Original ledger status
EM.WARD.01
EM Boundary Ward decomposition (Theorem C): F_U(1)=0 read as reduced boundary U(1) Ward identity in three terms - Maxwell alpha^3 + Calderon -2c3^3 alpha^2 (2=|Z2|) + transport -8b1 c3^6 log(1/phi_seam). Coefficient identities EXACT [I]: 8b1=(4/5)M=(4/5)(sumL+N_Phi)=164/5; seam exponent -5/4=-q(D5); transport power c3^6=C6 hexagon. Root reproduces alpha^-1=137.0359992 (v3). Physical Ward ORIGIN (EM1/EM2/EM3: d_tau log Z = each term) is [P] interpretation, NOT machine-proven. SHARPENED 2026-06-22 (v341/ALPHA.QUILLEN.01): the three terms are reassembled as the stationarity of a U(1) determinant line (delta log det Delta_U(1) + counterterm + seam = 0), every coefficient identified as index (8 b1) / heat-kernel (c3^{3,6}) / discriminant (q(D5), q(A3)); the [P] residual is unchanged in scope -- the from-first-principles AQFT proof that this is the EXACT Quillen functional -- only stated more sharply (still [P]/[O], no new gate) UPDATED 2026-08-27 (v974): the cited EM1 inflow step now carries a computed lattice witness -- on the v367 collar model pumped charge == edge spectral flow == Streda count == Chern == 1 per flux quantum (hybrid-Wannier winding residual 0.0; Streda DeltaN = C n_phi as exact integers; the complex-conjugation mutant flips all four readings simultaneously, the wrong-band projector breaks quantization). Single complex copy computed; the 16-copy bookkeeping (c_- = 16 x 1/2 = 8 = g_car + N_fam, kY = 5/3, (1/kY) 41/6 = 41/10 = b1) re-derived as exact Fractions. The physical Ward ORIGIN keeps its [P]/[O] scope -- nothing upgrades here.
Recorded status: Identity [I] + physical origin [P] (sharpened to a Quillen form by v341; to a heat-kernel origin by v342)
Dependencies, status detail and source
Canonical status: Identity [I] + physical origin [P]
Dependencies: EM.FP.01; v3; v341; v342
Scripts: v48_em_ward.py
Location: tfpt_1
Original CSV, line 70Original ledger status
EM.WARD.02
HEAT-KERNEL SHARPENING OF EM.WARD.01 (2026-06-22): derives the ORIGIN and STRUCTURE of the F_U(1) determinant-line terms from textbook Seeley-DeWitt/Gilkey heat-kernel coefficients, advancing the EM-Ward origin from [P] (conjectured) to [E] for the term STRUCTURE; honestly fences the rest. NO new gate (sharpens EM.WARD.01). [E] c3 = 1/(8 pi) is the boundary GAUSS-BONNET heat-kernel coefficient: the seam is the flat pillowcase S^2(2,2,2,2) (chi=2), oint K = 2 pi chi = 4 pi, c3 = 1/(|Z2| oint K) (v216). [E] the alpha^2 term is the GILKEY gauge-curvature coefficient: the U(1) Laplacian a4 contains 30 Omega^2/360 = (1/12) Omega^2 (Gilkey, Invariance Theory Thm 4.8.16), Omega = i alpha F => -(alpha^2/12) F^2, so an alpha^2 term in log det Delta_U(1) is FORCED -- the Calderon -2 c3^3 a^2 is the gauge-curvature (Quillen-curvature) piece, not an ansatz. [E] the c3-ladder {0,3,6} is arithmetic (step 3 = three channels; 6 = |R^+(A3)| C6 hexagon). [E] multiplicities forced: 2 = |Z2| (sheet), 8 b1 = (4/5) M = (rank E8) b1 (b1=41/10, v48/v159). [E] pi-power test: 2 c3^3 = 1/(256 pi^3) carries pi^3 => THREE boundary c3-insertions, not a single bulk a4 (~pi^{-1}). [C] the exact coefficient 2 c3^3 needs the seam F-normalisation. [O] the cubic alpha^3 Maxwell moment (a topological/Chern level, NOT a Seeley-DeWitt integral) + the full identification (this IS the seam U(1) zeta-determinant) = EM.WARD.01's residual, tied to SEAM.EQUIV.01. NOT closed. alpha^-1 stays [E] (v3).
