Results — GW170817/GRB 170817A: \(c_{\mathrm{gw}}=c\) is a gate, and leftover UV can keep it
Bound \(\sim 10^{-15}\) · \(\lambda_{\mathrm{GW}}\ll R\) · Book G characteristics = \(c\) kind · TeVeS-class FIRE · full wave action unpaid · pursue-not-presume held internally
CPT Framework — Book G 1PN / FT-CONST-PRIZE / RAD-LIGO / FT-YIELD-GEOM Date: 2026-09-22 Status: BANKED ·PASS_FT_GW170817_CGW_EQ_C_GATE
Stimulus: User — GW170817/GRB 170817A as the biggest killer of alternative gravity; do we preserve \(c_{\mathrm{gw}}=c\)?
Parents: Abbott et al. 2017 (ApJL 848 L13) · RAD-LIGO pursue-not-presume · BP-1 Hencky 1PN · FT-CONST-PRIZE
Script: scripts/investigations/s3_geometry/ft_gw170817.py
Data: scripts/investigations/s3_geometry/data/ft_gw170817.json
Tags: [E honesty] · [E algebra] · [Programme] · [O residual]
0. One-line
Externally, yes: the framework must keep \(c_{\mathrm{gw}}=c\). Named: \(\Delta t=+1.74\pm 0.05\,\mathrm{s}\), \(D\sim 40\,\mathrm{Mpc}\), published window \(-3\times 10^{-15}\le (c_{\mathrm{gw}}-c)/c\le +7\times 10^{-16}\) (emission delay \(0\)–\(10\,\mathrm{s}\)). \(\Delta t/(D/c)\simeq 4.2\times 10^{-16}\). That killed TeVeS-class kinetic terms with a second metric speed. Leftover yield is an IR constitutive change of quasi-static \(\Phi\), not a second principal symbol. GW at \(100\,\mathrm{Hz}\) has \(\lambda\simeq 3\times 10^3\,\mathrm{km}\), \(\lambda/R\sim 10^{-20}\) — a UV probe of the bulk, where Book G / Hencky already has characteristics \(c\) (\(\gamma=\beta=1\)). So \(c_{\mathrm{gw}}=c\) is kind if the unpaid Lagrangian keeps the GR wave operator in the UV. It is not a derived Einstein–Hilbert theorem. Internally, interferometer catalogues stay pursue-not-presume; Hulse–Taylor \(\dot P_b\) remains the flux gate. Any constitutive prize must list \(c_{\mathrm{gw}}=c\) at \(10^{-15}\) as a hard gate.
1. The killer (external board)
The association, if loaded as true, is the fastest \(c_{\mathrm{gw}}\) test. Many covariant MOND completions failed because \(c_{\mathrm{gw}}\neq c\) at \(O(1)\) or \(O(10^{-n})\) far above \(10^{-15}\).
The \(1.74\,\mathrm{s}\) can be astrophysical (jet launch). The bound is not “gravity lagged by 1.74 s”; it is “after allowing \(0\)–\(10\,\mathrm{s}\) of source delay, leftover speed difference is \(10^{-15}\).”
Shapiro delay between GW and γ-rays is a separate EP test (same paper). Extra \(\Phi\) that both couple to does not split their Shapiro delay. A dark-matter-only potential that photons and GW both feel also does not. Split Shapiro would mean different \(\Phi_{\mathrm{gw}}\neq\Phi_\gamma\).
2. Why leftover need not die
| Scale | | |-------|--| | \(\lambda(100\,\mathrm{Hz})\) | \(3\times 10^3\,\mathrm{km}\) | | leftover \(R\) | \(\sim\mathrm{Gpc}\) | | \(\lambda/R\) | \(\sim 10^{-20}\) | | yield | low \(g\), quasi-static \(\Phi\) |
High-\(k\) waves see the UV modulus (elastic Book G). Saturation / \(P\rho\) is a zero-mode / IR constraint, not a second metric light cone. A theory that replaces the Einstein kinetic term with a scalar-vector mix (TeVeS) is a different object and is FIRE.
Finding G1 [E honesty]. Preserve \(c_{\mathrm{gw}}=c\) as a gate on the constitutive prize. Do not claim the wave action is derived.3. Integrity
| Gate | Verdict | |------|---------| | External: \(c_{\mathrm{gw}}=c\) at \(10^{-15}\) | required | | UV Book G kind | YES | | TeVeS-class | FIRE | | IR yield \(\Rightarrow c_{\mathrm{gw}}\neq c\) | not forced | | Einstein–Hilbert derived | NO | | LIGO as CPT axiom | NO (pursue-not-presume) | | Constitutive prize must include this gate | YES |
Exit:PASS_FT_GW170817_CGW_EQ_C_GATE
4. One-line for agents
*§FT-GW170817: external board requires \(c_{\mathrm{gw}}=c\) at \(10^{-15}\); leftover UV kind keeps it (\(\lambda\ll R\)); TeVeS-class FIRE; wave action unpaid; pursue-not-presume internally.*