The published foundations of TFPT

ALPHA.QUILLEN.PROGRESS.01Honest attempt / reduction [E]/[O] (a solvable-model zeta-det mechanism + the reduction of ALPHA.QUILLEN.EXACT.01 to the named sub-target 'seam a_2 = 8 b1 c3^6'; the headline target stays OPEN, not closed)

ALPHA.QUILLEN.PROGRESS.02Second honest step / grounding [E]/[O] (a solvable 4D model exhibiting the nonzero a_4 conformal-anomaly order + the v391<->v342 connection; the headline target stays OPEN, not closed)

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)

ALPHA.QUILLEN.PROGRESS.04Fourth honest step / metric-independence test + conditional level typing [E]/[C]/[O] (the pi-power test isolates a^3 as the unique pi^0/c3^0 metric-independent topological rung; conditional on the CS/eta reading the a^3 coefficient is an integer level, =1 the unit; the EM1 CS-boundary proof and the headline target stay 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

CORRECTIONS.NUMERIC.01Numeric correction budget [E]/[C] (the typed budget v388 as actual first-correction magnitudes: fixed-point 0.227%, seam-gapped 8.78%/QG-capped 9.62%, exact-identity 0, external quoted -- a computed theoretical-uncertainty surface)

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.COUPLED.01Coupled hypergraph rewrite [E]/[O] (one local rule unifies carrier x family; joint attractor marks x e0; recovery (2/3)^6 after one hand; v324 fiber emerges as cusp readout; v299 growth unchanged) -- mechanism unified, phi0 + seed remain

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

HYP.PHI0.PUNCTURE.01Named target [E]/[O] (the phi0 puncture 48 c3^4 as the order-4 boundary Seeley-DeWitt contact term of the mu4 puncture, summed over Omega_adm=N_fam dim S+=48; a face of the seam boundary analysis, elevates v396's puncture residual to a citable target; no new gate)

RES.COXETER.SYMMETRY.01Structural lemma [E]/[C] (prime-2 necessary, not autonomous: the sheet involution has spectrum {+-1} and projector {0,1}, none in (0,1), so no prime-2-only attractor; reuses established atoms, no new number) -- closes the v394 open-question corollary

FORM.COXETER.PRIME2.01Lean formalisation [E] (no prime-2-only attractor: involution eigenvalues +-1, projector {0,1}, none in (0,1), while 2/3 is a contraction rate; axiom-pure) -- machine-proves the v409 corollary

FR.CLOCK.PROBE.01Clock probe of the frontier [E]/[C] (3 of 4 'external' scheme-numbers -- A_Lambda, Koide rate, axion spine -- land EXACTLY on the {2,3,5} clock; only the proton C_p is genuinely external; a falsifiable anti-numerology test)

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)

GRAV.NONLOCAL.01Nonlocal-gravity action contract [E]/[O] (Paper C: the entire form factor gives a ghost-free one-pole propagator whose IR projection is exactly the atom-scaled R+R^2; the entire-a assumption + perturbative-only stay [O]). Consolidates v304/v370/v380/v386, adds the IR-matching check

METROLOGY.CLOSURE.01Metrology closure [E]/[N]/[O] (Paper D: the final input set {a,pi,v_geo} -- 0 dimensionless dials + 1 unit; dimensional bookkeeping over all dimensionful observables; G-vs-Lambda over-determination 0.11%; v_geo theorem-forbidden). A metrology end-cap, no new derivation

FTRANSFER.SUITE.01F_transfer functor certificate [E]/[C] (Paper E: the four frontier sectors as one F_observable o F_threshold o F_RG with exact atom sources + kill-test coverage + the firewall; physical predictions stay conditional). A consolidation, no new number

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