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Original ledger classification: Construction [E]/[C]/[O] (conformal-mode GHP+IDG conditional resolution)

Recorded statement: THE CONFORMAL-MODE RESOLUTION (2026-06-22): the Gibbons-Hawking-Perry contour rotation (IR sign) + the infinite-derivative (IDG) dressing (UV pole) give a CONDITIONALLY convergent metric-sector measure; the residual is the nonperturbative…

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Paper context: Origin Theory

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QGAMB.CONFORMAL.01

Original ledger classification: Construction [E]/[C]/[O] (conformal-mode GHP+IDG conditional resolution)

Original claim text

THE CONFORMAL-MODE RESOLUTION (2026-06-22): the Gibbons-Hawking-Perry contour rotation (IR sign) + the infinite-derivative (IDG) dressing (UV pole) give a CONDITIONALLY convergent metric-sector measure; the residual is the nonperturbative validity of the contour (the v332 follow-up). [E] THE OBSTRUCTION: c_conf(4)=-(D-1)(D-2)/4=-3/2<0, so the unrotated conformal Gaussian integral(exp(+|c|phi^2)) DIVERGES. [E] GHP CONTOUR ROTATION: phi->i phi flips (i phi)^2=-phi^2, so +|c|phi^2 -> -|c|phi^2 and integral(exp(-|c|phi^2))=sqrt(pi/|c|) is FINITE -- the Gibbons-Hawking-Perry 1978 prescription makes the conformal measure convergent. [E] IDG UV DRESSING: the entire form factor a(p^2)=exp(p^2/M^2) is nowhere zero (no ghost pole, v304), the dressed per-mode action (1/2)|c| k^2 a(k^2) phi^2 is positive after GHP and UV-suppressed. [E] NEG: a polynomial truncation a=1+p^2/M^2 crosses zero at p^2=-M^2 (the Stelle ghost, v304/v278). [C] CONDITIONAL CONSTRUCTION: GHP (IR sign) + IDG (UV pole) give a formally convergent metric-sector Gaussian mode-by-mode -- a conditional construction (conditional on the rotation contour AND entire analyticity, v304). [O] THE RESIDUAL: whether the GHP-rotated IDG-dressed measure is the CORRECT nonperturbative QG.AMB measure (the contour rotation's nonperturbative validity, Euclidean QG's long-standing issue); gap-decoupled (Delta-31/(4 pi^2)~1.648>0, v76), so it blocks no test. NOT a closure.

Original classification detail

[E] the obstruction + the GHP sign flip + the IDG pole-freeness + the polynomial-ghost control; [C] the conditional GHP+IDG construction; [O] the contour's nonperturbative validity. Advances v332 to a conditional construction; does NOT close QG.AMB.01.

Dependencies as recorded

QGAMB.METRIC.01; QGAMB.IDG.01; QGAMB.MEASURE.01; v332; v304; v330; v76

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Origin Theory
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2026-06-22 (closing round: the CM-selection mechanism (the last keystone residual), the conformal-mode resolution, and the Conway–Sloane even-unimodular side in Lean: v333, v334, FORM.CARTAN.DET.01)Research changelog; TFPT — Introduction and reading guide

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The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
Honest statusinput 4 origin theory
The unique attractor: a gapped transport selects ONE fixed pointorigin theory
The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
2026-06-23 (Directions 3 \& 7 — the two hard functional-analysis residuals ADVANCED: the QG measure as one-loop fluctuations around the parameter-free saddle ( v365), and the seam collar verified IN MMST's free-fermion class so the scaling limit is [formula in source] ( v366))Research changelog; TFPT — Introduction and reading guide
2026-06-22 (the four black-hole-birth completion routes investigated: none closes all or is 100\% provable alone; all four converge on SEAM.EQUIV.01 [formula in source] the decoupled QG contour: v343)Research changelog; TFPT — Introduction and reading guide
Front matter / supportResearch contracts
Honest statusorigin theory

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v334_conformal_resolution.pyRegistered verification module · frontier
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The conformal-mode resolution: the Gibbons-Hawking-Perry contour rotation (IR sign) + the infinite-derivative (IDG) dressing (UV pole) give a CONDITIONALLY convergent metric-sector measure; the residual is the nonperturbative validity of the contour (the v332 follow-up). [E] THE OBSTRUCTION: c_conf(4)=-3/2<0, the unrotated conformal Gaussian diverges. [E] GHP CONTOUR ROTATION: phi->i phi flips the sign, int(exp(-|c|phi^2))=sqrt(pi/|c|) FINITE (GHP 1978). [E] IDG UV DRESSING: the entire form factor exp(p^2/M^2)>0 (no ghost pole, v304), dressed per-mode action positive post-GHP and UV-suppressed. [E] NEG: a polynomial truncation crosses zero (the Stelle ghost, v304/v278). [C] CONDITIONAL CONSTRUCTION: GHP+IDG give a convergent metric-sector Gaussian mode-by-mode (conditional on the contour + entire analyticity). [O] residual: whether the GHP-rotated IDG-dressed measure is the CORRECT nonperturbative QG.AMB measure (the contour's nonperturbative validity); gap-decoupled (v76), blocks no test. NOT a closure.

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