The published foundations of TFPT

ALPHA.QUILLEN.PROGRESS.02Second honest step / grounding [E]/[O] (a solvable 4D model exhibiting the nonzero a_4 conformal-anomaly order + the v391<->v342 connection; the headline target stays OPEN, not closed)

ALPHA.QUILLEN.PROGRESS.03Third honest step / grounding+reduction [E]/[C]/[O] (b1 = the U(1) a_4 heat-kernel coefficient via beta=a_4; residuals 1&3 collapse to one seam F-normalisation [C]; residual 2 the alpha^3 Chern level located but [O]; the headline target stays OPEN)

ALPHA.QUILLEN.PROGRESS.04Fourth honest step / metric-independence test + conditional level typing [E]/[C]/[O] (the pi-power test isolates a^3 as the unique pi^0/c3^0 metric-independent topological rung; conditional on the CS/eta reading the a^3 coefficient is an integer level, =1 the unit; the EM1 CS-boundary proof and the headline target stay OPEN)

HYP.PHI0.PUNCTURE.01Named target [E]/[O] (the phi0 puncture 48 c3^4 as the order-4 boundary Seeley-DeWitt contact term of the mu4 puncture, summed over Omega_adm=N_fam dim S+=48; a face of the seam boundary analysis, elevates v396's puncture residual to a citable target; no new gate)

FR.POLE.QED.01F_pole external [E]/[C]/[O]: the Koide source->pole transfer is a one-loop EM effect; Koide is rescaling-invariant (Q(c*m)=Q(m)) so the shift is flavor-split; the tree->pole gap 0.0022 is one-loop-EM-sized (=phi0/24 to 0.6%, =alpha/pi to ~5%), pole at 2/3 (IR attractor); a 1-loop QED per-lepton-log estimate shifts Koide by EM-loop order toward 2/3; the exact flow time t~2.84 is scheme-dependent external QED, only sized; F_pole stays [C], firewalled (v187) -- rate forced (v327/v82), flow external

QGAMB.NODEP.01No-Ambient-Dependency [E]/[C]: no frozen readout is computed from QG.AMB.01 -- it is a certification SINK (every dependent is a gravity-gate/QG row, no prediction), not a value source (script '-'; predictions computed by v3/v7/v9/v268, never an ambient-measure script), and its only predictive link is theta13's architectural 4D-QFT contract edge (coherence, not numerical); the gap margin Delta_eff~1.648>0 decouples its back-reaction (v337). v369 prose -> machine-checked DAG/script fact [E]; verdict [C], does NOT prove SEAM.EQUIV.01

DYN.TRANSFER.UNIVERSAL.01Single-flow reduction [E]/[C]: the four F_transfer flows are the ONE v238 recovery semigroup restricted to sectors (native gap 6 ln(3/2), native rates e^{-Delta}=(2/3)^6, b3=-7); F_pole=v99 generator at q=2, F_Boltzmann washout=that contraction (CP 4pi/3 native), F_QCD rate native -- only the ANCHORS (v_geo/C_p/M_R) external; F_relic's cosmological IC theta_i the one wall. Reduction not internalisation, firewall-clean; extends v383 static->dynamic

OVERDET.WITNESS.MAP.01Witness map [E]/[C]: disjoint grammars multiply, same-generator projections compress; the seven arithmetic witnesses are refined by v428 to COMPRESSION (facets of one (2,3,5)/E8 object, v236). The genuine multiplication is the multiply-forced inputs + foreign witnesses (alpha^-1~137); coincidence is expensive for the discrete core; does not by itself establish physics

OVERDET.WITNESS.RECLASS.01Witness re-classification [E]/[C]: v427's seven arithmetic witnesses are facets of ONE (2,3,5)/E8 object (v236) => compression, not seven multiplications. The genuine multiplication is the '8' forced four independent ways (rank E8, h(D5), phi(30), Milnor) + the foreign alpha^-1~137. Honest correction of v427 (consistent with v305/v236/v313)

ALPHA.QUILLEN.INFLOW.01Inflow level + embedding rigidity [E]/[C]/[O]: the a^3 coefficient = the COMPUTED bulk Chern |C| = 1 of the v367 collar (TKNN/ASS quantisation + Callan-Harvey inflow + APS/Witten eta=CS), replacing v435's minimality; the seam F-normalisation = the affine embedding index k_Y = 5/3 (Ginsparg 1987, (3/5)(41/6) = 41/10 = b1) -- zero independent content, a face of SEAM.EQUIV.01; one phase, two responses (c_- = 8, C = 1) feeding both named targets; ALPHA.QUILLEN.EXACT.01 stays [O]

ALPHA.QUILLEN.DETLINE.01Numerical [N] (finite Quillen shadow; gate unchanged)

GRAV.ENTROPIC.ACTION.01Formal/Numerical [E] (five exact identities + quantified gap) + [C] (compression conjecture, Q-target) + [O] (variational completion open)

