Resummed clock
v124_resummed_clock.py · registry
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THE RESUMMED CLOCK (R1's bend acquires a closed form — the transfer spectrum IS the geometric resummation of a weight-linear clock): SPECTRUM READING [I] — the frozen transfer eigenvalues {1, (2/3)⁶, (1/3)⁶} are EXACTLY λₙ = (1 − n/N_fam)^{p₂} for n = 0,1,2 (p₂ = 6 = the hexagon size); CLOSED-FORM CLOCK [I]: rate(n) = −6 ln(1 − n/3) reproduces {0, Δ, 6 ln 3} and the v107 bend log₃∕₂3 becomes a one-line consequence; THE LINEARISATION CARRIES THE SHEET [I]: rate(n) = 2n + n²/3 + 2n³/27 + … — the one-loop term has slope exactly |ℤ₂| = 2 relative to the integer classical Ginsparg–Perry clock {0,−1,−2}: quantum clock = sheet-doubled classical clock + geometric tail; THE WALL AT N_fam [I]: rate → ∞ as n → 3 (pole at the family count) ⇒ the cusp ladder ends at n = 2 — the three-level transfer spectrum is forced by the clock itself; R1 re-sharpened [P]: derive −p₂ ln(1 − n/N_fam) from the near-Nariai one-loop at κ = 1/(3π), first checkpoint = linear-response slope |ℤ₂|; all spectra frozen (v54/v69/v95/v104/v107)
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