# n212 — Construction 3, first execution: ADVERSE. The monitor rows are second-class — the audit is not the constraint algebra of GR

**Date:** 2026-07-11 · **Audit gate 38.1 / FP gate leg 2, run as a finite Dirac analysis.** In-session computation; three momenta, two stiffness models, full constraint-tower stabilization and first/second-class classification.

## The setup

Phase space (h_m, π_m) per momentum (6+6); the n166 rows promoted to phase-space functions by their own time structure: v₀ carries a frequency factor → C₀ = a₀·π (momentum-type); the three flux rows → C_i = b_i·h (configuration-type). Hamiltonian H = ½|π|² + ½h·K·h with K = gradient-type stiffness on the weighted complex (and an isotropic control). Dirac procedure: stabilize the tower, compute the bracket Gram matrix, classify.

## The result

| q | K | tower | first-class | second-class | DOF |
|---|---|---|---|---|---|
| on-axis | grad | 8 | **0** | 8 | 2 |
| on-axis | iso | 8 | **0** | 8 | 2 |
| (1,1,0) | grad | 10 | **0** | 10 | **1** |
| generic | grad | 12 | **0** | 12 | **0** |
| any | iso | 8 | **0** | 8 | 2 |

**Zero first-class constraints, at every momentum, under both stiffness models.** The pairing {C₀, C_i} = a₀·b_i ≠ 0 is kinematic — independent of K — so the verdict is robust within this embedding: **the monitor rows do not generate gauge transformations.** Second-class constraints eliminate phase-space pairs; they do not produce diffeomorphism redundancy. The audit's §31 suspicion is confirmed at the strongest level: the "audit = constraint surface of linearized GR" reading is dead at the canonical level. What survives of n197 is exactly what the walk-back already said: a projector fact.

Worse, under the physical (gradient) stiffness the tower keeps growing off-axis and **the degree-of-freedom count collapses anisotropically (2 → 1 → 0)** — the canonical structure is not even q-uniform in the current model.

## The structural diagnosis (why it failed — and the one door left)

The character mismatch was visible in hindsight: GR's momentum constraints are *momentum*-type (∂π), the audit's flux rows are *configuration*-type (they bill dk). And in ADM, the constraints are first-class in the (h_ij, π_ij) sector *because lapse and shift enter as multipliers* — the h₀₀ and h₀ᵢ components. Those are precisely the components this model does not have. **The failure localizes to the same hole every radiative diagnosis has hit: no h₀₀/h₀ᵢ dynamics.** The one remaining door for construction 3 is the ADM-style embedding on an enlarged phase space with multipliers — which requires building exactly what is absent. If that construction also yields second-class rows, the GR-recovery program in this sector is finished, and honestly so.

## Standing consequences (applied)

- FP gate leg 2: from "walked back to a projector" to **"canonical identification FAILED as attempted (n212); one named door remains (ADM embedding, requires h₀₀/h₀ᵢ)"** — status updated.
- The radiative scoreboard now reads: speed — no luminal point at any computed order (n202), repair rejected (§35); canonical structure — second-class, no gauge (n212). **Two of the sector's three decisive constructions are currently failing.** The sector's survival now rests entirely on the h₀₀/h₀ᵢ construction doing double duty (fixing both the embedding and, possibly, the speed).

**Class: [A-model, exact finite Dirac analysis]; the embedding and both K choices declared; adverse result reported at full strength, no rescue attempted.**