The physical initial state contract

FTRANSFER.SK.RHO0.01

Original ledger classification: Open (research contract; mechanism executed [N]/[C]; FTRANSFER.GENERATING.01 covers equilibrium only) | Round-3 v1024 gives a finite internal candidate and algebraic boundaries [E/N]; global rho_0 and SK uniqueness remain Open [O].

Original claim text

THE SCHWINGER-KELDYSH INITIAL-STATE CONTRACT [O] (registered 2026-08-28, review wave 3; mechanism executed 2026-08-29). DEMAND: cosmological transfers (F_relic, F_Boltzmann, and any nonequilibrium 4D readout) need the pair (S, rho_0), not W[J] alone -- the Euclidean-cap / KMS initial state. TYPED CANDIDATE: the theta_i = 3 pi/5 saddle S_init = -kappa cos(5 theta - 3 pi) as the selection. ARITHMETIC: stationary points theta = (3+k)pi/5, the mu4 orientation picks k = 0. RELATION: FTRANSFER.GENERATING.01 covers EQUILIBRIUM correlators of W[J] only; this contract is the SK completion. KILL: the (S, rho_0) pair is inconsistent with the W[J] of TFPT4D.LATTICE.ACTION.01; the 3pi/5 saddle is not selected by mu4 orientation (a different k is forced); the Euclidean cap fails KMS. EXECUTED UPDATE (2026-08-29, review wave 4, v1000): mechanism executed -- KMS/FDT ~1e-17 on the exact Bohr grid, rho_0-dependence contrast 3.550e-3 vs static 1e-16, saddle 5-fold degenerate with 3pi/5 unique in the chosen mu4 lift [C]. Display stays [O]; no cosmological solve. EXECUTED UPDATE (2026-08-30, review wave 7, v1009): finite uniqueness closed -- constrained minimizer uniquely the normalized KMS compression (Klein), Hessian spectrum [3.76, 12.6], center dim 1, compression identity ~8e-17. TYPED: V1000_CONSEQUENCE_MISMATCH (compression kills the SK response, RMS ~1.5e-31 vs frozen contrast 3.550e-3) -- the proposed constraint set is too restrictive; CENTER_FLATNESS_PREMISE_FALSE (Umegaki keeps uniqueness with a nontrivial centre). Canonical formula needs a weaker admissible set. Display stays [O]. EVENING (2026-08-30, v1012): 8-candidate table ALL unique. DOUBLE DIAGNOSIS: hard sectors kill the SK response (~1e-31); ALL response-alive sets return exactly rho_KMS even WITHOUT mu4 -- the entropic-proximity selection principle is VACUOUS at finite level. Verdict NO_SET_WORKS. BINDING: the canonical state requires a different principle (e.g. Euclidean-cap / orientation-branch). Display stays [O]. MONDAY MORNING (2026-08-31, v1016): R4 seam-modular cap is the unique finite-level non-entropic selector (D_tr(KMS)=0.1434, SK response alive 3.038e-3, mu4-invariant, 3pi/5 saddle preserved). R1 vacuous, R2 response-dead, orientation-free mutant loses saddles. Caveat: the difference lives in the neutral spectator factor -- finite proxy. Display stays [O]. EXECUTED UPDATE (2026-09-05, v1024): FTRANSFER.PARENT.Z5CAP.01 constructs a finite 12D internal cap with gap 0.197423715893, but the five-cycle is chosen, the cap breaks D4 (residual 1.094700) and it vanishes on a large complement, so it is not a global rho_0 selector. The Z5 Weyl divisibility result is scoped to the unprojected dimension; the Gauss-projected physical dimension is uncounted. The relative commutant is a prime/irreducibility obstruction, not a dynamic-coupling no-go. Parent status stays Open [O]. ROUND-4 CURRENT: v1028 constructs a symmetric gap-one internal cap, but D4 leaves a2D invariant-vector space and the vacuum-preserving extension selects no unique full-parent state. Order-five unitary is not a Weyl pair or derived selector; [O] unchanged.

Original classification detail

Open [O] + mechanism executed (v1000): KMS/FDT ~1e-17; rho_0 contrast 3.5e-3 vs static 1e-16; 3pi/5 unique in the mu4 lift [C]. WAVE-7 (2026-08-30, v1009): finite uniqueness closed [E-finite]; V1000_CONSEQUENCE_MISMATCH + CENTER_FLATNESS_PREMISE_FALSE typed; weaker admissible set needed. Display stays [O]. | EVENING (2026-08-30 v1012): double diagnosis -- hard sectors response-dead, KMS-affine sets selection-vacuous; canonical state requires a different principle (e.g. Euclidean-cap/orientation-branch). Display stays [O]. | MONDAY MORNING (2026-08-31 v1016): R4 first viable non-entropic selector (D_tr 0.143 + response alive + saddle preserved; finite-proxy caveat). Display stays [O]. | ROUND3 2026-09-05: 12D cap is arbitrary and D4-breaking, not global rho_0; divisibility/commutant scopes explicit. Display stays [O]. | ROUND-4 CURRENT: v1028 constructs a symmetric gap-one internal cap, but D4 leaves a2D invariant-vector space and the vacuum-preserving extension selects no unique full-parent state. Order-five unitary is not a Weyl pair or derived selector; [O] unchanged.

Dependencies as recorded

FTRANSFER.GENERATING.01; FR.TRANSFER.01; TFPT4D.LATTICE.ACTION.01