The published foundations of TFPT

SEAM.AREACOEFF.01Identity/Lie [I]/[L] (structure) + [A] (residual k=c3/2)

LAMBDA.BRANCH.01Identity [I] + observational [N] + [P] consequence

ANCHOR.VGEO.01Identity [I] (ratios) + [A]/[O] (closed metrology: R_+ unit torsor; one calibration by dimensional analysis)

SEAM.AREACOEFF.03Identity [I] (chain derived) + [A] (the one isolated residual)

GATE.WOLFRAM.02Numerical (second path, extension verified 623/623)

GATE.METRIC.10Identity [I] (exact census) + [P] (scoping conclusion)

GATE.METRIC.11Identity/Lattice [I]/[L] (the extension theorem exact) + [P] (the seam-side identification)

QGEO.EMERGE.01Numerical [N] (emergence confirmation on the real DtN/state) + premise [O] (selector is carrier input)

FR.MUONG2.01Physical bridge KILLED: dated kill test [X] fired 2026-08-04 (exact value stays [E]; the [C] vertex identification is excluded in its present form -- bridge dissolved, compiler core untouched)

HOR.BHCORE.01Open/synthesis [O] (a [P]-typed structural reading; not load-bearing) + [E] (the underlying anchor/attractor atoms)

DIAMOND.SPECTRAL.01Identity (exact)

PS.NCG.ORIENT.02Numerical (NCG; honest status) [E]/[C]

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.WP5D.01Formal [E] (the exact arithmetic: Cartan dets, KLM/Longo-Rehren quotients, Sigma d^2, theta_v at nu = 16, machine identities) + Lattice/Numerical [L]/[N] (the Gaussian lattice witnesses, ED-validated to 1e-15: extensivity, the ln 2 plateau, the duality-asymmetry witness) + [C] (the continuum dictionary offset = ln index -- KLM/Longo-Xu/CHMP -- and the interacting condensation step) + [O] (continuum Haag duality / local normality / split of the quotient net = WP5d-beta; Costello-Li = WP5e; SEAM.EQUIV.01 unchanged)

CELEST.WP5DB.01Formal [E] (the exact algebra spans/indices, the PP identities with integer attainment, the Lambda^2-compound and parity machine identities, the index consistency) + Lattice/Numerical [L]/[N] (the deficit tables, the nome ladder, the power laws, the Klich-Levitov slope; Gaussian-exact, ED-validated) + [C] (the KLM dictionary: Longo-Xu bounded-deficit dichotomy, Longo split heredity, CHMP order parameters) + [O] (the continuum proof for the seam quotient net and the condensed (E8)_1 net -- Xu's orbifold theorem cited, not claimed; WP5e/Costello-Li; SEAM.EQUIV.01 unchanged)

CELEST.WP5E.BETA.01Formal/Identity [E] (exact equivariant arithmetic: Atiyah-Bott denominators/characters, per-sector Okubo decomposition with the rigid 32 T3 residual, index bridge f(m) = ch2(T_m) with the -78 defect, geometric level dials, axion-slot weight arithmetic -- sympy/Fraction exact, Wolfram-mirrored) + [C] (the dictionaries above) + [O] (the global BCOV quantisation = WP5e proper; SEAM.EQUIV.01 unchanged)

CELEST.WP5E.EPS2.01Formal/Identity [E] (exact CPS-skeleton/pairing/lockstep/sector arithmetic: S^3 period (2 pi i)^2 N, exceptional flux 2 pi N, contraction 2N, pairing enumeration 48 -> 2, fluxes (64, 60, 64), current count (240, 0, 0, 0), #primaries (1, 3, 5, 10, 15, 27), lockstep theorem det(A-1) = -4 with the 0/24 negative probe, k = 2 / SO(16) / A2 controls -- sympy/Fraction exact, Wolfram-mirrored) + [C] (the CPS dictionary itself on PT/Z4: their geometry is the C^2 blow-up with one (-1)-sphere and so(8) at negative level, not the A3 ALE -- typed as an analogy until the backreaction is computed) + [O] (the type-I B-model backreaction on PT/Z4 -- twisted Kodaira-Spencer measure, the A3 Omega_N; the same fence as v502 S5.7/v505)

CELEST.WP5E.DELTA1.01DECIDED: kill under the derived measure, tension with v516 stated ([E] exact Weil/Q(zeta_8) algebra, loop words + koboundary defects + 1/960 phase arithmetic, ledgers, G = f1 f3, the decision table; [C] the f1f3/KS-weight identification + kernel-family convention + chi_k choice; [O] the BCOV-integral derivation that decides between the declared (v516) and derived (v518) measures -- since decided at probe level by v520 for the declared reading, residual [O] = the constructive w_m derivation; NO marker moves)

CELEST.WP5E.MEASURE.01DECIDED at probe level for the declared reading ([E] exact Weil/Q(zeta_8) algebra, exact invariant subspace, characters + 1/960 grid, ledgers, levelwise 4-design, Z2 anchor arithmetic, change-of-variables corollary, controls; numeric documented: transports 28+ digits, SVD memberships 1e-8/1e-3, certificates fresh tau, HM kernels 30+ digits; [C] the typed premises TP-1..TP-4; [O] the constructive BCOV derivation of w_m -- since DERIVED at probe level by v523, narrowing the [O] to the global BCOV integral beyond the fibre zero-mode factor; NO marker moves)

SEAM.BIT.RPBLIND.01Formal/Identity [E] (exact solveset censuses, exact Gram entries, exact Cl(16) implementers, 40-digit gap-certified inertia spectra, continuum axis elimination, precondition controls) + [C] (face #13 = a reformulation of the bit) + [O] (mark-decorated states / interacting A_hol); the bit stays the one [C] carrier input; NO marker moves