The published foundations of TFPT

SEAM.TAU.FLAG.01Formal/Identity [E] (complete V4/D4 symmetry census, flag/arc orbit arithmetic, odd-split and K3-indicator closed forms, twist mode identity, H4 Schur rigidity, negative controls -- sympy exact + mpmath 30 digits, Wolfram-mirrored) + [C] (the symmetry-lift bit itself: flag transitivity stays a postulate; the gain is the FORM, not a derivation)

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.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)

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)

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

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.THERMAL.KMS.01SUCCESS ([E] exact sympy/cyclotomic + 40-digit Tomita certificates; [C] bridge reading typed; [C-5] non-gating clock-vs-modular findings); 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)

COX.STAGEA.TENSOR.01Identity [E] (exact order/charpoly/trace arithmetic + honest kill-scope + coprimality controls -- sympy exact, Wolfram-mirrored) + [C] (the identification with the E8 Coxeter clock, as v223/v314) + [O] (the flip-atlas intertwiner COX.FLIP.INTERTWINER; Stage B metrization)

E8.DEGREE.MODULAR.01Identity [E, audit-only] (exact integer/q-series arithmetic incl. the j-series recomputation and all controls -- sympy exact, Wolfram-mirrored); explicitly NON-exclusive (D16 control passes); the fingerprint feeds no derivation (no-free-pattern rule honoured)

FTR.DISC7.NORM.01Identity [E] (exact norm/integrality/translation/discriminant arithmetic + negative controls -- sympy exact, Wolfram-mirrored) + [E, audit] (split prime 2, Heegner class number) + [C]/[O] (the arithmetic F_transfer frame: common Moebius action of the four solvers = preregistered next test; GATE.FTRANSFER unchanged)

CP.FIBER.PIN.01Identity [E] (exact theorems and certified character accounts with mutation controls -- Euler factorisation on fully generic homogeneous blocks, the one-generator bracket enumeration, the character split and the q_t continuum, the single-sine lemma with the crystallographic equivalence, the anchor tuple at 40 dps) + [C] (the Weyl 1946 FFT class boundary; the selection conditional on the Jarlskog anchor; the deck column a declared model); R1 decided, R2 selected, no marker moves