs are FIXED POINTS of the self-consistency, not free postulates. [E] g_car=5 IS THE ICOSAHEDRAL 5-FOLD, not the D5 rank: g_car = max prime of h(E8)=30, and h(E8)=30 = 2*3*5 is the icosahedral axis data; the atoms (|Z2|,N_fam,g_car)=(2,3,5) ARE the prime factorisation of the icosahedral Coxeter number 30. So the '5' the bootstrap selects is intrinsically icosahedral (golden), NOT the bare D5 rank (h=8) v349 mis-identified it with. [E] THE GOLDEN RATIO IS EMERGENT FROM THE GLUE, not external (correcting v349): D5 (h=8) and A3 (h=4) are individually non-golden, but the mu4 simple-current extension D5(+)A3 -> E8 (theorem v154, index 4=|mu4|) gives h(E8)=30 with 5|30 -> golden; the seam's OWN mu4 clock, gluing the carrier, PRODUCES the golden 5-fold -- v349 evaluated the un-glued pieces, the wrong object. [E] so v349's dichotomy was FALSE: the Coxeter-match bootstrap FORCES the pentagon (g_car=5 = the 5 in h(E8)=30); there is no 'count' alternative consistent with E8-closure. [O] THE RESIDUAL RELOCATES: the golden/icosahedral is NOT open (bootstrap-forced + the v154 extension theorem); the genuinely open thing is ONLY the PHYSICAL CONTINUUM REALISATION (the raw RP quasi-free collar realises the algebraic E8 fixed point, continuum-limit/OS, v336), NOT the golden ratio. HONEST CAVEAT: the bootstrap is self-consistency WITHIN the discrete E8-closure framework (the Coxeter-match uses h(E8)=30), so it is 'no free numerical dials given the framework', not 'from nothing'; the framework is the meta-input.
Recorded status: Correction [E]/[O] (inputs are bootstrap-forced fixed points; g_car=5 IS the icosahedral 5 of h(E8)=30; golden emergent from the mu4-glue; residual = the physical continuum realisation)
Dependencies, status detail and source
Canonical status: Correction [E]/[O] (inputs bootstrap-forced; g_car=5 icosahedral; golden emergent; residual = continuum realisation)
Dependencies: SEAM.EQUIV.GOLDEN.01; v6; v154; v56; v336; v274
Scripts: v350_bootstrap_inputs_correction.py
Location: origin_theory
Original CSV, line 104Original ledger status
FLAV.DELTA.01
delta=1/2 glue-norm origin + (g_car,N_fam)/|mu4| unification: the two E8-glue discriminant norms ARE the carrier rank and family count over the glue index, q(D5)=g_car/|mu4|=5/4 (rank D5=g_car=5), q(A3)=N_fam/|mu4|=3/4 (rank A3=N_fam=3, n+1=4=|mu4|). Then all FOUR arithmetic ops are forced compiler atoms: sum=(g+n)/|mu4|=rank(E8)/|mu4|=2 (E8 root norm), diff=(g-n)/|mu4|=|Z2|/|mu4|=1/2=delta (lepton transport, used in v20 for c_e=16/7,c_mu=4/3,c_tau=7/6), prod=g*n/|mu4|^2=dim su(4)/dim S+=15/16, ratio=g/n=5/3. (sum,ratio) invert uniquely to (5/4,3/4). So delta=1/2 is the carrier-minus-family count over the glue index, not a chosen rational; it also equals the harmonic-frame holonomy diagonal modulus 1/2 (v41). Hardens v20's chosen delta into a fully atomic readout [I]
Recorded status: Identity [I]
Dependencies, status detail and source
Canonical status: Identity [I]
Dependencies: BND.GLUE.01; v20; v41
Scripts: v51_boundary_half_step.py
Location: tfpt_1;tfpt_2
Original CSV, line 117Original ledger status
ARCH.CFT.01
