Scram PJ reach from the bounding-box union of:
- hot-standby box (mode_boundaries.q_shutdown)
- heatup-tight reach envelope (results/reach_heatup_pj_tight.mat)
- operation-LQR reach envelope (results/reach_operation_result.mat)
- LOCA operation envelope (results/reach_loca_operation.mat, 3s)
with precursor + temperature outliers clamped to physical bounds.
Results at probe horizons:
T=10s: 10890 sets in 480s wall — n ∈ [-8e-4, 0.047] T_c [231, 362]
T=30s: 16925 sets in 2892s wall — n ∈ [-4e-4, 0.021] T_c [229, 361]
T=60s: 23919 sets in 705s wall — n ∈ [-2e-4, 0.009] T_c [226, 359]
Monotone n decay, factor-of-5-per-minute even from the wide union.
This is the defensible scram-obligation version: starts from anywhere
the plant could plausibly be (including LOCA-perturbed operation
state), proves n decays. X_exit(scram)=n≤1e-4 still not reached in
60s — same T_max-vs-plant-decay mismatch previously flagged.
Fixed: missing Printf import that had failed the summary block on the
first run (results still computed correctly, just the final print
errored; the matwrite is after the print so the mat file wasn't
saved on that run).
Journal entry for 2026-04-21 extended with the fat-entry result +
the LOCA-reach 3s-horizon numerical-looseness apass. 38 pages.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
New entry 2026-04-21-polytopic-sos-tikhonov.tex covering:
- Polytopic barrier attempt (naive Nagumo check), why it fails
(safety polytope too large for LQR contraction from anywhere),
and the Blanchini pre-image algorithm as the right fix.
- SOS polynomial barrier success on the 2-state reduced projection:
CSDP returns OPTIMAL on a degree-4 polynomial B(x1, x2). First
non-quadratic barrier artifact for this plant. Full polynomial
coefficients embedded.
- Tikhonov singular-perturbation theorem derivation for the PJ
reduction. Writes the 10-state PKE in slow-fast form with
eps=Lambda, identifies the quasi-steady manifold h(x) = PJ
formula, shows fast subsystem exponentially stable under the
prompt_critical_margin_heatup invariant. Error bound:
|x(t) - x_PJ(t)| <= C*Lambda = O(1e-4) in state units, uniform
after boundary layer. Empirical validation data (0.1% max) is
consistent with K_1 ~ 40, K_3 ~ 70 problem constants.
- apass markers for remaining open items: scram entry expansion,
heatup steam-dump Q_sg, heatup controller-ref mismatch.
The Tikhonov derivation upgrades "we ran it and 0.1% error" to
"bounded by C*Lambda where C depends on problem properties bounded
by the safety halfspaces." Rigorous rate.
Journal: 38 pages, clean build.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
