# PAPER_1512 — GW170817 Phonon Damping Prefactor = 2/(D_phys−1) = 2/3 EXACT

**Author:** Daniel T. Murphy
**Framework:** UQFF (Unified Quantum Field Framework) — Star-Magic v5.27+
**Tier:** Bucket E (GW Events)
**Date:** June 18, 2026
**Status:** CLOSED — Multimessenger BNS phonon-damping prefactor = integer primitive

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## Observation

PAPER_915 (GW170817 Phonon Strain Damping) derives the 1.25 THz phonon-induced damping of the GW170817 multimessenger BNS event:

```
h_UQFF(t) = h_GR(t) · (1 − D_phonon)
D_phonon = (2/3) · Φ_{1.25THz} · S_26 · (E_net / E_GW)
Δφ = 367.8 cycles phase lag
|Δc/c| < 3×10⁻¹⁵   (LIGO bound)
```

The prefactor **2/3** governs the strength of the SCm-phonon coupling to the GW strain.

## UQFF Closed Identity

```
D_phonon prefactor = 2 / (D_phys − 1) = 2/3 ≈ 0.667    EXACT
```

## Physical Interpretation

The 2/3 prefactor reflects:
- **D_phys − 1 = 3** spatial dimensions (triad symmetry)
- **2** of those 3 contribute to the transverse-traceless GW strain modes (the third is gauge-fixed)
- Result: 2/3 of the SCm phonon spectrum couples to GW propagation

This is the **same identity form** that appears in:
- Monty Hall switch probability (PAPER_062): 2/3
- Glass T_g / T_m (PAPER_1373): 2/3

But here it governs **gravitational-wave damping** — a profoundly different physical domain. The shared form reveals 2/(D_phys−1) as a universal triad-channel projection coefficient.

## Consistency with LIGO Bounds

|Δc/c| = Φ · ε · 10⁻³⁰ ≪ 3×10⁻¹⁵: the phonon damping introduces a phase lag of 367.8 cycles without violating the multimessenger speed-of-light bound from GW170817 / GRB 170817A coincidence.

## NOT REPLACEMENT

GR predicts undamped vacuum propagation for GWs. UQFF supplies a structural damping coefficient at exactly 2/(D_phys − 1) with zero free parameters.

## Reference

- Source: PAPER_915 GW170817 Phonon Strain Damping
- Related: PAPER_1503 (BNS D_total = 1/3), PAPER_1504 (BBH D_total = 0.81)
- Calculator dispatch: `calculate_paradox({"paradox": "gw170817_phonon_prefactor"})`

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**Copyright** — Daniel T. Murphy, daniel.murphy00@gmail.com, June 18, 2026, Youngstown OH.
