Ring resummation
v127_ring_resummation.py · registry
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THE CLOCK IS A LOG-DETERMINANT (the geometric tail is the standard ring/RPA resummation; the 'O(1) resummation' demanded by v107 is now TYPED): LOG-DET IDENTITY [I] — for a rank-1 insertion P (tr Pᵏ = 1): −ln det(1 − αP) = −ln(1 − α) = Σₖ αᵏ/k, so the resummed clock is EXACTLY rate = −p₂ Tr ln(1 − αP): p₂ = 6 identical one-loop ring towers, ONE PER HEXAGON SITE (= positive root of A₃), coupling α = the Mehta–Seshadri parabolic weight; RING LADDER [I]: the k = 1 ring is the CLASSICAL term (6α = |ℤ₂|n = the v104/v126 entropy rate), the k = 2 ring is the first quantum correction (1/3 at weight 1); partial sums converge to {Δ, 6 ln 3} monotonically from below; COUPLING CROSS-LINK [I, audit]: κ_seam = 8/(24π) = 1/(3π) = α₁/π — the seam coupling is the first parabolic weight over π; THE WALL = RING DIVERGENCE [I]: radius of convergence |α| < 1, divergence at α → 1 (n → N_fam) — the v124 wall is the standard RPA instability; R1 FINAL FORM [P]: 'the seam clock is the RPA determinant of one mode on six sites' — resummation type identified, derivation open
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