A registered result in its source context

Original ledger classification: Gap-correction result [E]/[C]/[O] (Direction 2 declined: the calculable GR deviation is the R^2 scalaron already falsifiable via n_s/r; a new gap coefficient is not atom-forced -> declined per v354/v355)

Recorded statement: THE GAP-INDUCED HIGHER-CURVATURE CORRECTION TO GR -- THE DISCIPLINED RESULT (2026-06-23, Direction 2 of next-plan.md). Question: does the seam transfer gap {1,(2/3)^6,(1/3)^6} yield a NEW, calculable, FORCED deviation from GR (a near-term…

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Paper context: Frontier and open physical interfaces

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GRAV.GAPCORR.01

Original claim text

THE GAP-INDUCED HIGHER-CURVATURE CORRECTION TO GR -- THE DISCIPLINED RESULT (2026-06-23, Direction 2 of next-plan.md). Question: does the seam transfer gap {1,(2/3)^6,(1/3)^6} yield a NEW, calculable, FORCED deviation from GR (a near-term kill test) beyond the known R^2 scalaron? Run with the v354/v355 anti-numerology discriminator (a coefficient counts only if atom-forced, never a fit), the honest answer is NO -- and this is recorded rather than manufacturing a coefficient. [E] THE LEADING HIGHER-CURVATURE TERM IS THE R^2 SCALARON (already in TFPT): the spectral-action a4=R^2/72 (v36) gives R^2; TFPT fixes its scale M_scal^2/Mbar^2=c3^7 (exponent 7=g_car+N_fam-1), M_scal=c3^(7/2)Mbar~3.06e13 GeV -- the calculable beyond-Einstein correction. [C] IT IS THE ENTANGLEMENT-EQUILIBRIUM NEXT ORDER: the higher-curvature (Wald) entropy correction to the first law gives the f(R)=R+R^2 equation (v28), so the scalaron is the next-order term of the SAME route that gave the Einstein equation (v359) -- a structural confirmation, not a new term. [E] ALREADY FALSIFIABLE NOW: the R^2/Starobinsky attractor predicts n_s=1-2/N_star in [0.960,0.967] and r=12/N_star^2 in [0.0033,0.0048] (N_star in [50,60]) -- a live CMB-S4 kill test; Direction 2's calculable GR deviation already EXISTS and is testable. [E] THE GAP IS A DIMENSIONLESS RATE -> SEAM/PLANCK-SCALE CORRECTIONS: Delta=6 ln(3/2) is dimensionless; a distinct gap-induced curvature^2 term enters at xi*v_geo with xi=1/Delta~0.41 (seam units) and v_geo~M_Pl -- the seam/Planck scale, NOT near-term observable. [O] DECLINE (the discriminator): a NEW dimensionless deviation coefficient distinct from the scalaron needs the subleading heat-kernel/Wald data, which is NOT a forced atom combination (the scalaron exponent 7=g+N-1 and the gap exponent 6=2 N_fam are different structures; c3^7 and (2/3)^6 are unrelated). Per v354/v355 we DECLINE to manufacture an atom-unforced coefficient. HONEST CONCLUSION: Direction 2 yields no new near-term forced prediction; the answer is the existing scalaron + Planck-scale corrections.

Original classification detail

[E] the scalaron-as-leading-correction + its existing n_s/r kill test + the gap-is-dimensionless/Planck-scale reasoning; [C] the Wald-first-law consistency; [O] the explicit decline of a manufactured new coefficient. A disciplined-search record (like v355): the positive content is that the calculable GR deviation is the scalaron; the decline is the anti-numerology outcome. No new prediction added; nothing over-claimed.

Dependencies as recorded

GRAV.NONLINEAR.01; v359; v358; v36; v28; v354; v355

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Frontier and open physical interfaces
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2026-06-23 (Direction 2, the disciplined result: the gap-induced GR correction is the known [formula in source] scalaron — already falsifiable via [formula in source] ; a new forced near-term deviation does NOT survive the discriminator and is declined: v360)Research changelog; TFPT — Introduction and reading guide

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What this means for the theory-of-everything questionTFPT — Introduction and reading guide
Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Full quantum gravity — induced from the boundary kernelFrontier and open physical interfaces

Registered verification modules

v360_grav_gap_corrections.pyRegistered verification module · core
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Direction 2: the gap-induced higher-curvature correction to GR -- the disciplined result. Does the seam transfer gap give a NEW forced near-term GR-deviation beyond the known R^2 scalaron? With the v354/v355 discriminator: NO. [E] the leading higher-curvature term IS the R^2 scalaron (a4=R^2/72 v36; M_scal^2/Mbar^2=c3^7, exp 7=g+N-1) -- already in TFPT, already falsifiable via n_s=1-2/N*, r=12/N*^2 (CMB-S4). [C] it is the entanglement-equilibrium next order (Wald first law -> f(R)=R+R^2, v28/v359). [E] the gap Delta=6 ln(3/2) is dimensionless, so a distinct gap term sits at xi*v_geo ~ seam/Planck scale, not near-term observable. [O] DECLINE: a new dimensionless coefficient is not atom-forced (needs heat-kernel/Wald data; exp 7 vs 6, c3^7 vs (2/3)^6 unrelated) -> per v354/v355 declined. No new near-term forced prediction; the answer is the scalaron.

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