A registered result in its source context
Original ledger classification: Identity [I] (exact rigidity + closed-form ratio + audit coefficient) + [P] (finite-weight absorption)
Recorded statement: DET-RATIO CANCELLATION EXACT WITHIN THE SdS FAMILY (the v131 step closed in the within-family sense): e2-RIGIDITY - the traceless SdS cubic (t^3-3t+2c) forces r_b r_c = 1 - Delta^2/3 EXACTLY (Delta = horizon split; no higher corrections);…
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HOR.CLOCK.12
Original ledger classification: Identity [I] (exact rigidity + closed-form ratio + audit coefficient) + [P] (finite-weight absorption)
Original claim text
DET-RATIO CANCELLATION EXACT WITHIN THE SdS FAMILY (the v131 step closed in the within-family sense): e2-RIGIDITY - the traceless SdS cubic (t^3-3t+2c) forces r_b r_c = 1 - Delta^2/3 EXACTLY (Delta = horizon split; no higher corrections); with the v132 anomaly zeta(0)|det' = -2/3 per sphere, det'(L_r) = r^{4/3} det'(L_1), so the two-sphere non-zero-mode determinant ratio against Nariai is det'_n/det'_N = (1 - Delta^2/3)^{4/3} in CLOSED FORM: NO first-order term in the split (d/dDelta|_0 = 0 exactly) - v131's '1+O(deficit)' DERIVED from e2-rigidity + the established anomaly, not assumed. DEFICIT FORM (audit): eps = 1-c = (3/8)Delta^2 + O(Delta^4) => ratio = 1 - (32/27) eps + O(eps^2), coefficient 32/27 = |mu4|(|Z2|/N_fam)^3 = 4(2/3)^3 (the v103 canonical curvature x glue order; audit-typed). HONEST SCOPE [P]: the finite-weight comparison (S_n/S_dS in {1,2/3,1/3}) still runs through the v132/v133 anomaly budget - a naive global-rescaling reading would shift the Born exponent 6 -> 14/3 (not an atom), so the absorption must proceed via the Hubble-unit conversion (v132's reading); the frozen transfer spectrum is untouched
Original classification detail
Identity [I]: within-family det-ratio cancellation derived; absorption obstruction stated sharply
Dependencies as recorded
HOR.CLOCK.07; HOR.CLOCK.08; HOR.CLOCK.09; HOR.CLOCK.10; v101; v103
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- 2026-06-12 (R1–R5 attack round: four residual classes sharpened, v141– v144)Research changelog; TFPT — Introduction and reading guide
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- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- 2026-06-12 (external review integrated: [formula in source] typing, marker migration, website parity)Research changelog; TFPT — Introduction and reading guide
- 2026-06-12 (R1–R5 second round: every class at its floor, v145– v148)Research changelog; TFPT — Introduction and reading guide
- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Front matter / supportHorizon readouts
Registered verification modules
- v144_detratio_family.pyRegistered verification module · registry
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det-ratio cancellation (R1): r_b·r_c = 1−Δ²/3 exact (e₂-rigidity) ⇒ det′-ratio = (1−Δ²/3)^{4/3}: no first-order term in the horizon split; deficit coefficient 32/27 = |μ₄|(2/3)³; the finite-weight absorption stays [P] with its obstruction stated sharply (the bend since shown det′-clean, v147)
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