Boundary-CFT bridge (WZW central charges = compiler atoms) + SU(3)<->SU(4) reconciliation [I]/[L]; NOT a closure. (A) level-1 WZW central charges c=dim(g)/(1+h^v) are the atoms: c(E8)_1=248/31=8=rank E8, c(D5=SO10)_1=45/9=5=g_car, c(A3=SU4)_1=15/5=3=N_fam; coset c=8-5-3=0 = conformal-embedding criterion => (D5)_1x(A3)_1 ⊂ (E8)_1 is a conformal embedding (CFT mirror of the lattice glue (D5(+)A3)+mu4->E8); (5,3) split = central-charge additivity = rank split; the 8 in c3=1/(8pi) = c(E8)_1 (NOT oversold - the content is c_coset=0, per Alessandro's earlier caveat). (B) SU(3)<->SU(4) reconciliation: P^1\\mu4 has n=4 punctures => H_1=Z^(n-1) => N_fam=|mu4|-1=3; carrier side = puncture/center Z4=mu4 (A3=SU4); flavor side = monodromy rho on H_1=Z^3, SU(3)-valued, center Z3=triality, phases {0,1/3,2/3}=parabolic weights (NOT SU(4)_1 weights {0,3/8,1/2}); SU(3) ⊂ SU(4) via 4->3+1. => NOT one WZW for all gates (C falsified), but ONE geometry P^1\\mu4 with two dual sides. CHECKED: Cardy route c=8->S=A/4 is NOT a shortcut (c=8 is matter central charge; area law needs geometric Brown-Henneaux c~ell/G) - restates the open Seam-Horizon coefficient, does not close it
Recorded status: Identity/Lie [I]/[L]
Dependencies, status detail and source
Canonical status: Identity/Lie [I]/[L]
Dependencies: BND.GLUE.01; v6; v15; v19; SEAM.THEOREM.01
Scripts: v61_cft_bridge.py
Location: origin_theory
Original CSV, line 128Original ledger status
SEAM.AREALAW.01
Area-law evidence for the open Seam-Horizon step (necessary condition met, NOT a closure): (1) NUMERICAL [Python-only] - the simplest reflection-positive Gaussian system (harmonic chain) has ground-state block entanglement entropy that SATURATES to a constant when gapped (area law: 1D boundary=O(1) points) and grows ~(c/3)log L when gapless (CFT c-coefficient, c~1); demonstrated S(8)=S(16)=S(32)=0.271 gapped vs 2.197<2.409<2.602 gapless (Srednicki 1993, Bombelli-Sorkin). So an RP Calderon-type kernel GENERICALLY yields an area law - the form S=A/(4G_Sigma) needs. (2) GAP TIE: the physical sector is gapped by the SAME gap Delta=6log(3/2)>0 that makes the attractor unique (v56) => gapped => area law; one gap gives BOTH attractor and area-law structure. (3) EXACT [I]: 8=|Z2|*|mu4| (sheet x glue), c3=1/(|Z2||mu4|pi); 2pi=1/(4c3) (chaos bound/seam unit); scrambling beta/2pi=|mu4|M. HONEST: fixes the area-law FORM; the c3=1/(8pi) COEFFICIENT still needs the specific seam kernel (open [A]). Cascade D=60-2n monotone c-function-like, 60=2h(E8) [P/analogy]
Recorded status: Numerical + Identity [I] (necessary condition)
Dependencies, status detail and source
Canonical status: Numerical + Identity [I] (necessary condition)
Dependencies: SEAM.THEOREM.01; v56; v58
Scripts: v59_area_law_evidence.py
Location: origin_theory
Original CSV, line 130Original ledger status
SEAM.CYCLE.01
A cyclic element INSIDE the compiler hull (computed, not asserted): built from the E8 Cartan matrix, the Coxeter element c=s1...s8 has order EXACTLY h(E8)=30=|Z2|*N_fam*g_car=2*3*5 (verified by matrix powers, v55), and its eigenvalues are primitive 30th roots exp(2pi i m/30) with m the E8 exponents {1,7,11,13,17,19,23,29} = EXACTLY the phi(30)=8 totatives of 30. Hence rank E8=8=phi(30)=#exponents=#live phases of the order-30 cycle => the 8 in c3=1/(8pi) is the live-phase count of a primitive order-30 cyclic rotation of the hull, period 30=|Z2|*N_fam*g_car. PLUS one-alpha cross-sector: S_dS*rho_Lambda=1/(128 c3^4)=32 pi^4 (de Sitter Gibbons-Hawking entropy ~ 1/Lambda), so the SAME EM fixed point alpha^-1=137.036 sets the cosmic horizon entropy and Lambda smallness ~10^-122=e^(-2 alpha^-1). FURTHER: S_dS=2^g_car*pi^|mu4|*e^(2 alpha^-1) - the entropy prefactor 32 pi^4 = (Dirac spinor dim of D5=SO(10): S+ + S- =16+16=2^g_car) x pi^|mu4|, with 128=2^7 (7=scalaron exponent g+n-1): cosmic horizon entropy = carrier Clifford dim x pi^glue x EM fixed point. [I]/[L]; cyclic-cosmology reading is [P], not included
Recorded status: Identity/Lie [I]/[L]
Dependencies, status detail and source
Canonical status: Identity/Lie [I]/[L]
