A registered result in its source context
Original ledger classification: Nonlocal-gravity action contract [E]/[O] (Paper C: the entire form factor gives a ghost-free one-pole propagator whose IR projection is exactly the atom-scaled R+R^2; the entire-a assumption + perturbative-only stay [O]). Consolidates v304/v370/v380/v386, adds the IR-matching check
Recorded statement: THE NONLOCAL SPECTRAL-GRAVITY ACTION; LOCAL R+R^2 IS ITS IR PROJECTION (2026-06-24, Paper C / the 4D gravity-action contract): consolidates v304/v370/v380/v386 and adds the IR-matching check. Does NOT prove the entire-analyticity of the…
Statement, assumptions and sources
Paper context: Frontier and open physical interfaces
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GRAV.NONLOCAL.01
Original ledger classification: Nonlocal-gravity action contract [E]/[O] (Paper C: the entire form factor gives a ghost-free one-pole propagator whose IR projection is exactly the atom-scaled R+R^2; the entire-a assumption + perturbative-only stay [O]). Consolidates v304/v370/v380/v386, adds the IR-matching check
Original claim text
THE NONLOCAL SPECTRAL-GRAVITY ACTION; LOCAL R+R^2 IS ITS IR PROJECTION (2026-06-24, Paper C / the 4D gravity-action contract): consolidates v304/v370/v380/v386 and adds the IR-matching check. Does NOT prove the entire-analyticity of the resummed form factor (stays the cited heat-kernel resummation, the [O] of v304/v380); PERTURBATIVE only. [E] ENTIRE FORM FACTOR -> ONE POLE: the dressed spin-2 propagator 1/(p^2 a) with a(u)=e^u has its ONLY pole at p^2=0 (residue a(0)^{-1}=1>0, one healthy massless graviton, no Stelle ghost). [E] EVERY TRUNCATION CARRIES THE GHOST: T_1=1+u has the Stelle zero u=-1, and the nearest-zero modulus grows monotonically with order -> infinity, so 'entire'='do not truncate' (v380). [E] IR PROJECTION = R+R^2: a(u)=1+u+u^2/2+... reproduces the spectral-action R+R^2 structure (v28/v36) with the FIXED scale M_scal^2/Mbar^2=c3^7 (exponent 7=g_car+N_fam-1). [E] THE SCALE IS AN ATOM: M=M_scal=c3^{7/2}Mbar, the exponent 7 and half-power 7/2 carrier atoms (v253), determined not fitted. [O] RESIDUAL: (i) a(Box)=e^{Box/M^2}=the EXACT off-shell curved-space Hessian is the cited heat-kernel resummation (analyticity assumption); (ii) PERTURBATIVE graviton unitarity, NOT the nonperturbative ambient measure (QG.AMB.01, [C] redundancy v369).
Original classification detail
[E] the one-pole/ghost-free pole algebra + the monotone truncation-zero fact (v380) + the IR R+R^2 matching with the atom-fixed scale c3^7 + the carrier-atom scale exponent 7; [O] the entire-a analyticity assumption + perturbative-only (not the ambient measure). A contract + IR-matching module; consolidates v304/v370/v380/v386; no new number.
Dependencies as recorded
GRAV.AMPLITUDE.01; GRAV.LOOP.FINITE.01; v304; v370; v380; v386; v36; v28; v253; v369
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- Frontier and open physical interfaces
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- 2026-06-24 (The five TOE/QFT closure contracts v398– v402 + a ledger rescope)Research changelog; TFPT — Introduction and reading guide
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- SummaryFrontier and open physical interfaces
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Registered verification modules
- v400_grav_nonlocal_action.pyRegistered verification module · frontier
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Nonlocal spectral-gravity action; local R+R^2 is its IR projection (Paper C): entire form factor one pole + truncation-zero monotone + IR matching to R+R^2 with scale c3^7
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