Original ledger status
GRAV.BACKREACT.01
GRAV.BACKREACT.01
THE MATTER-GRAVITY BACKREACTION WITH THE EXPLICIT J3 FLUX (2026-06-23, Direction 5 of next-plan.md). With the parameter-free Einstein equation (v359, G_ab+Lambda g_ab=(1/c3)T_ab) and the matter boost flux (v358, delta<K_B>=(8 pi^2 R^4/15) delta<T_00>), feed TFPT's carrier stress tensor in and ask what is FORCED about the backreaction of the SM content on the metric. Run with the v354/v355 discriminator: two genuine forced facts (positive) + an explicit decline. [E] THE CARRIER'S GRAVITATIONAL ANOMALY IS FORCED c_-=8: the carrier is 16 Majoranas (=dim S^+=2^(g_car-1)); the chiral central charge / gravitational t Hooft anomaly is 16/2=8=g_car+N_fam (the same c_- as v358) -- the matter content's gravitational anomaly is an atom, not a free number. [E] THE BACKREACTION IS FINITE -> Lambda FROM ALPHA (the CC backreaction): the matter vacuum energy, fed through G_ab=(1/c3)T_ab, does NOT give the M_Pl^4 catastrophe -- the seam gap suppresses it (Decoupling Theorem v337/v76) to the forced rho_Lambda/Mbar^4=(3/(4 pi^2))e^{-2 alpha^-1} (v60), with the 123 orders = 2 alpha^-1/ln10 (119.03, the EM fixed point) + log10(256 pi^4/3) (3.92); the loop (v359 equation + v60 Lambda + the carrier vacuum) closes. [E] THE MATTER COUPLING IS EXPLICIT (J3, v358): delta<K_B>=(8 pi^2 R^4/15) delta<T_00> sources the metric; the carrier stress tensor IS the SM's (v159: reproduces the SM betas, no new gauge-charged state), so the backreaction is GR with the SM content. [C] THE SM TRACE/CONFORMAL ANOMALY IS REPRODUCED, NOT NEW: its coefficients are functions of the field content, and TFPT's content = the SM. [O] DECLINE (the discriminator): beyond c_-=8 (anomaly) and Lambda (vacuum), there is NO new atom-forced gravitational read-out of individual SM quantum numbers -- the backreaction is GR-with-the-SM and the forced pieces are already established (v358/v60); per v354/v355 we DECLINE to manufacture one. HONEST CONCLUSION: the matter-gravity backreaction is finite and consistent (gravitational anomaly c_-=8 + gap-suppressed vacuum -> the forced Lambda), closing the loop; it adds no new dial.
Recorded status: Backreaction result [E]/[C]/[O] (Direction 5: carrier gravitational anomaly c_-=8 forced + finite backreaction -> Lambda from alpha, loop closes; no new SM-quantum-number read-out -> declined per v354/v355)
Later scope correction: the DtN form estimate alone does not prove the transfer gap.
Dependencies, status detail and source
Canonical status: [E] the carrier gravitational anomaly c_-=8 + the finite-backreaction-to-Lambda loop closure + the explicit J3 coupling; [C] the SM trace-anomaly reproduction; [O] the decline of a new per-quantum-number read-out. A disciplined consolidation (positive content + an honest decline): the backreaction is finite and forced (c_-=8, Lambda), but adds no new free quantity. Nothing over-claimed.
Dependencies: GRAV.NONLINEAR.01; v359; v358; v60; v337; v159; v354; v355
Scripts: v361_grav_backreaction.py
Location: tfpt_4
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