Dependencies: v6; v8; v3; h(E8)=30
Scripts: v55_coxeter_cycle.py
Location: tfpt_3;origin_theory
Original CSV, line 134Original ledger status
FLAV.PENCIL.02
Operator-pencil geometry of (K,Q,R,L) - the anchor plane as a small area in operator space (validated review block; all in admissible classes). STRONG: [2] ANCHOR SINGULARITY THEOREM det B(K+xQ)=9x^2+21x+10=(N_fam x+|Z2|)(N_fam x+g_car)=(3x+2)(3x+5), oriented anchor area degenerates at x=-|Z2|/N_fam=-2/3 (Koide target/gap base (2/3)^6) and x=-g_car/N_fam=-5/3 (D5/A3 glue asymmetry) => 2/3 is the FIRST SINGULAR POINT of the mass<->transport anchor plane, not just a recurring fraction [I/L]; [4] buildup chain (3,7,6,4) partial sums (3,10,16,20)=(N_fam,A_Lambda,dim S+,det L), scalaron 7=A_Lambda-N_fam [I]; [6] type checker det B_Q=9=N_fam^2, det B_K=10=A_Lambda, det B_R=16=dim S+, det B_L=40=|R(D5)| [I/L]. AUDIT (exact values [I], reading decorative [P]): [3] differential spectrum D,D',D'' at -1,0,1,2 = (2,4,20,68),(1,6,29,70),(-4,14,32,50) (29=top E8 exp, 32=2^gcar, 50=A4xA4 block); [5] F4xG2 shadow det B_{R+Q}=52=dim F4, chi_[K,Q]=t^3+5t+14 (14=dim G2), |Pl_R(K)|_1=26, 248=52+14+26*7 = real E8->F4xG2 branching (52,1)+(1,14)+(26,7) - an operator shadow, not a Lie-theoretic embedding proof
Recorded status: Identity/Lattice [I]/[L] + audit [P]
Dependencies, status detail and source
Canonical status: Identity/Lattice [I]/[L] (anchor singularity, type checker) + [P] (atlas/F4xG2 shadow audit)
Dependencies: FLAV.PENCIL.01; FLAV.KQ.01; v37; v52; v74
Scripts: v80_operator_pencil_geometry.py
Location: tfpt_2
Original CSV, line 147Original ledger status
FLAV.PENCIL.03
The mass-transport pencil P(x)=K+xQ as a projective line with two anchor-block singularities, and the DOUBLE COVER branched over them (validated review block; all in admissible classes). CENTRAL [I/L]: det B(K+xQ)=(3x+2)(3x+5) is quadratic => y^2=det B(K+xQ) is a 2:1 cover ramified exactly over its zeros, so the Koide/gap point x=-|Z2|/N_fam=-2/3 and the carrier point x=-g_car/N_fam=-5/3 are THE TWO BRANCH POINTS of one double cover; deck involution y->-y of degree 2=|Z2|=the sheet (line-bundle reflection of the Spin(10)->SO(10) half-spinor cover the carrier lives on). Branch locus = -(spine ends 2,5)/N_fam; discriminant = 81 = N_fam^4 (perfect square => rational/split, sqrt=9=N_fam^2=det B_Q); separation = 1 = one transport period (deck-translation x->x+1 maps carrier->Koide). So 2/3 is not a recurring quotient but ONE ramification point of the mass<->transport double cover; sharper open question: why does the leptonic source-to-pole transfer renormalise onto a branch point and which sheet (y->+-) does parity select. DEEPER: the branch divisor symmetric functions ARE the core atoms - sum of branch points = -scalaron/N_fam = -7/3, product = A_Lambda/N_fam^2 = 10/9, integer labels {|Z2|,g_car}={2,5} have sum=7=scalaron, product=10=A_Lambda, diff=3=N_fam, so the scalaron is the TRACE of the branch divisor and all earlier scalaron readouts collapse to this one geometric origin; the fiber y^2=det B is A_Lambda at K and 4A_Lambda at L (transport K->L multiplies the fiber by |Z2|), and the Z2 sheet endpoint x=-1 lies between the branch points where y^2=-|Z2|<0 (the sheet lives on the imaginary cut joining Koide and carrier); the clean cover is a property of the anchor 2-plane <1,a> (the full-3-space cubic det(K+xQ) has disc -1132 with an irrational real root), so the anchor projection regularises the geometry (anchor-first). CLEARING MATRICES [I/L]: Koide C_{2/3}=3K-2Q reproduces D5+A3 glue (tr=15=dim A3, sum=45=dim D5, det=60=D_start), rank-one (forced) anchor block B(C23)=(g_car,7)^T(N_fam^2,11)=(5,7)^T(9,11), sum=240=|R(E8)|; carrier C_{5/3}=3K-5Q charge-neutral (sum=0), chi=(lam+|Z2|)(lam^2+lam+|R+A3|)=(lam+2)(lam^2+lam+6). Scalaron 7 = mixed anchor discriminant/N_fam = (det B_L - det B_K - det B_Q)/N_fam = (40-10-9)/3 (B_L=B_K+B_Q linearity; 7 is an interference area, not a leftover) [I]. c_u/c_d=55/117 diagnostic readout at sheet endpoint K-Q (Plucker v37 canonical) [I]
