Following user's review feedback (point 1):
prompt_critical_margin_heatup: a new entry under safety_limits that
proves the PJ reduction's validity condition (beta - rho > 0 with
margin) rather than hand-waving it. Controller-specific
specialization for heatup: under feedback linearization,
rho_total = Kp*(T_ref - T_c), so rho ≤ 0.5*beta iff T_c ≥ T_ref -
32.5. Worst-case T_ref = T_c0 at ramp end, so T_c ≥ 275.85 is
sufficient, which our tight-entry reach clears trivially.
Conjoined into inv1_holds. Safety proofs now target BOTH the
physical bounds AND the conditions that make the PJ approximation
sound. Saves Dane's rigor-over-vibes instinct (saved to memory).
plot_reach_tubes.jl: four-panel visualization of a reach-result .mat:
(1) T_c / T_hot / T_cold envelopes overlaid
(2) ΔT_core = T_hot - T_cold (power proxy, right-axis MW)
(3) rho envelope in dollars, with ±1$ prompt lines
(4) n envelope
Operation-mode plot saved to docs/figures/reach_operation_tubes.png.
Heatup PJ version pending — needs full per-step data from the
running reach_heatup_pj_tight_full.jl.
reach_heatup_pj.jl + reach_heatup_pj_tight_full.jl now save
per-timestep envelopes (t_arr, Tc_lo_ts, Tc_hi_ts, ...) so the
plotting script can overlay tubes vs time.
Next up: polytopic / SOS barriers, Tikhonov error bound for PJ.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Singular-perturbation reduction of the PKE+T/H system: set dn/dt=0,
solve algebraically n = Λ·Σλ_i·C_i / (β-ρ). State drops 10 -> 9 (no
n), removes Λ⁻¹ stiffness. Validated against full state on the heatup
scenario:
t [s] |Δn|/n_full T_c err [K]
60 3.7e-5 4e-6
300 3.8e-4 1.9e-4
1200 1.0e-3 2.2e-3
3000 5.0e-4 7.2e-3
Maximum relative error 0.1% on n, peak 7 mK on temperatures over
50 minutes. PJ approximation is excellent for slow heatup transients
(sub-prompt-critical regime).
Files:
- code/src/pke_th_rhs_pj.jl: reduced 9-state RHS
- code/scripts/validate_pj.jl: side-by-side sim
- code/scripts/reach_heatup_pj.jl: TMJets reach with PJ model
(probing T = 60, 300, 1800, 5400 s)
App v2 (Pluto):
- §9b: live ingestion of reach_operation_result.mat with per-
halfspace margins computed from JSON-defined inv2_holds.
- §9c: 2D projection chooser (n, T_f, T_c, T_cold) with reach
tube envelope overlay.
- §9d: PJ heatup reach summary (placeholder until first run lands).
Journal:
- Added 2026-04-20-overnight-prompt-jump.tex with PJ derivation,
validation table, soundness ledger update. apass markers for
the in-progress reach results.
This commit captures state mid-run; next commit will add the
populated reach results once TMJets returns.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
