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A registered result in its source context

Original ledger classification: Identity [I] (static pin, tower, clock spectrum, rate) + Physical [P] (quantum clock)

Recorded statement: THE CLASSICAL NARIAI CLOCK IS THE ANCHOR (third appearance) + honest (2/3)-test (executes the HOR.TRISECT.01 clock question at the classical level): STATIC PIN [I] - phi(rho) = rho solves d/drho[(1-L rho^2)phi'] = -2L phi EXACTLY on the…

Statement, assumptions and sources

Paper context: Horizon readouts

The exact identifier, original classification and full claim are available below.

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HOR.CLOCK.01

Original ledger classification: Identity [I] (static pin, tower, clock spectrum, rate) + Physical [P] (quantum clock)

Original claim text

THE CLASSICAL NARIAI CLOCK IS THE ANCHOR (third appearance) + honest (2/3)-test (executes the HOR.TRISECT.01 clock question at the classical level): STATIC PIN [I] - phi(rho) = rho solves d/drho[(1-L rho^2)phi'] = -2L phi EXACTLY on the dS2 static patch, so the exact SdS family itself pins the S^2-radius modulus mass m^2 = -2L = -|Z2|L (the Laplace-type form of the Nariai linearization is standard GR - Ginsparg-Perry 1983 / Bousso-Hawking 1997 - typed external; the VALUE is pinned internally). Horizon split linear in the canonical angle, coefficient 1/sqrt(N_fam) [I]. GINSPARG-PERRY TOWER [I]: (l(l+1)-2)L has exactly ONE negative mode -|Z2|L (l=0), zero modes l=1. THE CLOCK [I]: in Hubble units chi_clock(lambda) = lambda^2+lambda-2 = (lambda-1)(lambda+2) = THE ANCHOR QUADRATIC; eigenvalues {1,-2} = the distinct anchor roots; Nariai cubic = (t-1) x chi_clock - the anchor appears as configuration roots (HOR.NARIAI.01), curvature base (HOR.TRISECT.01) and clock spectrum; entropy-deviation rate = 2H = |Z2| x Hubble exactly [I]. HONEST (2/3)-TEST NEGATIVE for the classical clock: eigenvalues are integers (anchor roots), not (2/3)-powers; the 2/3-powers stay in the functional; the one-loop conversion curvature -> rate (quantum (anti-)evaporation) remains external [P] - the flavor-rate bridge is NOT closed; the seam variational principle now has exactly one missing object: the QUANTUM clock

Original classification detail

Identity: clock spectrum = anchor roots; quantum clock = the one [P]

Dependencies as recorded

HOR.TRISECT.01; HOR.ORIENT.01; HOR.NARIAI.01; ARCH.CORE.01 (anchor)

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Location recorded in the ledger

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Registered verification modules

  • v104_nariai_clock.pyRegistered verification module · registry
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    The CLASSICAL Nariai clock is the anchor (third appearance) + the honest (2/3)-test: static pin — φ(ρ) = ρ solves the dS₂ static-patch equation with m² = −2Λ = −|ℤ₂|Λ exactly (the exact SdS family itself pins the modulus mass; Laplace-type linearization = standard GR, Ginsparg–Perry 1983 / Bousso–Hawking 1997, typed external); Ginsparg–Perry tower (l(l+1)−2)Λ with exactly ONE negative mode; THE CLOCK in Hubble units: χ_clock(λ) = λ²+λ−2 = (λ−1)(λ+2) = the anchor quadratic, eigenvalues {1,−2} = the distinct anchor roots; Nariai cubic = (t−1)·χ_clock — anchor = configuration roots (v101) + curvature base (v103) + clock spectrum; entropy-deviation rate 2H = |ℤ₂|·Hubble exactly; HONEST (2/3)-TEST NEGATIVE for the classical clock (integer eigenvalues, not 2/3-powers) — the quantum clock (one-loop curvature→rate) is the one remaining [P] of the seam variational principle

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