Recorded status: Identity/Lattice [I]/[L] + audit [P]
Dependencies, status detail and source
Canonical status: Identity/Lattice [I]/[L] (double cover / branch locus, clearing matrices, mixed-disc scalaron) + [P] (per-entry atlas reading of clearing matrices)
Dependencies: FLAV.PENCIL.01; FLAV.PENCIL.02; v37; v52; v74; v80
Scripts: v81_singular_pencil_matrices.py
Location: tfpt_2
Original CSV, line 148Original ledger status
CAR.PASCAL.01
Red-team Target B residual REDUCED [I]/[L]: the carrier 'K=2 Pascal truncation' flagged by the red team as a free postulate is NOT free. K=(g-1)/2 is the Pascal-row MIDPOINT: sum_{k<=(g-1)/2} C(g,k) = 2^(g-1) for every odd g (verified g=3,5,7,9), i.e. the half-spinor split of the 2^g Dirac spinor. Equivalently the carrier is the even Clifford half-spinor Lambda^even(C^g_car): C(5,0)+C(5,2)+C(5,4)=1+10+5=16=2^(g_car-1)=dim S+. So Target-B's residual is not 'why K=2' but the single standard input 'carrier = half-spinor of Spin(2 g_car)', already used in the D5+A3 glue (v1/v15); the Lean arithmetic 2^g=g^2+g+2<=>g=5 stays [F]
Recorded status: Identity/Lattice [I]/[L] (B residual reduced to the half-spinor input)
Dependencies, status detail and source
Canonical status: Identity/Lattice [I]/[L]: K=(g-1)/2 is the half-spinor midpoint, not a free truncation; B residual reduced to the standard half-spinor carrier
Dependencies: REDTEAM.B.01; FORM.CAR.01; CAR.UNIQ.01; v2; v44
Scripts: v83_e8net_holomorphic_uniqueness.py
Location: tfpt_5_redteam;tfpt_1
Original CSV, line 157Original ledger status
GATE.METRIC.05
Red-team Target A residual (ii) CONDITIONALLY CLOSED [L] -> Target A = ONE residual: bulk-reconstruction uniqueness is NOT independent of residual (i). By the AQFT classification of full 2D CFTs over a chiral net (Longo-Rehren 1995; Kawahigashi-Longo-Mueger 2001; Bischoff-Kawahigashi-Longo-Rehren arXiv:1405.7863) the possible bulks = haploid commutative Q-systems = physical modular invariants of Rep(A); for a HOLOMORPHIC net Rep(A)=Vect so the bulk pairing is UNIQUE. MACHINE-CHECKED CONTRAST: the same-c rival SO(16)_1 (discriminant category Z2xZ2 of D8, q=(0,1/2,1,1), mu-index=4, S/T built explicitly, S^2=I, (ST)^3=I) admits exactly SIX modular invariants (Z>=0 integer, Z_00=1, [Z,S]=[Z,T]=0, entries<=2): diagonal, s<->c swap, BOTH E8-extension invariants |chi_0+chi_{s,c}|^2 (= the lattice glue E8=D8 u (D8+s): h_s=1 bosonic/condensable, index 2, det=4/4=1 even unimodular, cf v1/v83) and two twisted pairings => without holomorphy the c=8 bulk is MULTIPLY ambiguous; with one primary trivially Z=(1) unique. CONSEQUENCE: the whole of Target A reduces to the SINGLE theorem 'seam-Calderon boundary net is holomorphic with c=8' - then (E8)_1 (v83/GATE.METRIC.04) AND the unique bulk (this row) follow; the hypothesis stays [P]/[A]. Honest scope: nothing here proves the seam net IS holomorphic
Recorded status: Lattice [L] (classification + machine contrast) + [P]/[A] (the one remaining hypothesis)
Dependencies, status detail and source
Canonical status: Lattice [L]: bulk uniqueness rides on holomorphy; Target A = ONE residual
