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A registered result in its source context

Original ledger classification: Identity [I] (dimensional bookkeeping exact) + [A] (the anchor stays declared)

Recorded statement: THE R3 NORMALISATION IS THE DIMENSIONFUL ANCHOR (not a separate open item; SEAM.THEOREM.01's residual list shrinks to the kernel premise alone): (1) THE COEFFICIENT IS A LOG-RATIO [I] - the conical part of the massive 2d determinant is…

Statement, assumptions and sources

Paper context: Origin Theory

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SEAM.EHMODEL.03

Original ledger classification: Identity [I] (dimensional bookkeeping exact) + [A] (the anchor stays declared)

Original claim text

THE R3 NORMALISATION IS THE DIMENSIONFUL ANCHOR (not a separate open item; SEAM.THEOREM.01's residual list shrinks to the kernel premise alone): (1) THE COEFFICIENT IS A LOG-RATIO [I] - the conical part of the massive 2d determinant is zeta_corner(s) = C(gamma) (m/mu)^{-2s} (the zeta-scale mu enters with the dimensionful mass m), so Delta log det' = 2 C(gamma) ln(m/mu) and k = ln(m/mu)/(12 pi); the bare ln m is scale-ambiguous, only m/mu is physical; (2) PINNING k FIXES A PURE RATIO [I]: k = c3/2 = 1/(16 pi) <=> ln(m/mu) = 12 pi c3/2 = 3/4, i.e. m/mu = e^{3/4}; (3) THAT RATIO IS THE INDUCED-GRAVITY ANCHOR [I]: in d=2, 1/(16 pi G) = k = ln(m/mu)/(12 pi), so fixing m/mu IS fixing 1/G in seam units (1/(16 pi G)|_{G=1} = c3/2 exact) - the v68 statement verbatim, the one declared dimensionful anchor; R3's normalisation is that anchor in dimensionless form; (4) ANCHOR COUNT UNCHANGED [I]: v_geo (flavour, v78), 1/G (gravity, v68) and m/mu (seam EH normalisation) are ONE anchor in three readings - the irreducibles stay {one scale, pi}. AUDIT [recorded, NOT promoted]: the required log-ratio is 3/4 = q(A3) = N_fam/|mu4| - the target VALUE the anchor takes in seam units, NOT a derivation (a dimensionless anchor has no compiler-forced value). CONSEQUENCE: SEAM.THEOREM.01 stays open [A] but its residual is now precisely the kernel-identification premise alone - the normalisation has merged into the standing anchor

Original classification detail

Identity [I]: R3 normalisation = the v68 anchor in dimensionless form; residual = kernel premise alone

Dependencies as recorded

SEAM.EHMODEL.02; SEAM.EHMODEL.01; SEAM.KHALF.01; v68; v78; v150

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Registered verification modules

  • v152_norm_is_anchor.pyRegistered verification module · registry
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    R3 normalisation IS the dimensionful anchor: k = ln(m/μ)/(12π) — ln m is scale-ambiguous, only m/μ is physical; k = c₃/2 ⟺ m/μ = e^{3/4} is the induced-gravity anchor 1/G (v68), not a separate gap; the irreducibles stay {one scale, π}; audit: the log-ratio = 3/4 = q(A₃) is the target value, NOT a derivation

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