# n220 — Gate D leg 1: FAIL. The pinned two-ledger theory is globally unstable — and the obstruction has a name from crystal physics

**Date:** 2026-07-11 · **Frozen test:** all three dark-channel stiffness functions κ(q) = u″ + λG(q) − R(q) ≥ 0 over the zone, zeros only at the pinned points. **Result: 202 violations.** κ_cross dips to −0.098, κ_EM to −0.0027, κ_plus to −0.0076. The pinned theory condenses. No dial exists to fix it — that was the point of being pinned.

## The autopsy: the Zener obstruction

The violations near q → 0 are not numerical. The marginality condition was imposed through the + channel (u″_g = R₊(0) − λ_g·G₊(0)); the × channel's mass is then κ_×(0) = (R₊−R₊)(0) − λ_g(G₊−G_×)(0) ≠ 0 — because on a cubic-symmetry lattice **the two gravitational polarizations are not equivalent**: h_xx−h_yy belongs to the e_g irrep, h_xy to t_2g. They are different channels with independent constants — exactly the classical elasticity fact that cubic crystals have three constants (C₁₁, C₁₂, C₄₄) and isotropy requires the **Zener condition** C₁₁−C₁₂ = 2C₄₄ as an *extra* equation. Our single λ_g can impose speed equality (as n219 did) **or** double masslessness — not both. Two Zener-type conditions, one knob. The n219 pinning silently spent λ_g on the speeds and left the × channel massive-tachyonic; the frozen scan caught it. (Also flagged: the pinned λ_g drifts 3.31 → 3.72 between 40³ and 28³ grids — ~12% grid sensitivity, a second defect the leg-1 scan surfaced.)

## The fork this leaves (registered, not chosen)

1. **Orbit-resolved ledgers**: axes and body diagonals are inequivalent edge orbits of the lattice group, and standard lattice-EFT does assign couplings per orbit — but the count goes to ~8 parameters vs 5 conditions, a three-parameter family: the survival review's "parameterized evasion" warning bites in full, and the ledger cascade begins to look like epicycles. Admissible only with a new independent pinning principle.
2. **A degenerate-TT complex**: find a point group where both TT patterns sit in one 2D irrep at generic momentum, making + and × equivalent by symmetry (no cubic group does this exactly; emergent isotropy at loop level is the honest long shot).
3. **Accept the verdict**: P3′-as-proposed is dead at leading order — the two-ledger vacuum joins the one-ledger vacuum, killed by the next-deeper layer of the same lesson: *channels that symmetry does not make equivalent will not behave equivalently, and gravity needs an equivalence the lattice does not supply.*

## Standing state

Gate B's structural discovery survives (the axes+body complex uniquely carries photon zero + rank-6 sampling + exact TT kernel — that is now a permanent fact about the class). The **pinned dynamics on it fails its first no-dial test.** P3′ remains a proposal with a failed leg 1; per its own kill list (§5.4's spirit), the failure is reported at full strength. The program's honest chain: one ledger → chooses light; two ledgers → the Zener split; the fabric keeps telling us that **isotropic gravity does not live on these lattices at leading order.**

**Class: [A-model, frozen-scan execution]; the Zener diagnosis [A — irrep arithmetic]; the fork [registered options, none adopted]. No rescue attempted.**