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A registered result in its source context

Original ledger classification: Identity [I] (heat-kernel arithmetic + numerical continuation) + Physical [P] (full budget)

Recorded statement: THE DET-RATIO ANOMALY IS THE KOIDE CONSTANT (the HOR.CLOCK.08 'last step' acquires its first exact invariant): (1) SPECTRAL SETUP (re-pinned): the Ginsparg-Perry sphere operator on the unit S^2 is L = -Delta - 2 (the -2 = -|Z2| = the…

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Paper context: Horizon readouts

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HOR.CLOCK.09

Original ledger classification: Identity [I] (heat-kernel arithmetic + numerical continuation) + Physical [P] (full budget)

Original claim text

THE DET-RATIO ANOMALY IS THE KOIDE CONSTANT (the HOR.CLOCK.08 'last step' acquires its first exact invariant): (1) SPECTRAL SETUP (re-pinned): the Ginsparg-Perry sphere operator on the unit S^2 is L = -Delta - 2 (the -2 = -|Z2| = the HOR.CLOCK.01 modulus mass); eigenvalues mu_l = l(l+1) - 2 = (l+2)(l-1), degeneracy 2l+1; kernel = the 3 zero modes (l = 1); one negative mode (l = 0). (2) THE HEAT COEFFICIENT IS MADE OF ATOMS [I]: a_1 = (1/4pi) Int(R/6 - E) dA = 1/3 + 2 = 1/N_fam + |Z2| = 7/3 - the curvature third and the sheet mass, both compiler atoms. (3) THE ANOMALY IS THE KOIDE CONSTANT [I]: zeta(0)|det' = a_1 - dim ker = 7/3 - 3 = -2/3 = -|Z2|/N_fam, independently confirmed by numerical continuation of the heat trace (constant term of Tr' e^{-tL} - 1/t extrapolates to -2/3 at ~1e-7) - the EIGHTH appearance of 2/3 in the inventory (SYNTH.INVENTORY.01 counted seven) and the first as a SPECTRAL anomaly. (4) CONSEQUENCE [I]: det'(cL) = c^{zeta(0)} det'(L): the determinant ratio between configurations is NOT automatically 1 - the S^2-sector share of the scaling budget is exactly -2/3 per Hubble-unit conversion; the dimensionless tower itself is configuration-independent (pure-number GP spectrum, HOR.CLOCK.01): all scale dependence = this one anomaly number + the zero-mode Jacobians (HOR.CLOCK.08). (5) THE BUDGET STATEMENT [P] (recorded, not claimed): show the FULL zeta(0) budget of the 4d Nariai fluctuation problem (dS2 sector + gauge/ghost sectors + this S^2 sector) vanishes or is absorbed into the established power law; the S^2 share is pinned exactly at -|Z2|/N_fam - nothing claimed about the total

Original classification detail

Identity: zeta(0) of the det'-operator = -2/3 = -|Z2|/N_fam (a1 = 1/N_fam + |Z2| = 7/3); det-ratio question = one zeta-budget statement; S^2 share pinned

Dependencies as recorded

HOR.CLOCK.08; HOR.CLOCK.01; SYNTH.INVENTORY.01 (2/3 inventory); HOR.NARIAI.01

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Registered verification modules

  • v132_detratio_anomaly.pyRegistered verification module · registry
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    THE DET-RATIO ANOMALY IS THE KOIDE CONSTANT (the v131 'last step' acquires its first exact invariant): SPECTRAL SETUP — the Ginsparg–Perry sphere operator on unit S² is L = −Δ − 2 (the −2 = −|ℤ₂| = the v104 modulus mass), eigenvalues (l+2)(l−1), kernel = 3 zero modes (l=1); THE HEAT COEFFICIENT IS MADE OF ATOMS [I]: a₁ = R/6 − E = 1/3 + 2 = 1/N_fam + |ℤ₂| = 7/3; THE ANOMALY IS THE KOIDE CONSTANT [I]: ζ(0)|det′ = a₁ − dim ker = 7/3 − 3 = −2/3 = −|ℤ₂|/N_fam, independently confirmed by numerical continuation of the heat trace (~1e−7) — the EIGHTH appearance of 2/3 and the first as a SPECTRAL anomaly; CONSEQUENCE [I]: det′(cL) = c^{ζ(0)} det′(L) — the determinant ratio between configurations is NOT automatically 1: the S²-sector share of the scaling budget is exactly −2/3 per Hubble-unit conversion, while the dimensionless GP tower is configuration-independent; BUDGET STATEMENT [P]: show the FULL 4d ζ(0) budget (dS₂ + gauge/ghost + S² sectors) vanishes or is absorbed — the S² share is pinned exactly, nothing claimed about the total

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