# AP1-R2c p=42 bounded-method diagnostic checkpoint v1.1

Timestamp: `2026-09-02T09:59:10Z`

The authoritative continuation parent remains the repeatedly validated
41-node PASS. No 42-node vector from this diagnostic was stored or used as a
seed.

Starting only from that PASS, an endpoint-preserving degree-2/3 B-spline
extrapolation with `beta=2.5`, a partial `rho_chi` projection with
`alpha=1.25e-5`, and two bounded frozen-Lobatto defect-correction stages
reduced the 42-node full DAE norm to `2.5836112519572583e-4`. This improves
the preceding bounded diagnostic by a factor of `0.8665270896886014` and the
original p42 NONPASS by a factor of `0.5857561368752219`.

Three independent full checks returned the same DAE value. The threshold
remains `1e-4`, so the candidate remains NONPASS. Every other unchanged gate
passes:

- Ward: `2.1794407870617619e-7` (threshold `2e-6`)
- source closure: `2.056727924509347e-5` (threshold `1e-4`)
- Friedmann residual: `1.5127661435732624e-16`
- Wronskian relative error: `1.42e-49`
- minimum `H`: `8.312595082091879e-8`
- minimum `P_X`: `1.8132335484729594`
- minimum `K`: `3.016188545394498`

Additional lower-beta/rho grids, scalar and coupled trust regions, smooth
Chebyshev minimax corrections, valid-parent sparse lifts, a tighter p41
Newton attempt, an alternative full-PASS p41 branch, and a stronger
defect/rho rebalance were excluded. The stronger defect correction crosses a
sharp source-closure cliff above `sigma_alpha=3e-6`.

Equations, physics, and gates were unchanged. G22 remains ORANGE and
production curves remain locked.