# n202 — The shear speed at scale: 0.46 reproduced, the complex family mapped, and no luminal point found


**CORRECTION (n215, 2026-07-11):** every 9- and 13-complex number in this note was contaminated by a direction-vector mutation bug in the Rust (found by two-backend reconciliation, audit §5's prescription). The corrected map: cubic 0.51 (was clean, unchanged) is the FAMILY MAXIMUM; 9-uniform 0.38, 9-derived 0.32, axes-0.25 0.26, fcc 0.27, 13-complexes 0.31–0.34. The '0.85 maximum near isotropy' does not exist — isotropy makes the deficit WORSE. The conclusion strengthens in the adverse direction: no complex reaches half the cone.

**Date:** 2026-07-11 · **Tool:** `cg-rust/` — zero-dependency Rust; exact two-phonon Brillouin-zone sums (512² / 96³ / 64³ grids, seconds per config). **Reproduce:** `cd cg-rust && cargo run --release`. **Target:** FP gate leg 3 / condition B — the standing c_g² = 0.46 failure.

## Method (independent of n178)

The blind shear channel has no bare dynamics: its gradient stiffness and inertia are both *induced* by the scalar vacuum. Both are second derivatives of one two-phonon response sum R(ω, q), so the induced speed is the convention-free ratio c_g² = lim [R(0,0)−R(0,q)] / (q²·∂R/∂ω²) — normalizations, couplings, and signs cancel. Free-scalar vacuum, declared; this is the leading induction order, not n178's dressed pinned point.

## Results (μ → 0, q → 0; ratio = c_g²/c_scalar² on the same complex)

| complex | c_g² | scalar c² | **ratio** |
|---|---|---|---|
| 2D square | 0 | 1 | **0 — 2D shear does not propagate at all** |
| 3D cubic, uniform | 0.515 | 1 | **0.51** (n178's 0.46: same class, independently confirmed) |
| 9-complex, uniform | 3.489 | 5.0 | 0.70 |
| 9-complex, axes ½ (n197 weights) | 3.660 | 4.5 | 0.81 |
| 9-complex, axes 0.25 | 3.614 | 4.25 | **0.85 — the family's maximum** |
| 9-complex, axes 0.10 | 3.478 | 4.10 | 0.85 |
| 9-complex, fcc (axes 0) | 3.331 | 4.0 | 0.83 |
| 13-complex, iso A / iso B | 3.603 / 2.061 | 9.0 / 6.0 | 0.40 / 0.34 |

## The three findings

1. **The 0.46 problem is real and reproduced independently** — the cubic-class value (0.51 here, 0.46 at n178's dressed point) is not a bug of the pinned-state machinery; it is the free-induction physics of that complex.
2. **The speed is a property of the complex, and the map is nontrivial**: the ratio spans 0.34–0.85 across the scanned family, with an interior maximum ≈ 0.85 near axis-weight 0.2 — close to, but not at, the audit-isotropy point (n197's ½). Richer complexes (13 directions) do *worse*, not better: more directions ≠ more luminal.
3. **No computed complex reaches c_g = c.** At leading induction order over a free scalar vacuum, the blind shear channel is subluminal by at least ~15% everywhere in the scanned family. The eighth critique's demand — resolve 0.46, don't subtract it — now has a quantitative floor: any completion (interactions, the guard's dressing, higher induction orders, or a complex outside this family) must beat a mapped 15% deficit, not an unexplored one.

## What this does and does not decide

Condition B (c_g ≠ c surviving the honest continuum limit → GW170817 executes) is **not fired**: this is the leading order over the free vacuum, and n178's dressed point already shows interactions move the number (0.51 → 0.46 — the wrong way, for the record). What is decided: the "lattice-analytic contamination" hope is dead as stated — the deficit is not an artifact that isotropy or continuum extrapolation removes; it is a structural property of free induction. The sector's survival now requires a *mechanism* that closes 15%, and the search is mechanized (the Rust scan runs any complex in seconds). Inversion worth recording: if such a point exists, GW170817's 10⁻¹⁵ becomes the sharpest substrate-selection principle the theory has — data forcing the complex, as clusters forced R = 1 and isotropy forced the weights.

**Class: [A-model, exact sums; free-vacuum induction declared]; the n178 confirmation [A]; the no-luminal-point statement is scoped to the scanned family and leading order.**