A registered result in its source context
Original ledger classification: Perturbative graviton amplitude [E]/[C] (entire-form-factor exchange: finite, ghost-free, UV-softened, tree-unitary; perturbative-only)
Recorded statement: The entire-form-factor graviton-exchange AMPLITUDE is finite, UV-softened and tree-unitary (2026-06-24) -- perturbative gravity as an explicit scattering problem, extending v304/v370/v380 from the propagator to the amplitude. The dressed…
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Paper context: Frontier and open physical interfaces
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GRAV.AMPLITUDE.01
Original ledger classification: Perturbative graviton amplitude [E]/[C] (entire-form-factor exchange: finite, ghost-free, UV-softened, tree-unitary; perturbative-only)
Original claim text
The entire-form-factor graviton-exchange AMPLITUDE is finite, UV-softened and tree-unitary (2026-06-24) -- perturbative gravity as an explicit scattering problem, extending v304/v370/v380 from the propagator to the amplitude. The dressed spin-2 propagator P(p^2)=e^{-p^2/M^2}/p^2=1/(p^2 a) with a(u)=e^u (u=p^2/M^2), M=M_scal. [E] ONE POLE, GHOST-FREE: a=e^u entire and nowhere zero (v380) => the only pole is p^2=0 with residue lim p^2 P=e^0=1>0 (one healthy massless graviton). [E] UV-SOFTENED: the dressed/GR ratio e^{-u} at u=1,5,10,20 = 0.37,6.7e-3,4.5e-5,2.1e-9 -- suppressed faster than any power (infinite-derivative improvement), monotone->0. [E] LOW-ENERGY = GR + CALCULABLE CORRECTION: e^{-u}=1-u+u^2/2-...; the leading deviation -u=-p^2/M^2 (M=M_scal=c3^{7/2}Mbar~3.06e13 GeV, v253). [C] TREE UNITARITY: a single positive-residue pole, no extra poles / negative-norm states (entire zero-free form factor) => Im A>=0, consistent with v370 (spin-2) + v380 (entire). [C] AMPLITUDE STRUCTURE: A=(kappa^2/2)(T.P2.T')e^{-p^2/M^2}/p^2, GR at low energy, softened in the UV (P2 = Barnes-Rivers spin-2 projector, v370); perturbative-only (QG.AMB.01 stays a [C] redundancy, v369).
Original classification detail
[E] the single positive-residue pole + the UV softening (e^{-u} faster than any power) + the GR limit and first correction; [C] the tree unitarity and the amplitude structure (perturbative-only). Extends v304/v370/v380 from propagator to amplitude; does NOT touch the non-perturbative measure (QG.AMB.01); the scale M=M_scal (v253) and the form factor = the seam KMS cutoff (v259), no new number.
Dependencies as recorded
v259; v304; v370; v380; v253; v369
Open the original ledger source, row 449Location recorded in the ledger
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- Frontier and open physical interfaces
Sections that explicitly cite this claim
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- 2026-06-24 (Harvesting the QFT/gravity machinery: v385 the UV-branch kill-test surface, v386 the graviton-exchange amplitude, v387 the gap-driven correction calculus)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- 2026-06-24 (Website: an animated ``Universal Gap Lab'' visualising v383– v391)Research changelog; TFPT — Introduction and reading guide
- 2026-06-24 (The five TOE/QFT closure contracts v398– v402 + a ledger rescope)Research changelog; TFPT — Introduction and reading guide
- SummaryFrontier and open physical interfaces
- 2026-06-24 (Graviton loop finiteness: v389 the entire form factor is UV-finite at the loop level by power counting)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v386_grav_amplitude.pyRegistered verification module · frontier
Read the description recorded in the module registry
GRAV.AMPLITUDE.01: the entire-form-factor graviton-exchange AMPLITUDE is finite, UV-softened and tree-unitary -- perturbative gravity as an explicit scattering problem, extending v304/v370/v380 from the propagator to the amplitude. The dressed spin-2 propagator P=e^{-p^2/M^2}/p^2=1/(p^2 a), a(u)=e^u, M=M_scal. [E] one pole, ghost-free: a entire & nowhere zero (v380) => only pole at p^2=0, residue e^0=1>0. [E] UV-softened: ratio e^{-u} at u=1,5,10,20=0.37,6.7e-3,4.5e-5,2.1e-9 (faster than any power). [E] low-energy = GR + a calculable -p^2/M^2 correction (M=M_scal=c3^{7/2}Mbar, v253). [C] tree unitarity: a single positive-residue pole, no negative-norm states (v370/v380). [C] the amplitude A=(kappa^2/2)(T.P2.T')e^{-p^2/M^2}/p^2 is GR at low energy, softened in the UV (perturbative-only; QG.AMB.01 a [C] redundancy v369). No new number.
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