# n219 — The survival review answered: Gate B PASSES on a complex the review didn't consider, and the theory pins itself completely

**Date:** 2026-07-11 · **Responds to:** `P3_SURVIVAL_REVIEW.md`. **Verdict accepted in full** — including the two numerical errors it caught in the proposal (λ_g: 2.020 → the executable's 2.15; common c: 0.457 → 0.437 — both were stale hand-values; corrected per rule 5, and both are now superseded anyway). The review's decision ("execute Gate B first — cheap and potentially fatal") was executed the same day. It was not fatal. It was the door.

## Gate B: PASS — the {axes + body-diagonal} complex

The review's decisive failure (§3: axial edges lose h_cross; diagonals kill the EM zero) considered face diagonals. **Body diagonals evade the dilemma**: k\*·(1,1,1) = 3π ≡ π, so every body-diagonal term of A(k\*) vanishes *individually* — the staggered photon zero survives exactly. Checked at machine precision, all four requirements simultaneously:

| requirement | result |
|---|---|
| staggered Gauss zero | \|A(k\*)\|² = 7×10⁻³¹ — exact, any weights |
| rank-6 symmetric-tensor sampling | rank(N) = 6 (axes give the diagonal components; body diagonals give all off-diagonals) |
| controlled isotropy | weights (8/9, 1) — one equation, no freedom; residual 2×10⁻¹⁶ |
| two TT polarizations, generic momentum | four-row dark space: dim 2, traceless-transverse to 10⁻¹⁶ at every tested q |

A lattice-arithmetic bonus with physical content: **the + polarization lives entirely on the axes; the × polarization entirely on the body diagonals.** The two gravitational polarizations are carried by different edge families.

## The full pinning — the review's §2 objection consumed

The review correctly showed the P3′ family was one-parameter (λ_e = 7.567 had no authority; the common cone varied along the family). On the Gate-B complex the structure closes itself: because + and × live on different edge families, **c₊ = c₊ is a nontrivial condition** — and GR requires the two polarizations to co-propagate. The full system:

- C1, C2 (masslessness ×2) fix u″_g, u″_e;
- **C3′ (c₊ = c₊, physical requirement)** fixes λ_g = 3.31;
- **C3 (c_g = c_EM, GW170817)** fixes λ_e = 12.96.

**Four parameters, four conditions, zero freedom — and the solution exists and is physical**: all three channels stable and massless, both λ positive, λ_g inside its window. The common cone becomes a *prediction of the structure*: **c² = 0.369 (c = 0.607 c_substrate)**, robust across grid/mass/momentum sweeps (0.358–0.370; the pinned λs move by ≲3%). The equal-speed conditions hold to four digits internally (the + = × = EM check column).

## Standing state against the review's gates

- **Gate B: PASS** (this note) — the review's "potentially fatal" test instead produced the unique admissible complex.
- **Gate C: moot in its original form** — the family is now a point; the variation table the review requested is replaced by the robustness table above.
- **Gates A (local doubled-cell action), E (nonlinear mixing/RG), F (matter cone — still the most exposed flank), G (dressed recomputation): open and owed**, in the review's order. Gate D (independent normalization) sharpens beautifully: with zero parameters left, the Coulomb and Newton normalizations are now *predictions with no dials* — the next computation.
- P3′ remains a **proposal**; adoption still waits on A/E/F/G. But its status changes character: it is no longer an underdetermined family with a chosen member — it is a fully pinned structure that happened to exist when nothing forced it to.

**Class: Gate B [A — exact checks, machine precision]; the pinning [A-model, leading order, robustness swept]; the common-cone prediction [conditional on P3′ + leading order]; everything else inherits the review's open gates.**