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A registered result in its source context

Original ledger classification: Open (conditional narrowing of the perturbative Stelle-ghost attack; NOT a QG.AMB.01 closure)

Recorded statement: INFINITE-DERIVATIVE / NONLOCAL READING OF THE GRAVITY SECTOR (2026-06-19): a CONDITIONAL narrowing of the red-team rt_F / v278 Stelle-ghost attack -- NOT a closure of QG.AMB.01 and NO new parameter (the cutoff is the v259 seam KMS weight).…

Statement, assumptions and sources

Paper context: Red-team audit

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QGAMB.IDG.01

Original ledger classification: Open (conditional narrowing of the perturbative Stelle-ghost attack; NOT a QG.AMB.01 closure)

Original claim text

INFINITE-DERIVATIVE / NONLOCAL READING OF THE GRAVITY SECTOR (2026-06-19): a CONDITIONAL narrowing of the red-team rt_F / v278 Stelle-ghost attack -- NOT a closure of QG.AMB.01 and NO new parameter (the cutoff is the v259 seam KMS weight). [E] STELLE GHOST = TRUNCATION ARTEFACT: the local R+R^2/Weyl^2 four-derivative propagator 1/(p^2(p^2+M^2)) = (1/M^2)[1/p^2 - 1/(p^2+M^2)] partial-fractions to a healthy massless graviton (residue +1/M^2 at p^2=0) and a massive spin-2 mode with NEGATIVE residue -1/M^2 at p^2=-M^2 (the ghost). [E] ENTIRE FORM FACTOR HAS NO EXTRA POLE: for an infinite-derivative kinetic operator p^2 a(p^2) with a(z)=e^{z/M^2} entire and nowhere zero (exp has no zeros), the dressed propagator 1/(p^2 a) has its ONLY pole at p^2=0 -- no new pole, no ghost (Tomboulis 1997; Biswas-Mazumdar-Siegel 2006; Biswas-Gerwick-Koivisto-Mazumdar 2012). [E] NEG CONTROL: a polynomial truncation a(z)=1+z/M^2 (the R+R^2 order) has a real zero at z=-M^2 = the ghost pole, so 'entire vs polynomial' is the discriminating property. [C] the spectral-action cutoff is the beta=1 seam KMS weight f(u)=e^{-u} (v259/PS.SPECACT.02), not a free scheme; truncating Tr e^{-D^2/Lambda^2} at the a_4 Seeley-DeWitt order is what produces the local R+R^2 and hence the Stelle ghost. [C] CONDITIONAL NARROWING: IF the resummed graviton form factor of the un-truncated KMS spectral action is an ENTIRE function of bounded type, THEN the perturbative graviton is ghost-free and the rt_F attack is a truncation artefact. [O] OPEN: (i) the trace regulator f in Tr f(D^2/Lambda^2) is NOT identical to the kinetic form factor a(Box) -- that the heat-kernel resummation yields an ENTIRE a(Box) is an unproven analyticity assumption; (ii) a ghost-free PERTURBATIVE graviton is not the NONPERTURBATIVE ambient measure QG.AMB.01 demands.

Original classification detail

[E] the truncation-artefact algebra (Stelle ghost from the local R+R^2 propagator; entire form factor has no extra pole; polynomial truncation re-introduces the ghost); [C] the KMS-cutoff link (v259) and the conditional ghost-freedom under entire analyticity; [O] the entire-analyticity assumption of the resummation + the nonperturbative gap. A conditional perturbative narrowing of rt_F, consistent with the SEAM.EQUIV.01 firewall; QG.AMB.01 stays [O].

Dependencies as recorded

QG.AMB.01; v259; v278; rt_F

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Registered verification modules

  • v304_idg_nonlocal_ghost.pyRegistered verification module · frontier
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    QGAMB.IDG.01 — the KMS spectral-action cutoff suggests a NONLOCAL (infinite-derivative) graviton form factor; under entire analyticity the Stelle ghost is a TRUNCATION ARTEFACT — a CONDITIONAL narrowing of the red-team rt_F perturbative-gravity attack, NOT a closure of QG.AMB.01 (no new parameter: the cutoff is the v259 seam KMS weight). [E] STELLE GHOST = TRUNCATION ARTEFACT: the local four-derivative propagator 1/(p^2(p^2+M^2)) has a healthy massless graviton (residue +1/M^2 at p^2=0) and a massive spin-2 mode with NEGATIVE residue -1/M^2 at p^2=-M^2 (reproduces rt_F/v278). [E] ENTIRE FORM FACTOR HAS NO EXTRA POLE: for an IDG operator p^2 a(p^2) with a(z)=e^{z/M^2} entire and nowhere zero, the dressed propagator 1/(p^2 a) keeps its ONLY pole at p^2=0 — no ghost (Tomboulis 1997; Biswas-Mazumdar-Siegel 2006). [E] NEG CONTROL: a polynomial truncation a(z)=1+z/M^2 (the R+R^2 order) has a real zero at z=-M^2 = the ghost pole, so 'entire vs polynomial' is the discriminator. [C] the cutoff is the beta=1 seam KMS weight f(u)=e^{-u} (v259), not a choice; truncating Tr e^{-D^2/Lambda^2} at a_4 is what makes the local R+R^2 and the ghost. [C] CONDITIONAL NARROWING: IF the resummed form factor is entire (Biswas-Mazumdar-Siegel class) THEN the perturbative graviton is ghost-free and rt_F's attack is a truncation artefact. [O] OPEN: (i) the trace regulator f is NOT the kinetic form factor a(Box) — entire analyticity is unproven; (ii) a ghost-free perturbative graviton is not the nonperturbative ambient measure — QGAMB.IDG.01 stays [C]/[O], not a QG.AMB.01 closure.

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