Dependencies: GATE.METRIC.04; REDTEAM.A.01; v83; v77
Scripts: v87_bulk_uniqueness_reduction.py
Location: tfpt_5_redteam
Original CSV, line 161Original ledger status
GATE.METRIC.06
CARRIER INDEX LEMMA [L] - the Gate-A theorem gets an equivalent index-theoretic form (sharper as a target): by Kawahigashi-Longo-Mueger (mu_A=[B:A]^2 mu_B; lattice nets mu=|discriminant|=det Cartan) the carrier inclusion has Jones index [(E8)_1:(D5)_1x(A3)_1]=sqrt(16/1)=4=|mu_4|=|Z2|^2 - the glue-group order IS the inclusion index. The extension is the mu_4 simple-current extension at level 1: adjoint branching 248=(45,1)+(1,15)+(16,4b)+(16b,4)+(10,6)=45+15+64+64+60; the three non-vacuum glue sectors are CURRENTS (h=1 exactly: 1/2+1/2, 5/8+3/8, 5/8+3/8); 1+3=4 sectors = the same Z4 glue as the lattice construction (v1). mu-additivity: an index-4 simple-current extension of the carrier has mu=16/16=1, so HOLOMORPHY FOLLOWS from the index statement - it need not be assumed. CONSEQUENCE: (H) 'seam-Calderon net holomorphic with c=8' <=> (H') 'seam net contains the carrier net with Jones index 4 as its mu_4 simple-current extension'. Why sharper: both ends of (H') are constructed objects (v77), finite index is controllable by Longo index theory, and the gap Delta_eff>0 (v76) supports finiteness. Negative control: mu(SO(16)_1)=4!=1 (v83/v87). Honest scope: the seam-side index computation is NOT done here; the boundary-net identification stays [P]/[A]
Recorded status: Lattice [L] (index arithmetic + reframing) + [P]/[A] (seam-side identification)
Dependencies, status detail and source
Canonical status: Lattice [L]: Gate A <=> index-4 mu_4 simple-current extension of the carrier net
Dependencies: GATE.METRIC.05; GATE.METRIC.04; E8.GLU.01; v77
Scripts: v89_carrier_index_lemma.py
Location: tfpt_5_redteam;tfpt_research_contracts
Original CSV, line 163Original ledger status
GATE.METRIC.07
GLUE UNIQUENESS [I]/[L] - the carrier extension tower completely classified (Gate A loses its last structural freedom): extensions of the carrier net/lattice correspond to isotropic subgroups of the discriminant form (Z4xZ4, q=(5x^2+3y^2)/8; q reproduces the level-1 sector weights of v87/v89). Exhaustive enumeration of all 15 subgroups: isotropic = {1, Z2, Z4, Z4}. (a) Exactly TWO Lagrangian glues <(1,1)> and <(1,3)>, each det=16/16=1 even unimodular rank 8 => E8 (unique, Minkowski-Siegel v83); they are swapped by EITHER single spinor conjugation (D5 or A3) and fixed by the simultaneous one => the mu_4 glue is unique UP TO THE SHEET Z2 - the two chiralities, matching exactly the two E8-extension modular invariants |chi_0+chi_{s,c}|^2 of v87. (b) The UNIQUE halfway extension {(0,0),(2,2)} has H_perp/H=Z2xZ2 with induced q={0,0,0,1/2} = the D8 discriminant form => SO(16)_1 is the ONLY intermediate of the tower (and is excluded by holomorphy, mu=4!=1). TOWER: carrier (mu=16) -> SO(16)_1 (mu=4) -> (E8)_1 (mu=1, sheet pair) - nothing else exists. CONSEQUENCE: with v89 (index 4 <=> holomorphy) and this row, Gate A is the BARE index statement 'the seam-Calderon inclusion has Jones index 4'; which extension it then is carries NO freedom. Seam-side identification stays [P]/[A]
Recorded status: Identity/Lattice [I]/[L] (exhaustive classification) + [P]/[A] (seam side)
Dependencies, status detail and source
Canonical status: Identity/Lattice [I]/[L]: extension tower = carrier -> SO(16)_1 -> E8 (sheet pair); no freedom left in WHICH extension
Dependencies: GATE.METRIC.06; GATE.METRIC.05; E8.GLU.01; v83; v87
Scripts: v92_glue_uniqueness.py
Location: tfpt_5_redteam;tfpt_1
Original CSV, line 166