The published foundations of TFPT

HYP.REWRITE.01Construction/proof [E]/[O] (cusp weight from a minimal rewrite)

FORM.QGEO.BW.01Formal

QGEO.OSGAP.01Reduction [E]/[O] (OS gap = transfer gap + single premise)

FORM.CARTAN.DET.01Formal

SEAM.EQUIV.UNIFY.01Synthesis/reduction [E]/[O] (one keystone theorem; QGEO.SYM corollary; QG.AMB decoupled)

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

DECOUPLING.THEOREM.01Theorem [E] (factorization through the gap => ambient-measure independence)

ALPHA.QUILLEN.01Reformulation [E]/[O] (alpha = stationarity of a named U(1) determinant line; sharpens the existing [P] EM.WARD.01; no new gate)

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])

DYNAMICS.UNIVERSAL.01Universal synthesis [E]/[C] (every sector = a gapped operator with a unique attractor + spectral gap => parameter-free; extends v303 theory-wide; 3 gaps computed, the cross-sector identification [C])

COXETER.PRIME2.01Prime-2 facet of the Coxeter clock [E]/[C] (h(E8)=30=2*3*5; one quadratic facet field per prime, ramified at it; the prime-2/Gaussian/Z4-seam facet completes v383's golden and family facets)

ALPHA.QUILLEN.PROGRESS.03Third honest step / grounding+reduction [E]/[C]/[O] (b1 = the U(1) a_4 heat-kernel coefficient via beta=a_4; residuals 1&3 collapse to one seam F-normalisation [C]; residual 2 the alpha^3 Chern level located but [O]; the headline target stays OPEN)

SEAM.S3.SCALINGLIMIT.01Scaling-limit convergence evidence [E] (the finite-size central charge converges to c=8 and Richardson-extrapolates there -- the existence-relevant observable) + the abstract existence stays [O] (cited MMST v336); an honest attack that strengthens, does not close

COXETER.ATOMS.01Clockwork coherence [E]/[C] (Coxeter primes = anchor atoms = facet fields; chi=3^6/(3^6-2^6); both dynamic rates carry prime-2; 30=5x6) -- a bird's-eye re-reading, no new number

HYP.PHI0.01phi0 leading term [E]/[C]/[O] (phibase = F/(g_car N_fam) c3 = 1/(6 pi); F/h = |Z2|/N_fam; Gauss-Bonnet consistent; puncture 48 c3^4 still analytic) -- combinatorial reinterpretation, not full phi0 closure

SEAM.RIGIDITY.01Seam State Rigidity contract+evidence [E]/[O] (Paper A: the G_net keystone as one named theorem -- RP-definability hinge + band-limited mu4-character core swept N=4..64 + holomorphy=>(E8)_1; the one residual = full-L^2 / intrinsic BW). NOT a closure of SEAM.EQUIV.01

GRAVITY.COMPLETE.01Gravity-completeness accounting [E]/[C]/[O] (Paper B: the explicit verdict = local parameter-free equation + ambient redundancy; O_phys subset A_Sigma over 5 readout classes; residual = SEAM.EQUIV.01 + intrinsic BW, no new gate)

ARITH.HULL.01Arithmetic hull [E]/[C] (the three facet fields compose to K=Q(i,sqrt-3,sqrt5): degree 2^3=8=rank E8, Galois (Z/2)^3, 7 subfields = 4 imaginary (|mu4|) + 3 real (N_fam), ramified only at {2,3,5}; 2^omega(h)=rank is E8-special) -- a synthesis, no new number

E8.CMDUAL.01E8 character CM-duality [E]/[C] (chi_E8(i)=12 vs chi_E8(omega)=0: the (E8)_1 character maximal at the seam tau=i, zero at the family tau=omega; the two are the only elliptic points so the values are forced) -- the seam/flavor rigidity duality, extends v282

SEAM.EQUIV.02Dual keystone at tau=omega [E]/[C]/[O] (the family/flavor sector as the order-3 Eisenstein/A2 face: chi_E8(omega)=0, A2 Cartan det 3=N_fam reads R in E6xA2 with det R=8=dim A2, delta=the tau=omega CM phase, cusp weights=the order-3 deck; dual to the seam=(E8)_1 at tau=i). A named contract, NOT a closure