The published foundations of TFPT

QGEO.SYM.01Conformal-symmetry/deck face of SEAM.EQUIV.01 [O] (downstream per v323) + [E] (equivariant uniformisation + the weakening)

QGEO.ENERGY.02Geometric premise [O] (energy-commutator proof target; sharper, non-circular IFF sub-claim 2)

FORM.QGEO.01Formal [F] (conditional theorem) + [O] (the seam-deck premise)

CMNORM.DUAL.01Identity (exact ring arithmetic)

E8.CHAN.01Identity (exact)

GATE.HOLO.02Lattice/CS realisation (exact) [E]/[O]

GATE.HOLO.03Lattice/topological-order (exact) [E]/[O]

DHR.SECTORS.01Numerical (finite MTC) [E]/[C]

DHR.MODULAR.01Numerical (finite MTC) [E]/[C]

ARCH.K3.01Lattice (K3/Kummer) [E]/[C]

QFT.MSC.01Numerical (assembly certificate) [E]/[C]/[O]

QGAMB.ROUTEII.01Lemma decomposition [E] (3/4 discharged + route coincidence) + [O] (unified lemma)

WITNESS.ECON.01Identity/Numerical [I]/[N] (structural firewall)

GOLD.ATOMS.01Identity/Lattice [E] (spectral) + [C] (quasicrystal direction)

SEAM.EQUIV.CONTINUUM.01Reduction [C]/[O] (continuum lemma narrowed + literature-anchored)

ALPHA.QUILLEN.EXACT.01Named target [E]/[O] (the Quillen determinant-line variation-exactness; a face of SEAM.EQUIV.01, elevates EM.WARD.01's residual to a citable target; no new gate; 2026-08-28: the v974 CHANNEL-SWAP face resolved at the finite level by mu4-character grading, v985; completeness wave: finite KMS rigidity-premise [E] v995, ln-2-rate detline shadow v996 -- continuum Bismut-Freed stays [O])

SEAM.GALOIS.NET.01Galois<->Net bridge / four-fold mu4 identity [E]/[C]: the seam mu4=Gal(Q(zeta5))=(Z/5)^x is the SAME cyclic Z/4 as the (E8)_1 glue <(1,1)> AND the discriminant disc(A3)=disc(D5)=Z/4 (D5 cyclic because rank 5 odd; D8 even=Klein control); only the carrier prime 5 gives (Z/p)^x=Z/4; glue order 4 => 16/4^2=1=E8 (vs Klein/order-2 => D8 det 4); cyclic Z/4 selects E8, Klein excluded -- the v419 Galois gearbox IS the holomorphic net's glue, a direct Galois->G_net bridge. Deck/divisor=Galois=discriminant=simple-current is a compression per v428 (one object read four ways), not four witnesses [C]

FORM.SEAM.RESIDUAL.01Formal [F] (Lean kernel): the G-block arithmetic (one-sided 8=|Z2|*intK/pi, reflection C->-C, c_-=8, MMST range 8<=8<=16, decoupled additivity, 248=8+240=120+128, 240=112+128, det K 1 vs 4, + v461 winding=|C|=1!=0 obstruction + v462 Fock counts 120/128/256 + v463 holomorphy selector forced dimV1=248=E8) all kernel-proved by decide; the two cited theorems MERGED into ONE combined axiom seam_realisation_theorem so seamResidualClosed depends on FOUR axioms (down from six); v464 one-particle rigidity is numerical; residual reduced to ONE realization axiom + ONE combined cited theorem; PLUS the v469 parallel peer-reviewed route seamResidualClosed' (invariant-level collar_invariants + crossedproduct_route_theorem; new kernel facts lr_locality_integer, glue_locality_integers, klm_holomorphic, sixteenfold_pin, all [propext only]); SEAM.EQUIV.01 stays [O]

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]

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)