VAL-B1-EXTCOORD-PHI2-DERIV · CLOSED GATE · WAS A LIVE FRONTIER
Nested radial-spacing refinement passes for both first and second derivatives at all four certification radii. That gate remains closed. Four-point RSET DEV is now HOLD because of the separate Mτ source/sign question.
Checkpoint ladder
DERIVATIVE
Modewise derivation
PASSDERIVATIVE
Same-ladder profile
PASSDERIVATIVE
N/L deriv convergence
PASSDERIVATIVE
Mixed error budget
PASSDERIVATIVE
Nested h refinement
PASSDERIVATIVE
⟨φ²⟩ derivatives
PASSREVIEW
RSET unlock review
COMPLETENEXT
Four-point RSET DEV
HOLD| Layer | Checkpoint | Status |
|---|---|---|
| DERIVATIVE | Modewise derivation | PASS |
| DERIVATIVE | Same-ladder profile | PASS |
| DERIVATIVE | N/L deriv convergence | PASS |
| DERIVATIVE | Mixed error budget | PASS |
| DERIVATIVE | Nested h refinement | PASS |
| DERIVATIVE | ⟨φ²⟩ derivatives | PASS |
| REVIEW | RSET unlock review | COMPLETE |
| NEXT | Four-point RSET DEV | HOLD |
Per-radius PASS / PASS matrix
ξ_rad = 1.2
Coarse D(h) unavailable. Certification is h/2 → h/4 stability, source-derived modewise agreement, N/L spot referee, and mixed error budget. Not a measured three-level Richardson order. October 9: this PASS is the old implementation and tolerance, not the repaired scalar budget.
ξ_rad = 1.8
Second-derivative successive differences are slightly non-monotonic at very small absolute scale. Interpreted as numerical floor / error-budget stability, not physical divergence. Do not display negative formal p_est as a physics failure.
ξ_rad = 3.0
Both first and second nested-h refinements pass under the full gate combination then in force.
ξ_rad = 5.0
Second-derivative successive differences are slightly non-monotonic at very small absolute scale. Interpreted as numerical floor / error-budget stability, not physical divergence.
| ξ_rad | h_refine_d1 | h_refine_d2 | Qualifier |
|---|---|---|---|
| 1.2 | PASS | PASS | Coarse D(h) unavailable. Certification is h/2 → h/4 stability, source-derived modewise agreement, N/L spot referee, and mixed error budget. Not a measured three-level Richardson order. October 9: this PASS is the old implementation and tolerance, not the repaired scalar budget. |
| 1.8 | PASS | PASS | Second-derivative successive differences are slightly non-monotonic at very small absolute scale. Interpreted as numerical floor / error-budget stability, not physical divergence. Do not display negative formal p_est as a physics failure. |
| 3.0 | PASS | PASS | Both first and second nested-h refinements pass under the full gate combination then in force. |
| 5.0 | PASS | PASS | Second-derivative successive differences are slightly non-monotonic at very small absolute scale. Interpreted as numerical floor / error-budget stability, not physical divergence. |
Historical nested-h HOLD is resolved by B1_EXTCOORD_PHI2_DERIVATIVE_NESTED_H_FINAL_CLOSURE_2026-09-14. The HOLD is retained as dated history, not deleted.
At ξ_rad = 1.2 the coarse D(h) value is unavailable. Certification there is based on h/2 → h/4 stability, source-derived modewise agreement, N/L spot referee, and mixed error budget. Do not claim a measured three-level Richardson convergence order at ξ = 1.2.
Closing this derivative gate did not promote RSET. The PASS is nested-h stability under the implementation and tolerance then in force. October 9 reassessment: a blanket massless skip and a wrong static-mode boundary coefficient were found later. Do not read this stamp as the repaired scalar budget. The current live comparison is the r=6M empirical trace.
Qualifiers
Correction chain
prior
Original STOP_AT_D failure on the derivative path. Retained in the correction chain.
cache-poison
Derivative cache poison. Later: FIXED / RETEST PASSED.
2026-09-15
Nested-h final closure. PHI2_DERIVATIVES = PASS.
Updated 2026-09-15. All checkpoints · VAL-B1-SCALAR-TRACE-R6 · VAL-B1-PMR-CNG-CONFIRMATION · VAL-B1-PUBLISHED-HH-CURVES · VAL-B1-HADAMARD-E-CANDIDATE · VAL-B1-PMR-CNG-DISCOVERY · VAL-B1-PMR-ASYMPTOTIC-AUDIT · VAL-B1-PMR-ANGULAR-GATE · VAL-B1-MTAU-SIGN-REPRO · VAL-B1-EXTCOORD-HH · VAL-B1-EXTCOORD-RSET-4PT · VAL-B1-HOWARD-242-246