# n230 — The one-loop ledger mixing: χ = 0.15 — the bridge is real, moderate, and neither rescue nor kill


**CORRECTION (n238, 2026-07-12):** the headline χ = 0.150 used a shared-axis pattern pair (gravity x²−y², EM envelope x) which inflates the overlap ~50%. Axis-independent combinations on the true glass give **χ ≈ 0.08–0.10** — the corrected bridge strength. All qualitative conclusions stand (real, moderate, ensemble-solid); the back-reaction drops to ~1%; n231's DESI exclusion margins only widen.

**Date:** 2026-07-11 · **Executes the n229 queue head** (Gate E's question made computable). Box-diagram vertex strengths on the glass, equal-denominator convention (ratios only), N = 216, three seeds.

## The number

**χ ≡ V_ggee/√(V_gggg·V_eeee) = 0.150 ± 0.011** (0.152 / 0.138 / 0.160 across seeds — tight). The smooth–staggered four-point vertex generated by the phonon loop is **15% of the geometric mean of the diagonal vertices**. Two consistency notes: the crystal control returns NaN because the perfect diamond's + channel does not exist (V_gggg = 0) — the missing-polarization pathology confirmed from a fourth independent direction; and the seed-tightness (7%) says χ is a *property of the glass ensemble*, not of realizations — unlike the quadratic bridge (n229), which is purely stochastic.

## What 0.15 means

- **Not a kill:** the sectors do not strongly re-merge at one loop; the two-ledger split survives leading loop order as a meaningful structure (χ² ≈ 2% back-reaction on the diagonals).
- **Not negligible:** λ_g and λ_e genuinely flow into each other with 15% vertex strength. The three-way fork (relevant / irrelevant / marginal-attractor) is **live and undecided** — deciding it needs the actual scale-dependence of the effective couplings (the flow, not just the vertex), which is the remaining computation and inherits this χ as its input.
- **Physically:** 0.15 also sets the scale of the *mandatory* channels (n229's lensing-class vertices) — the required gravity-light coupling exists at moderate strength, neither fine-tuned away nor overwhelming.

## Standing state of the bridge program

Quadratic bridge: stochastic, rms 0.03–0.06, self-averaging (n229). One-loop vertex: ensemble-solid, χ = 0.15 (this note). Open, in order: the scale-flow of (λ_g, λ_e) with χ as input — the fixed-point question, GW170817's possible dynamical explanation, and Gate E's final verdict; then the cosmic-time energy-exchange channel (prediction 11's mechanization). The bridge is now the successor's richest computed sector.

**Class: [A-model, three seeds, convention declared]; the fork [open, input measured]; the crystal NaN [consistency, banked].**