The published foundations of TFPT

CELEST.WP5E.EPS1.01Formal/Identity [E] (exact slot/residue/GH arithmetic: equivariant Penrose ledger block by block d <= 6, character series P_m, Molien hypersurface relation degree 8, Okubo perfect square (6<x,x>)^2, measure chain mu-exact excluding 3 and 12, flux single-channel iff k = 1, GH centre dichotomy, period lockstep 4 pi t0 (i-1)(1, i, i^2), Coxeter clock from geometry, EH log ledger with asymptotic coefficient exactly 0, multipole selection rule m = 0 mod 4 -- sympy/Fraction exact, Wolfram-mirrored) + [C] (Costello's flat-PT matching lambda_g^2 E = A: the measure chain is CLASSICAL bookkeeping) + [O] (the quantised BCOV one-loop coefficient on PT/Z4; the twisted channels 32 T3 not covered by the bulk axion -- M1-M3 preregistered with success + kill criteria)

CELEST.WP5E.M1.01Formal/Identity [E] (exact residue/family/period/kernel arithmetic: Poincare residue three routes, cover factor 4 = |mu4|, closed twistor family XY = Z^4 + 4 t0^2 la^2 Z^2 - t0^4(1 - la^4)^2, CY-compatible clock lift Omega -> +Omega, period lockstep 2 pi i t0 (i-1)(1, i, i^2) with covariance Pi -> i Pi, BM kernel (2 pi i)^2 anchor + dK = 0 + scale degree 0, lens forcing N in 4Z, 12 conifold nodes on Z8 -- sympy exact, no floats, Wolfram-mirrored) + [C] (global patching of the local BM kernels on the resolved 3-fold; Hitchin small resolution; the CPS 'exceptional-curve branes = glue currents' dictionary) + [O] (M2: the twisted KS measure per sector; M3: the a0 uplift; the quantised BCOV coefficient on PT/Z4)

CELEST.WP5E.M2.01Formal/Identity [E] (exact weight/contact/table/control arithmetic: completion-weight identity w = 4h = -4 ch2 with no free scale, parameter-free locks (T5 = 0 any scale, 4:3 ratio, T3 budget => c = |mu4|), contact term two bases, per-sector Okubo squares 36<x,x>^2/det_j, total (5/4) x 36, certificate kills 32 -> 0 / 72 -> 0 / psi 64 -> 0, exchange-span remainder, mu-blind chain, all five controls -- sympy/Fraction exact, Wolfram-mirrored) + [C] (the DECLARED completion reading: loop = unphased sector trace with the same zero-mode measure -- supported by the delta-1 modular-completion finding, not derived) + [O] (the BCOV-integral derivation of the completion reading, delta-1b/1c/1d; SEAM.EQUIV.TWISTOR.01 unchanged)

CELEST.WP5E.M3.01Formal/Identity [E] (exact kernel/expansion/period/monodromy arithmetic: null-coordinate harmonicity for arbitrary kernels, residue V-ledger identity 1/(2r), kernel log coefficient 4 = |mu4| with first correction a0/eta^4 and exact m-grading, GLT tower p_{4k} = 4(-a0)^k with the n = 0 mod 4 selection rule, exceptional-locus log 4 log t0 + clock phase 4i, period response 1/4 integrating to monodromy i, a0-rigid node support and (2 pi i)^2 fluxes, all four controls -- sympy exact, Wolfram-mirrored) + [C] (the GLT dictionary eta_p log eta_p = the GH Kahler-potential kernel; Lindstrom-Rocek / Ivanov-Rocek) + [O] (the full nonlinear Kahler potential of the resolved A3 ALE; SEAM.EQUIV.TWISTOR.01 unchanged)

CELEST.WP5E.DELTA1.01DECIDED: kill under the derived measure, tension with v516 stated ([E] exact Weil/Q(zeta_8) algebra, loop words + koboundary defects + 1/960 phase arithmetic, ledgers, G = f1 f3, the decision table; [C] the f1f3/KS-weight identification + kernel-family convention + chi_k choice; [O] the BCOV-integral derivation that decides between the declared (v516) and derived (v518) measures -- since decided at probe level by v520 for the declared reading, residual [O] = the constructive w_m derivation; NO marker moves)

SEAM.EQUIV.MMST.01Conditional [C] (closed modulo cited theorems: the MMST/OS continuum existence, v336; every computable level pinned [E]; Lean FORM.SEAM.MMST.01)

