A registered result in its source context
Original ledger classification: perturbative graviton unitarity sector-by-sector (spin-2 ghost-free via the entire KMS form factor, spin-0 via GHP) [E]/[C]/[O]
Recorded statement: Track 2 (2026-06-23): the Barnes-Rivers spin decomposition of the graviton propagator -- perturbative graviton unitarity SECTOR-BY-SECTOR. Extends v304 (scalar pole algebra) to the tensor spin structure and combines it with v334 (spin-0…
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Paper context: Red-team audit
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GRAV.SPIN2.UNITARITY.01
Original ledger classification: perturbative graviton unitarity sector-by-sector (spin-2 ghost-free via the entire KMS form factor, spin-0 via GHP) [E]/[C]/[O]
Original claim text
Track 2 (2026-06-23): the Barnes-Rivers spin decomposition of the graviton propagator -- perturbative graviton unitarity SECTOR-BY-SECTOR. Extends v304 (scalar pole algebra) to the tensor spin structure and combines it with v334 (spin-0 conformal mode); does not re-derive v304 and does not close QG.AMB.01. [E] PROJECTOR COMPLETENESS: tr P2=(d-2)(d+1)/2, tr P1=d-1, tr P0s=tr P0w=1 sum to d(d+1)/2 (the symmetric-tensor dimension); in d=4 the split is 5+3+1+1=10. [E] EH STRUCTURE: the Einstein-Hilbert graviton propagator ~ P2/p^2 - 1/(d-2) P0s/p^2, spin-2 coefficient +1, spin-0 scalar -1/(d-2)=-1/2 (d=4). [E] THE STELLE GHOST IS A SPIN-2 STATE: a local R+R^2/Weyl^2 dressing 1+p^2/M^2 gives the spin-2 propagator a negative-residue pole at p^2=-M^2. [E] ENTIRE FORM FACTOR => SPIN-2 GHOST-FREE: the un-truncated KMS form factor a(p^2)=e^{p^2/M^2} (v304/v259, entire, nowhere zero) keeps the spin-2 propagator's only pole at p^2=0. [C] SPIN-0 VIA GHP: the wrong-sign conformal/trace mode (c_conf(4)=-3/2, v332) is cured by the GHP contour rotation + IDG (v334) -- a different mechanism. [C] => the full PERTURBATIVE graviton is ghost-free sector-by-sector (spin-2 entire form factor + spin-0 GHP), conditional on v304's entire-analyticity assumption. [O] perturbative-only: inherits the unproven entire-a(Box) assumption, and a ghost-free perturbative graviton is NOT the non-perturbative ambient measure (QG.AMB.01). [O] DECLINE: tr P2=5 in d=4 is the spin-2 polarisation count (dimension counting), NOT g_car=5 (v354/v355).
Original classification detail
[E] the Barnes-Rivers projector completeness + EH structure + the spin-2 pole algebra; [C] the entire form factor (inherits v304) + GHP (v334) + the sector-by-sector unitarity conclusion; [O] perturbative-only + the open analyticity assumption. Extends v304 to the tensor sector; does NOT close QG.AMB.01. tr P2=5 != g_car (declined).
Dependencies as recorded
QG.AMB.01; v304; v334; v332; v259; v278; v354
Open the original ledger source, row 80Location recorded in the ledger
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- Red-team audit
Sections that explicitly cite this claim
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- 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
- Target F — the perturbative 4D-QFT [formula in source] scale round (v269–v275)Red-team audit
Navigation through a shared verification script
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- Status: what is now written out, and what is honestly leftStandard Model and flavor structure
- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Honest statusinput 4 origin theory
- 2026-06-23 (External-review closure: the two genuine residual targets named — v381 the all-order Epstein–Glaser/BRST contract for [formula in source] , and v382 the Quillen determinant-line variation as a tracked target)Research changelog; TFPT — Introduction and reading guide
- How the legacy layers simplify (bridge map)tfpt 2 standard model
- The ambient closure: one spectral-action measure, IR-complete by decouplingtfpt 2 standard model
- Status: what is now written out, and what is honestly lefttfpt 2 standard model
- How the legacy layers simplify (bridge map)Standard Model and flavor structure
All 28 linked sections
- 2026-06-23 (Status propagation: the v365– v380 [formula in source] FORM.SEAM.MMST.01 status carried into the remaining papers, the README and the Zenodo description)
- 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 Contract 1 — [formula in source]
- Honest status
- 2026-06-23 ( v380 — the KMS Entire Hessian: the Stelle ghost is EXACTLY the Seeley–DeWitt truncation, and resummation pushes it to infinity)
- What this means for the theory-of-everything question
- 2026-06-24 (The five TOE/QFT closure contracts v398– v402 + a ledger rescope)
- The honest open-items list
- Honest status
- The honest open-items list
- The honest open-items list
- The ambient closure: one spectral-action measure, IR-complete by decoupling
- (4) Constructive QFT closure of the admissible physical sector /
- Summary
- 2026-06-24 (Graviton loop finiteness: v389 the entire form factor is UV-finite at the loop level by power counting)
- Front matter / support
- Honest status
- Research Contract 1 — [formula in source]
- (4) Constructive QFT closure of the admissible physical sector /
- Front matter / support
Registered verification modules
- v370_grav_spin2_unitarity.pyRegistered verification module · frontier
Read the description recorded in the module registry
Track 2: the Barnes-Rivers spin decomposition of the graviton propagator -- perturbative graviton unitarity SECTOR-BY-SECTOR (extends v304's scalar pole algebra to the tensor spin structure + combines with v334's spin-0 conformal mode). [E] projector completeness: tr P2=(d-2)(d+1)/2, tr P1=d-1, tr P0s=tr P0w=1 sum to d(d+1)/2; the d=4 split is 5+3+1+1=10. [E] EH structure: spin-2 coefficient +1, spin-0 scalar -1/(d-2)=-1/2. [E] the Stelle ghost is a SPIN-2 state (a local 1+p^2/M^2 dressing puts the negative-residue pole at p^2=-M^2). [E] the entire KMS form factor e^{p^2/M^2} (v304/v259) makes spin-2 ghost-free (only the p^2=0 pole). [C] the wrong-sign spin-0 conformal mode (c_conf(4)=-3/2, v332) is cured by the GHP contour (v334) -- a different mechanism. [C] => perturbative graviton unitarity sector-by-sector, conditional on v304's entire-analyticity assumption. [O] perturbative-only + the open analyticity assumption; NOT the non-perturbative measure (QG.AMB.01). [O] decline: tr P2=5 is dimension counting, NOT g_car (v354/v355).
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