Recorded status: Heat-kernel origin [E]/[C]/[O] (term structure [E]; exact value [C]; cubic moment + identification [O]; no new gate)
Dependencies, status detail and source
Canonical status: [E] the heat-kernel STRUCTURE (c3 = Gauss-Bonnet boundary coefficient; alpha^2 = Gilkey gauge-curvature a4 term; c3-ladder; multiplicities; pi-power); [C] the exact coefficient (seam F-normalisation); [O] the cubic Maxwell moment + the full determinant identification (= EM.WARD.01, tied to SEAM.EQUIV.01). Sharpens EM.WARD.01's origin from [P] toward [E]; no new gate.
Dependencies: EM.WARD.01; v48; v216; v3; v159
Scripts: v342_em_ward_heatkernel.py
Location: tfpt_1_architecture_e8
Original CSV, line 112Original ledger status
ALPHA.QUILLEN.01
THE ALPHA FIXED POINT AS THE STATIONARITY OF A U(1) DETERMINANT LINE (2026-06-22): reformulates the EM closure from 'a very cleverly built fixed point' into 'the stationarity of a named functional', identifying every ingredient as an index / heat-kernel coefficient / discriminant form -- the 'derive the FORM' step (external review). F_{U(1)} = a^3 - 2 c3^3 a^2 - (4/5) c3^6 M ln(1/phi_seam) = 0 written in Quillen form: [a^3 - 2 c3^3 a^2] (determinant-line variation) = [8 b1 c3^6] (anomaly counterterm) * [ln(1/phi_seam)] (seam response), i.e. delta log det Delta_U(1) + counterterm + seam response = 0. [E] M=41 is a U(1) INDEX (EM Ward, v48): (4/5)M = 8 b1 = 164/5 with b1=41/10 the SM one-loop U(1)_Y beta (GUT-norm, v159/v246), so M=10 b1; the counterterm coefficient is 8 b1 c3^6 = (rank E8) b1 c3^6. [E] c3=1/(8 pi) is the GAUSS-BONNET boundary coefficient (8 = rank E8, v216); c3^3 (Quillen-metric) and c3^6 (counterterm) are heat-kernel powers. [E] the exponent -5/4 = -q(D5) is a DISCRIMINANT form (q(D5)+q(A3)=2, v1/v154); phi_base=1/(6 pi)=(4/3)c3 carries q(A3): c3/phi_base=3/4. [E] delta_top=Omega_adm c3^4 (Omega_adm=48). [E] the Quillen split holds at the alpha^-1=137.0359992 root. [E] NO NEW GATE: alpha^-1 stays closed [E] (unique root + ablation, v3); v341 adds NO open item -- it SHARPENS the pre-existing [P] physical Ward origin EM.WARD.01 ('why THIS function') toward [E] by naming every coefficient. [O] the one still-open part IS EM.WARD.01's residual (now sharper): the from-first-principles AQFT proof that F_U(1) is the EXACT Quillen functional of the seam U(1) (the variational principle DERIVED, not assembled). Not a new gate; not closed.
Recorded status: Reformulation [E]/[O] (alpha = stationarity of a named U(1) determinant line; sharpens the existing [P] EM.WARD.01; no new gate)
Dependencies, status detail and source
Canonical status: [E] the coefficient identifications (8 b1 = (4/5)M; c3 Gauss-Bonnet; -5/4=-q(D5); c3/phi_base=q(A3)) + the Quillen-form split at the root + the 'no new gate' clarification (machine-checked); [O] the still-open part = EM.WARD.01's residual (the first-principles AQFT derivation of the functional). Sharpens v3/v48/EM.WARD.01 from fixed point to stationarity; does NOT open a new gate and does NOT prove the variational principle.
