The published foundations of TFPT

SEAM.EQUIV.ONEPARTICLE.01one-particle rigidity + scaling limit [E]/[C]: via Araki self-dual CAR (state<->symbol P, cited) the gapped ground state is the UNIQUE quasi-free realisation (P^2=P), its kernel is Cauchy (~1/N, limit exists), and the limit is the c=1 Dirac CFT (EE c-fit ~1 => c_-=16*1/2=8); Shale-Stinespring makes the Bogoliubov map implementable, upgrading R1 from a bald axiom to an audited [C]; with v463 the residual is entirely certification, zero open internal mechanism; SEAM.EQUIV.01 stays [O]

FLAV.THIRDGEN.PATTERN.01Numerical [N]/[C]/[O] (candidate pattern; record of v84 untouched)

FLAV.DM2RATIO.01Numerical [N]/[C]/[O] (candidate relation; informal pi phi0 table heuristic superseded as comparator)

SEAM.EQUIV.CROSSEDPRODUCT.01Net-level crossed-product certification + R1 invariant reduction [E]/[C]/[O]: h_s = 16/16 = 1 in Z => the LR locality criterion holds, the Z2 crossed product SO(16)_1 -> (E8)_1 is a LOCAL index-2 extension by 1995-2001 PEER-REVIEWED subfactor theory (LR/Boeckenhauer/BE/KLM), AGT/AMT demoted to second witness; mu4 glue h(J^k)={1,1,1} parallel; R1 reduced to computed invariants (FHS |C|=1, nu=16, c_-=8, the Kitaev-E8 16-fold-way class); SEAM.EQUIV.01 stays [O]

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]

SEAM.EHMODEL.04Numerical [I] (lattice determinants vs exact conical constants) + [A/O] (continuum leg + anchor stay open)

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)

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)