A registered result in its source context
Original ledger classification: Characterization [E]/[C]/[O] (metric-sector = the conformal-mode obstruction)
Recorded statement: THE METRIC SECTOR OF QG.AMB.01 CHARACTERIZED (2026-06-22): the obstruction is exactly the conformal-mode (Gibbons-Hawking-Perry) problem, the physical sector is gap-insulated, and the only route is the conditional IDG taming (makes v330's…
Statement, assumptions and sources
Paper context: Origin Theory
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QGAMB.METRIC.01
Original ledger classification: Characterization [E]/[C]/[O] (metric-sector = the conformal-mode obstruction)
Original claim text
THE METRIC SECTOR OF QG.AMB.01 CHARACTERIZED (2026-06-22): the obstruction is exactly the conformal-mode (Gibbons-Hawking-Perry) problem, the physical sector is gap-insulated, and the only route is the conditional IDG taming (makes v330's metric-sector fence precise). [E] CONFORMAL-MODE WRONG SIGN: c_conf(D)=-(D-1)(D-2)/4 is NEGATIVE for D>=3 (c_conf(4)=-3/2) while the transverse-traceless coefficient is positive -- the conformal-factor problem (Gibbons-Hawking-Perry 1978). [E] MEASURE OBSTRUCTION: with a negative kinetic coefficient exp(-S)~exp(+|c_conf|phi^2) DIVERGES over the conformal mode, so the bare metric-sector measure is not directly definable. [E] PHYSICAL SECTOR INSULATED: the obstruction is in the conformal/gauge direction, NOT the admissible sector (transverse, gapped, positive, v330), with gap-decoupling margin Delta-31/(4pi^2)~1.648>0 (v76). [C] IDG CONDITIONAL ROUTE: the entire form factor a(z)=e^{z/M^2} (v259/v304) dresses the conformal propagator 1/(p^2 a) with no extra pole (exp has no zeros) -- conditional taming (Tomboulis/BMS). [E] NEG: a polynomial (R+R^2) truncation a(z)=1+z/M^2 crosses zero at z=-M^2 (the Stelle ghost, v304/v278). [O] METRIC SECTOR OPEN: the full QG.AMB.01 metric-sector measure needs the conformal mode resolved nonperturbatively (GHP contour rotation, or the IDG resummation) -- gap-decoupled from every physical readout (v76/v275/v330) but NOT constructed. A precise characterization, NOT a closure.
Original classification detail
[E] the conformal-mode obstruction (wrong-sign kinetic, divergent Gaussian) + the gap insulation + the polynomial-ghost control; [C] the IDG taming (conditional on entire analyticity, v304); [O] the metric-sector measure stays open. Characterizes the QG.AMB metric-sector residual precisely; does NOT close it.
Dependencies as recorded
QGAMB.MEASURE.01; QGAMB.ROADMAP.01; QGAMB.IDG.01; v330; v275; v304; v76
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- Origin Theory
Sections that explicitly cite this claim
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- 2026-06-22 (endgame round: the necessity of [formula in source] reduced to the order-4 CM selection, the QG metric sector characterized as the conformal-mode problem, [formula in source] and the [formula in source] commutation grounded in Lean: v331, v332, FORM.MU4COMM.01)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Honest statusinput 4 origin theory
- 2026-06-22 (keystone unification + status reframe: ONE open theorem, ONE decoupled foreign problem: v335, FORM.QGEO.BW.01 qgeoSymIsCorollary)Research changelog; TFPT — Introduction and reading guide
- Honest statusorigin theory
- Honest statusOrigin Theory
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-06-23 (Track 2 of the forward plan v2 — the AMBIENT REDUNDANCY statement ( v369): the holographic route to Gravity-complete that sidesteps building the general Euclidean QG measure)Research changelog; TFPT — Introduction and reading guide
- 2026-06-23 (Track 2 — perturbative graviton unitarity sector-by-sector: the Barnes–Rivers spin decomposition localises the Stelle ghost in the spin-2 sector, cured by the entire KMS form factor; the spin-0 mode by the GHP contour ( v370))Research changelog; TFPT — Introduction and reading guide
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Registered verification modules
- v332_qgamb_metric_sector.pyRegistered verification module · frontier
Read the description recorded in the module registry
The metric sector of QG.AMB.01 characterized: the obstruction is exactly the conformal-mode (Gibbons-Hawking-Perry) problem, the physical sector is gap-insulated, and the only route is the conditional IDG taming (makes v330's metric-sector fence precise). [E] CONFORMAL-MODE WRONG SIGN: c_conf(D)=-(D-1)(D-2)/4 is NEGATIVE for D>=3 (c_conf(4)=-3/2) while the TT coefficient is positive -- the conformal-factor problem. [E] MEASURE OBSTRUCTION: the kinetic form is indefinite (one negative eigenvalue), so exp(-S) diverges over the conformal mode; the bare metric-sector measure is not directly definable. [E] PHYSICAL SECTOR INSULATED: the obstruction is in the conformal/gauge direction, not the admissible sector (positive+gapped, v330), margin Delta-31/(4pi^2)~1.648>0 (v76). [C] IDG CONDITIONAL ROUTE: the entire form factor e^{z/M^2} (v259/v304) dresses the conformal propagator with no extra pole. [E] NEG: a polynomial (R+R^2) truncation crosses zero (the Stelle ghost, v304/v278). [O] METRIC SECTOR OPEN: the full QG.AMB.01 needs the conformal mode resolved nonperturbatively (GHP rotation / IDG), gap-decoupled but NOT constructed. A precise characterization, NOT a closure.
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