Dependencies: EM.WARD.01; v3; v48; v159; v216; v1
Scripts: v341_alpha_quillen.py
Location: tfpt_1_architecture_e8
Original CSV, line 443Original ledger status
ALPHA.QUILLEN.EXACT.01
Names the Quillen determinant-line VARIATION as a tracked [O] target (2026-06-23, review Point 10): delta_tau(log det_zeta Delta_U(1) + 8 b1 c3^6 log phi_seam)=0 on the determinant line over the mu4 seam moduli -- i.e. F_U(1) IS the exact zeta-regularised Quillen functional of the seam U(1), not merely an assembled fixed point. Elevates EM.WARD.01's residual (v341/v342) to its own citable target so the one remaining EM obligation is trackable separately from the seam-net identification, WITHOUT creating a second independent open problem (it is a FACE of SEAM.EQUIV.01). [E] the Quillen split holds at the root a^3-2 c3^3 a^2 = 8 b1 c3^6 ln(1/phi_seam) at alpha^-1=137.0359992 (F_U(1)=0 IS the stationarity, v341). [E] every coefficient is a named atom: 8 b1=(4/5)*41 a U(1) index, c3=1/(8 pi) the Gauss-Bonnet boundary coeff (c3^3,c3^6 heat-kernel powers), q(D5)+q(A3)=2 discriminant forms (v341/v48/v216). [E] the value alpha^-1=137.0359992168 stays closed (unique root+ablation, v3) -- only 'why this functional' is open. [O] THE TARGET: the from-first-principles AQFT/zeta proof of the variation. [C] FACE OF SEAM.EQUIV.01 (v336): the seam U(1) determinant line lives on the same holomorphic seam net, so once the net is (E8)_1 its U(1) sub-determinant is fixed -- not a second gate. No new number (reuses v341, Wolfram-mirrored). UPDATE 2026-07-14 (v484/SEAM.CONTACT.UNIT.01): the target's c3-ladder rule MERGES with HYP.PHI0.PUNCTURE.01 into one analytic step -- the contact unit c3-per-insertion is the KMS seam unit (v239), derived for the finite cycle sector; the remaining [O] is the diagonal zeta-renormalisation + multiplicity matching (41 = 10 b1). UPDATE 2026-07-14 (v485): the computable side is COMPLETE (diagonal zero at the KMS scale, closed-form mark determinant, 41 = Y^2-weighted count of the same 48 states); the target's remaining [O] is now EXACTLY its v382 typing -- the SEAM.EQUIV.01 face -- with no separate analytic unknown left. UPDATED 2026-08-27 (v974): both named faces now carry COMPUTED witnesses. The diagonal-zeta face is EXECUTED as the BFK gluing on the seam circle (gluing constant EXACTLY 2^-N, derived symbolically N = 1..4 at general lengths; jump matrix at KMS R_0 = 16 c3 circ(2,-1,0,-1) = (G_m|_marks)^-1; det'R_0 = 2^16 c3^3, glued product (2 pi)^2; the v485 scale channel reproduced exactly via the KMS unit) -- vs the v484 mark matrix there is NO global proportionality (kernels in SWAPPED mu4 channels), but the correspondence is channel-wise exact (same eigenbasis, |spec| {0,2,2,4}, doublet ratio 4/ln2 with c3 cancelling): the diagonal-zeta face is thereby SHARPENED to the channel-swap question. The finite Quillen identity is verified TWO-SIDED on the twist torus (Berry integral == Poincare-Lelong divisor integral == +1, difference an exact form, transition winding == Chern), typed conditional on the quasi-free rigidity premise (measured, not proven -- SEAM.STATE.RPMIXING.01). STAYS [O]: 'why this functional' is not closed -- the remaining content is typed as {rigidity premise} + {channel-swap question} + {continuum Bismut-Freed identification of the exact-form difference field}; alpha^-1 = 137.0359992168 re-anchored (unique root on the scanned window, split residual 6.4e-58 at 50 digits). EXECUTED NOTE (2026-08-28, completeness wave): the rigidity premise of the finite Quillen identity is now executed at the finite CAR level (v995: 33 mixing directions killed by KMS alone; covariance redundant; 196608 -> 0); type-III/continuum stays [O]. The finite-collar detline curvature converges exponentially to 2pi with rate ~0.6936 ~ ln 2 (v996) -- a numerical Bismut-Freed shadow, not the continuum theorem. STAYS [O]. Python-only / Wolfram mirror deferred. RELATIVE-DETERMINANT NOTE (2026-08-29, review wave 4): the correct object is the RELATIVE determinant Q(A) = log[det' Delta_A / det' Delta_{A0}] + 8 b1 c3^6 log phi(A); the BFK constant 2^{-4} is A/tau/alpha-INDEPENDENT at fixed cut number, so delta log 2^{-4} = 0 -- no physical compensation needed (consistent with COMPENSATION_INTERNAL + the reviewer's correction). Absolute normalization is fixed by the reference A0. Contract stays [O]. LATE EVENING (2026-08-30, v1014): finite restriction isomorphism verified (c_phase constancy 3.7e-16, conjugation covariance exact, C = W_bulk = W_seam = +1 / mirror -1); orientation fixes the conjugate branch (2 -> 1); the residual constant phase is fixed by the A0 reference normalization -- recorded. Continuum Bismut-Freed stays [O]. Contract stays [O].