GRAV.ENTROPIC.HODGE.01Formal/Identity [E] (operator-level Clifford/weights/enumeration, exact) + [C] (physical Q choice) + [O] (AP2 + R^2 unchanged)

GRAV.ENTROPIC.SCALARON.01Formal/Identity [E] (exact tensorial factors, scalaron mass, positivity witness) + [C] (verdict/surviving route) + [O] (AP2 + R^2 gate unchanged)

FLAV.NUSCALE.03Decision executed [E-num]/[C]/[X|P]/[O] (integer rung excluded as unstructured pin; 5/3 structure escape recorded and declined; window candidate stands)

SEAM.CONTACT.UNIT.01Unification/reduction [E]/[C]/[O] (the two analytic targets merge; contact unit = KMS seam unit, derived for the finite cycle sector; diagonal renormalisation + multiplicity matching stay open)

SEAM.CONTACT.UNIT.02Completion of the computable side [E]/[C]/[O] (diagonal zero at the KMS scale; closed-form resummation; multiplicity dichotomy; residual = the SEAM.EQUIV.01 face alone)

CELEST.WP1.01Formal/Identity [E] (exact Z4-orbifold/character/spin arithmetic, sympy, negative controls) + [C] (the named clock^2 = deck identification, verdict B) + [O] (celestial programme; SEAM.EQUIV.01 unchanged)

CELEST.SEAM.01Open (research contract; WP1-WP5d executed [E]/[C]/[L] via v492/v493/v495/v496/v497/v498/v500/v501/v504 -- WP5d: alpha (mu-index) + beta (split + strong additivity) executed via v501/v504, all three KLM ingredients witnessed on the lattice, continuum uplift stays [O] (Xu's theorem cited); WP5e alpha stage [E] via v502 + beta stage [E] via v505 (equivariant twistor skeleton; kill not fired) + gamma stage [E] via v508 (exchange no-go with certificate (0, 32, 72); negative result, kill not fired) + epsilon-2 stage [E] via v509 (level-from-flux: the one-level statement is now a THEOREM of clock invariance, the sector-counter dial #prim((E8)_k) = 1 <=> k = 1 pins the level; the PT/Z4 back-reaction stays [O]); + delta-2 stage [E] via v511 (the full-tensor ledger: collapse confirmed by innerness, the cubic d-symbol channel opens T3 with the weaker certificate psi = 64, relaxed solution c_d = 1920 = |W(D5)|); + epsilon-1 stage [E] via v514 (epsilon-1 executed via v514: the O(-2) bulk-axion slot is a construction (equivariant Penrose ledger), lambda-tilde = 6 pinned by three exact ledgers (Okubo / measure cancellation excluding 3 and 12 / flux), and the GH/A3 back-reaction step re-derives the v493 family and the Coxeter clock from geometry -- the quantised BCOV coefficient and the twisted channels stay [O] (M1-M3 preregistered)); WP5e-M1 DONE (v515: M1 executed via v515: the back-reacted Omega_N is closed-form on the A3 twistor family, all S3/Z4 periods are (2 pi i)^2-integral with the lockstep flux vector and clock covariance, and the lens geometry FORCES the source charge 4 = |mu4|; honest fence: integrality alone does not discriminate -- the discriminator is the lockstep phase structure (0/24 on the forbidden family)); WP5e-M2+M3 DONE (v516/v517: M2+M3 executed via v516/v517 -- the v514 fence M1-M3 is fully worked off: the twisted KS measure (declared completion reading, ch2-weighted) cancels the 32 T3 residual and delivers the psi = 64 slice without the cubic d-channel, and the a0 uplift couples to the centre count on four scales; what stays [O]: the BCOV measure question -- the delta-1 chain itself is DECIDED by v518 (kill under the derived measure, tension with v516 stated) -- and SEAM.EQUIV.TWISTOR.01); the global BCOV quantisation [O] (single remaining milestone -- the exchange sub-branch closed by v508, the epsilon-2 flux dial executed by v509, the delta-2 tensor ledger executed by v511, the epsilon-1 axion slot executed by v514, the M1-M3 back-reaction milestones executed by v515/v516/v517 (the v514 fence fully worked off); named remaining target: the BCOV MEASURE QUESTION -- the delta-1 chain is DECIDED by v518 (CELEST.WP5E.DELTA1.01: kill under the derived measure, all three testers fail; tension with v516 stated), so what remains is which of the two exact measures (the declared v516 completion reading vs the v518 derived chiral measure) is the true BCOV measure; the cubic GS term stays dissolved (psi = 64 delivered by v516, no branch fires under the derived measure, v518)))

CELEST.WP3.01Formal/Identity [E] (exact Okubo/Killing/lambda arithmetic for all 8 algebras, Fraction/sympy, sl4 negative control, look-elsewhere battery) + [C] (the convention typing of the 8 pi and sqrt 3; the alignment reading with the look-elsewhere caveat, verdict B) + [O] (celestial programme WP5; SEAM.EQUIV.01 unchanged)