The published foundations of TFPT

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)

E8.DEGREE.JOINT.01E8 degree joint-lock [E] (the two structural integers g_car=5, N_fam=3 = unique roots of x^2-8x+15 with coeffs rank E8=8 and h/2=15; all E8 combinatorics fixed by its degrees; consolidation of v6/v66/v355/v431, no new mining)

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)

OVERDET.FLOOR.02Assumption-minimal counting floor [E]/[C] (the alpha census 1/94500 = 4.40 sigma with no subjective probability; monotone concession ladder; independent of v432's subjective pieces; honest 5-sigma gap; hardens OVERDET.FLOOR.01)

TFPT.SELFLOOP.01Capstone rethink [E]/[A]/[O] (a unique self-consistent loop with zero free dials; pi a fixed geometric constant; the one residual is the continuum closure; the fork is philosophical not numerical)

TFPT.IRREDUCIBLE.01Synthesis/inventory [E]/[O] (both axioms bootstrap-forced; irreducibles = framework + pi; the framework is the tested meta-axiom)

SEAM.EQUIV.BOOTSTRAP.01Correction [E]/[O] (inputs are bootstrap-forced fixed points; g_car=5 IS the icosahedral 5 of h(E8)=30; golden emergent from the mu4-glue; residual = the physical continuum realisation)

SEAM.EQUIV.GOLDEN.01Honest negative/clarification [E]/[O] (the raw seam does NOT carry phi; golden is the icosahedral input; L2 = 'is g_car=5 a pentagon or a count?')

SEAM.EQUIV.RIGID.01Route B / reduction [E]/[O] (rigidity + the icosian-ring identity reduce L2 to one question: does the raw seam carry the golden ratio?; NOT closed)