SEAM.EQUIV.TWISTOR.01Open (research route [O]: the Costello-Li construction; preparation [E]/[C] via the CELEST.SEAM.01 work packages v492-v518)

WOIT.OS.TWISTOR.01Open (research contract)

WOIT.THETA.FREE.01Identity/Lattice (exact sympy + exact Cl(16); 40-digit gap-certified RP inertia certificates)

CELEST.WP5E.MEASURE.01DECIDED at probe level for the declared reading ([E] exact Weil/Q(zeta_8) algebra, exact invariant subspace, characters + 1/960 grid, ledgers, levelwise 4-design, Z2 anchor arithmetic, change-of-variables corollary, controls; numeric documented: transports 28+ digits, SVD memberships 1e-8/1e-3, certificates fresh tau, HM kernels 30+ digits; [C] the typed premises TP-1..TP-4; [O] the constructive BCOV derivation of w_m -- since DERIVED at probe level by v523, narrowing the [O] to the global BCOV integral beyond the fibre zero-mode factor; NO marker moves)

SEAM.BIT.RPBLIND.01Formal/Identity [E] (exact solveset censuses, exact Gram entries, exact Cl(16) implementers, 40-digit gap-certified inertia spectra, continuum axis elimination, precondition controls) + [C] (face #13 = a reformulation of the bit) + [O] (mark-decorated states / interacting A_hol); the bit stays the one [C] carrier input; NO marker moves

WOIT.BETA1.GSO.01UNDECIDED per the frozen preregistration ([E] exact Hermiticity witness + censuses, time-like reflection census, GSO 2-torsion identification, 40-digit gap-certified GSO-fixed RP certificates, exact Cl(16) Kramers restriction, Ramond/wrong-projection/site-cut/family-A controls; [C] contract precision (iii) -- prose only; [O] beta1 proper via beta2, kill tests live on A_hol); NO marker moves

CELEST.WP5E.WM.01Formal/Identity [E] (exact Q(i)/Q(sqrt2)/cyclotomic mode ledgers, Abel values, tensor-trace splitting, reflection-formula zeta determinants, Quillen arithmetic, delta-1f block constant terms, the full v516 chain, all controls -- sympy/Fraction exact, Wolfram-mirrored; numeric documented: Hurwitz/Lerch and stripped block limits at 40 digits) + [C] (the typed premises TP-REG/TP-Q/TP-NUM/TP-CH) + [O] (the global BCOV integral beyond the fibre zero-mode factor)

WOIT.BETA2.OS.01SUCCESS per the frozen preregistration, [C]-typed per contract precision (iii) ([E] exact Hermiticity/semigroup/square identities, exact clock spectrum {1, sqrt(2)-1}, exact wrap-artifact resolution and censuses, 40-digit gap-certified inertia/spectral certificates; [C] the precision-(iii) operationalisation of 'the clock acting unitarily'; [O] beta3 next, all seven kill tests live on A_hol); NO marker moves

SEAM.BIT.TWISTBLIND.01Formal/Identity [E] (Pfaffian-exact insertion machinery cross-validated three ways, exact integer incidence frame, exact congruence mechanisms, 40-digit gap-certified inertia/spectrum/energy/parity certificates) + [C] (each lifting is a construction choice, all tested) + [O] (the genuinely interacting A_hol with non-Pfaffian-reducible OS data); the bit stays the one [C] carrier input; NO marker moves

SEAM.CLOCK.SILVER.01STRUCTURE SUCCESS + CONNECTION KILL ([E] exact sympy Hankel/trig + 40-digit census); NO marker moves

SEAM.BIT.TWISTCLASS.01SUCCESS ([E] exact integer/symbolic + 40-digit certificates; [C] measurement sketch principle-only); the bit remains formal input; NO marker moves

SEAM.INT.FKTOY.01F1=KILL / F2=KILL / F3=ERFOLG ([E] exact Fraction/Clifford + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves

SEAM.STRADDLE.CONE.01V1=KILL / V2=ERFOLG ([E] exact integer/Fraction census + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves

DIAMOND.CENTER.QUOTIENT.01Identity [E] (exact integer linear algebra: fixed line, unimodular quotient, self-coding row sums, resolvent factorisation, honest uniqueness controls -- sympy exact, Wolfram-mirrored) + [C] (the Lie-dimension readings of the quotient ladder, audit-typed like v414) + [O] (full selector-stratum ablation)