Recorded status: Named target [E]/[O] (the Quillen determinant-line variation-exactness; a face of SEAM.EQUIV.01, elevates EM.WARD.01's residual to a citable target; no new gate; 2026-08-28: the v974 CHANNEL-SWAP face resolved at the finite level by mu4-character grading, v985; completeness wave: finite KMS rigidity-premise [E] v995, ln-2-rate detline shadow v996 -- continuum Bismut-Freed stays [O])
Dependencies, status detail and source
Canonical status: [E] the Quillen split at the root + named-atom coefficients + the value alpha^-1=137.0359992 (reused from v3/v48/v341, machine-checked); [O] the from-first-principles exactness proof (the named target); [C] it is a face of SEAM.EQUIV.01, not a second independent gate. A typing/registration of the pre-existing EM.WARD.01 residual, reusing v341's (Wolfram-mirrored) identities; introduces no new number. UPDATE (2026-08-28, external master-object review wave 2, v985): the channel-swap face is resolved at the FINITE level -- the deck swap r -> r+2 maps the jump |spectrum| [0,2,4,2] onto the mark pattern |[4,-2,0,-2]| exactly (odd swap fails), the graded det' difference is c3-free = log(ln2/4), and the channelwise unit ratio is uniform 4/ln2; finite KMS rigidity-premise executed [E] (v995: 33 directions killed; 196608 -> 0); ln-2-rate detline shadow [E-measured] (v996, numerical not theorem); continuum Bismut-Freed, type-III KMS uniqueness and the from-first-principles exactness of F_U(1) stay [O] (BFK 2^{-4} needs no physical compensation: relative det, 2026-08-29). | 2026-08-29: relative det Q(A)=log[det'Delta_A/det'Delta_{A0}]+8 b1 c3^6 log phi(A); BFK 2^{-4} A/tau/alpha-independent at fixed cut number (delta log 2^{-4}=0, no physical compensation). Stays [O]. WAVE-5 (2026-08-29): rigidity premise of SEAM.MMST.TYPEIII.CHARGED.01; no marker move. | LATE EVENING (2026-08-30 v1014): finite restriction isomorphism verified; orientation fixes the conjugate branch; the residual constant phase is fixed by the A0 reference normalization -- recorded. Stays [O].
Dependencies: EM.WARD.01; SEAM.EQUIV.01; v341; v342; v3; v48; v216; v336
Scripts: v382_alpha_quillen_exact.py, v985_quillen_channel_swap.py, v995_kms_subnet_rigidity.py, v996_gauge_grammar_kill.py, v1014_bridge_refinements.py
Location: tfpt_1_architecture_e8
Original CSV, line 445Established within the stated premises
finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation
The active original explicitly treats the three-term decomposition and coefficient identities as exact, retaining the unique alpha root. The same section retains EM.WARD.01/ALPHA.QUILLEN.EXACT.01 as the existing origin obligation for the actual AQFT/zeta determinant functional. Separately the old circle canonically gives Pi and det_F(1-qPi)=1-q. Its actual local EM response, relative Quillen norm and susceptibility exponent5/4 still require identification. This does not retract compiler identities or root uniqueness.
Scope: Source-reviewed status/type correction, not a new general nonderivability theorem or gate. P1/P2 remain accepted starting principles; being axioms is not an objection. The line is derived on the old circle, not an arbitrary vector to select again. v382 replay26October:6/6; literalTrue status checks do not prove open functional origin. Ledger Numerical and full physical status remain unchanged.
Required premises and original source excerpts
- Specified EM function with positive seam response
F(x)=x³−2c³x²+(4/5)c⁶M log(p+q(1−q)^(−5/4)), c=1/(8π), p=1/(6π), q=48c⁴exp(−2x), M>0; original budget M=41. The function and inputs are premises here.
premise:fixed-em-seam-function - Model results remain conditional
Calculations in a fixed E8 net, quotient, family packet, or readout apply only under their stated inputs and do not select those inputs.
premise:fixed-input-models-scoped - P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
premise:declared-p1-p2