The published foundations of TFPT

GRAV.SPIN2.UNITARITY.01perturbative graviton unitarity sector-by-sector (spin-2 ghost-free via the entire KMS form factor, spin-0 via GHP) [E]/[C]/[O]

SEAM.S3.LATTICE.01S3 realised as an explicit gapped chiral-Majorana lattice model (numerical Chern |C|=1, c_-=8, det K 4->1) [E]/[C]/[O]

SEAM.S3.INFLOW.01edge existence forced by the invertible bulk (anomaly inflow) -- realised non-gappable chiral edge on the lattice strip [E]/[C]/[O]

FR.POLE.SOLVE.01Koide source->pole: standard QED running EXCLUDED (wrong sign) -- the transfer is the non-QED 53/54 operator/Moebius generator [E]/[C]

FR.BOLTZMANN.SOLVE.01eta_B from the integrated BDP Boltzmann ODE at the frozen M1 -- near-hit (factor ~1.1) with no M_R dial [C]/[X]

FR.RELIC.SOLVE.01axion relic finite-T solve DECIDES the branch -- spine 3pi/5 lands on Omega_DM (in band), hilltop 170deg over-produces [C]/[X]

FR.QCD.BUDGET.01m_p/m_e uncertainty budget: the observed 1836.15 is inside the propagated +-7.5% (alpha_s, C_p) band; lattice-tightening is the kill [C]/[N]/[X]

OBSERVATORY.REGISTRY.01a status-typed CI over freeze_file.csv -- falsifiability complete + the live scorecard (theta13 flagged at 2.0 sigma) [E]/[N]

SEAM.S3.CENTRALCHARGE.01central charge c=8 from finite-size entanglement scaling of the lattice (chiral, c_-=8) [E]

SEAM.S3.E8CHARACTER.01the chiral c=8 content is (E8)_1 (248 currents, 1 primary) via the exact character + mu4/GSO promotion [E]

SEAM.S3.MODULAR.01torus GSD=1 / modular uniqueness -- the genus-1 holomorphy discriminator closes the v344 hard part [E]

SEAM.S3.RP.01reflection positivity (OS axiom) of the explicit collar verified by an EXACT positive-mixture Gram identity (symbolic PSD: M = V^T diag(1/K) V, sum of squares; eigenvalue check retained as diagnostic, T133 hardening); C7 then discharged via v369 [E]/[C]

FORM.SEAM.MMST.01Formal [F] (Lean kernel; closed modulo the cited MMST/Adamo theorems)

GRAV.KMS.HESSIAN.01the Stelle ghost = the Seeley-DeWitt truncation; resummation decouples it (root modulus -> infinity) => entire spin-2 form factor [E]/[C]

QGAMB.REDUNDANCY.01Ambient measure proved boundary-REDUNDANT (the holographic route); QG.AMB.01 reframed as a non-fundamental certification object [C]/[O] (conditional on SEAM.EQUIV.01 + BW)

E8.UNMAPPED.BANDWIDTH.01Bandwidth search [E]/[C]/[O] (forced set-level structure sum=128=spinor/product=|W|/exponents=totatives; subchain flagged; per-degree matches declined; no new physical hit; reconciles v66+v354)

E8.REVERSE.AUDIT.01Reverse anti-numerology audit [E]/[O] (3/8 Casimir invariants mapped, 5/8 hull overhead; economy not promiscuity; phi is unmapped structure not numerology)

E8.OTHERSIDE.AUDIT.01Sheet/deck reverse audit [E]/[O] (the double-cover 'other side' = degree-2 + the 128-spinor, forced-disjoint from the 5 unmapped degrees; the complement of v354/v355)

E8.DEGREE.LADDER.01E8 degree-ladder structure theorem [E]/[I] + [P] functorial residual (degrees = 6*spine U det-ladder, forced by 2,3,5; reclassifies v354/v355 overhead)

OVERDET.FLOOR.01Unconditional over-determination floor [C] (disjoint pieces only, compression removed; floor ~1e-10 vs v100 conditional 10^-30.7; bounds numerology only, firewall)