A registered result in its source context

FTRANSFER.KMSCOSET.01

Original ledger classification: Theorem-grade [E] sympy-exact derivation chain + blind classification with the non-circularity of the classifier gated on its own source; completes the fiber classification of the executed clock contract; no marker move (Python-only per GATE.WOLFRAM.02).

Original claim text

the coset assignment of the fibered clock functor is a THEOREM from KMS/modular typing (18/18 checks incl. the three must-fire controls, ~3 s; discovery probe ftransfer_kms_coset_probe.py, 2026-08-05, verdict KMS-COSET-THEOREM; frozen before the first run). THE THEOREM: S_transported = -(ln lambda)^2/2 with lambda the PGL2 multiplier of the flow's time-1 holonomy per clock e-fold -- the coset is COMPUTED from the typing datum lambda, never case-inspected. THE CLASSIFIER uses NO Schwarzian and NO derivative of any order (non-circularity gate on its own source): (i) the holonomy grounded as an exact functional identity y(x+1) = T(y(x)), (ii) the PGL2 class of T (scalar -> degenerate; parabolic -> autonomous, lambda = 1; else hyperbolic candidate), (iii) the detailed-balance multiplier cross-ratio m(x) -- the discrete KMS signature -- exactly constant -> modular with lambda = m. DERIVATION CHAIN sympy-exact: Lemma A {M(e^{ax}), x} = -a^2/2 identically for GENERIC Moebius M; Lemma B {M(x), x} = 0; Lemma C -a^2/2 = -Delta^2/2 iff a = +-Delta, affine dictionaries change nothing. BLIND PROTOCOL: the four deployed clock charts classify F_pole/F_Boltzmann MODULAR with |ln lambda| = Delta = 6 log(3/2) exactly, F_QCD AUTONOMOUS (parabolic), F_relic DEGENERATE; unblinding: predicted cosets == transported Schwarzians EXACTLY (sympy zero) -- the fiber classification of the executed contract (v777, FTRANSFER-FIBERED-CARRIES) is now DERIVED. CONTROLS: C1 fake-KMS witness caught (functional identity fails AND the ratio is non-constant); C2 affine reparametrization x -> -x + c leaves typing and |ln lambda| unchanged; C3 the v578 Moebius clock t = e^{Delta sigma} flips the QCD chart to modular and the theorem PREDICTS -Delta^2/2, confirmed by the transported Schwarzian -- the K1-duty transplant as the positive case. Completes the three-probe chain executor -> fibered groupoid -> coset theorem: the CONTRACT.F.01 fibered refinement's clock-fiber classification is a derived statement. Freeze guards: prereg YAML + both data tables byte-identical. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.

Original classification detail

KMS-COSET-THEOREM: S = -(ln lambda)^2/2 from the time-1 PGL2 holonomy multiplier per clock e-fold; classifier Schwarzian-free and derivative-free (non-circularity gated); blind assignment F_pole/F_Boltzmann modular (|ln lambda| = Delta), F_QCD autonomous, F_relic degenerate; unblinding exact (sympy zero); controls fire incl. the Moebius-clock positive case; the executor -> groupoid -> coset chain whole; no RH statement.

Dependencies as recorded

CONTRACT.F.01; FTRANSFER.CLOCKS.01; v777; v578; v99; v425