# PAPER_1504 — GW Damping Factor BBH = (N_CH/SO_5)² = 0.81 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 — BBH gravitational-wave total damping = exact (9/10)²

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## Observation

PAPER_011 (Stochastic Gravitational-Wave Background — UQFF Implications) derives the BBH damping factor D_total(BBH) = 8.10×10⁻¹ = 0.81, contrasting the much-stronger BNS damping (0.333). The factor 0.81 governs the bulk of LIGO/Virgo detections.

## UQFF Closed Identity

```
D_total(BBH) = (N_CH / SO_5)² = (9/10)² = 81/100 = 0.81   EXACT
```

## Physical Interpretation

The first appearance of **N_CH (the 9-channel primitive) in a binding closure** rather than a purely structural role. The two integer primitives compose as:

- N_CH = 9 channels through which SCm phonon information flows
- SO_5 = 10 dimensions of the SO(5) symmetry group enclosing them
- (N_CH/SO_5)² captures the projection of 9 active channels onto the 10-D coverage, squared because the strain amplitude h enters quadratically in the energy density Ω_GW

Together: **only 9 of 10 dimensional channels efficiently transmit BBH gravitational-wave strain**.

## Comparison to BNS

| Source | D_total | UQFF identity |
|---|---|---|
| BNS | 0.333 | 1/(D_phys − 1) = 1/3 |
| BBH | 0.81 | (N_CH/SO_5)² = (9/10)² |

The two damping regimes arise from fundamentally different vacuum-coupling channels: BNS taps the triad-symmetry denominator, BBH taps the 9-channel/10-dim projection.

## NOT REPLACEMENT

GR has no native damping mechanism in vacuum. UQFF predicts both factors structurally, giving distinct integer-primitive identities for BBH vs. BNS regimes.

## Reference

- Source: PAPER_011 Stochastic GW Background UQFF Implications
- Related: PAPER_1503 (BNS damping)
- Calculator dispatch: `calculate_paradox({"paradox": "gw_damping_bbh_n_ch_so5_sq"})`

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