# 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]**

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## 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.

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## 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 \(\Phi_{\mathrm{gw}}\neq\Phi_\gamma\).

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## 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.

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## 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`

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## 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.**