# n249 — The glass momentum audit constructed: dipole silenced, capacity theorem, and the photon's true name

**Date:** 2026-07-12 · **Executes n248's mandatory construction.** Three attempts, each teaching: cell-coarse rows watch uniform flows and miss local dipoles (wrong); per-site divergence rows on the 4-coordinated glass saturate everything — dark dimension zero (the counting wall); **per-site signed-divergence rows on a dense glass (z = 10) work.**

## The construction that works

Momentum rows = the discrete divergence of the momentum current: G_{i,α} = Σ_{e∋i} σ_e(i)·(d̂_e)_α·dk_e, signed by edge orientation (the glass-native descendant of n166's (q·d̂)(d̂_i) rows, whose q-factor was precisely a divergence). On the dense true glass:

| Source | dark (radiative) fraction | Verdict |
|---|---|---|
| monopole | **0.0000 exactly** | Birkhoff — a bookkeeping identity, disorder-proof (unchanged) |
| **dipole** | **0.0000 exactly** | **watched — momentum conservation emerges as bookkeeping too; the pulsar survival requirement (n248) is MET** |
| quadrupole (both) | 0.15–0.18 | the emission channel survives the full audit — quadrupole-led radiation, as GR demands |

## The capacity theorem (the night's structural discovery)

The full audit needs room: 4 budget rows per site against E/N edges per site. **z = 4 (diamond-class): dark dimension = 0 — the complete theory cannot live there. z = 10: dark dimension = 307 — everything fits.** The audit + radiative content constrain the substrate's coordination from below (z > 8): **the vacuum must be a dense glass.** A postulate-level constraint derived from the theory's own bookkeeping — and a flag: all n221–n248 glass numerics ran at z = 4; the topology/statistics results (photon kernel existence, polarization equality, no-pinning) are construction-independent, but the *channel numbers* (speeds, families) need re-verification at high coordination. Registered.

## The photon's true name on the glass

The full-audit dark space (307 modes) lives in ker(A) ∩ ker(G): unsigned-sum-free AND divergence-free — **cycle currents.** The smooth transverse *envelopes* used as photon probes since n223 are watched by the momentum audit (they are flows with divergence); the surviving light is the **circulation modes** — which is exactly what the crystal theory always said (n159: the photon = the kernel; the kernel = the cycle space). The glass EM-channel numbers (c_EM, the equal-cone family) must be re-measured with cycle-current probes — flagged as the successor's next computation, with the honest possibility that the cone numbers move.

**Class: the construction [A-model, two seeds, exact zeros]; the capacity theorem [A — counting, verified at z = 4 and 10]; the photon rename [structural, forces a re-probe — flagged]. The pulsars demanded momentum conservation; the glass, once dense enough, supplies it as an identity — and in passing tells us the vacuum's minimum density and the photon's real shape.**