The published foundations of TFPT

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

GRAV.ENTROPIC.COMPRESS.01Numerical [N] (lattice exhibits) + Formal [E] (block identity) + [C] (retyped conjecture) + [O] (AP2 continuum statement open)

GRAV.ENTROPIC.SCALEFLOW.01Formal/Identity [E] (scale-flow + moment dictionary + closure identity, exact) + [C] (measure is TFPT input) + [O] (R^2 gate unchanged)

GRAV.ENTROPIC.LEGS.01Numerical [N] (high-precision lattice exhibits) + Formal [E] (single-scale corollary) + [C] (meeting-point reading) + [O] (both legs open)

SEAM.KRONHEIMER.01Reduction/citation [E]/[C]/[O] (graph->geometry bridge discharged to Kronheimer 1989; finite input data compiler-exact; premise transforms, stays open)

QGEO.MULTILOCAL.01Mechanism exhibit [E-num]/[N]/[C]/[O] (bedrock omega o rho = omega manifest at the 4-interval state level; multi-interval modular theory cited; raw-seam premise open)

FLAV.NUSCALE.02Candidate [P]/[N]/[X]/[C]/[O] (carrier normalisation collapses the trade-off; window bracketing; integer rung declined at 1-loop; decision computation named)

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)

HYP.PHI0.GEOM.01Reduction [E-num]/[E]/[O] (geometric side exact: t-independent rational twisted traces; value reduces to the one per-mark coupling rule)

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)

HYP.REWRITE.02Construction/uniqueness [E]/[O] (full spectrum from the unique lazy Z2-pair walk; split selection stays open)

HYP.REWRITE.03Construction/proof [E]/[O] (split forced by clock-ladder faithfulness; arity + clock derivation stay the open inputs)

FLAV.NUSCALE.04Enumeration/decision [E]/[O] (the 3/5 Clebsch door closed; negative result; window candidate stands)

FLAV.NUSCALE.05Candidate [C]/[N] + mechanism [O] (structured point inside the v481 window; scalaron-trace hypothesis typed, not derived; no seesaw closure)

SEAM.CCC.01Lattice [E] (modular-commutator ground-state measurement + controls + exact additivity) + [O] (continuum limit; SEAM.EQUIV.01 unchanged)

SEAM.MU.01Lattice [E] (parity census double-determined + exact 16-fold-way arithmetic + TEE fence) + [C] (KLM condensation step cited) + [O] (continuum; SEAM.EQUIV.01 unchanged)

P2.PARTITION.01Formal [E] (partition lemma + corollaries + negative controls + v53 sharpening, sympy exact, Wolfram-mirrored) + [C] (weight-typing postulate: splitting-type integrality, h^0 = 0 positivity, (U) sum rule; AX.P2.01 stays Axiom)

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)))