steam-dump heatup reach: quantifies the cost of modeling the disturbance

Morning-review point 3 result: tight-entry heatup PJ reach with
Q_sg in [0, 5% P0] as a bounded parameter (augmented state x[10]).

  T=60s:  7042 sets in 394s — T_c in [270.97, 291.0] — low-trip × loose
  T=300s: 100k sets budget exhausted in 5400s —
          T_c in [219.4, 316.3] — low-trip × loose

Compared to the no-disturbance tight-entry run (all 6 halfspaces at
300s, T_c in [281.05, 291.0]), the bounded steam-dump disturbance
costs the low-T_avg-trip discharge even at 60s. Physically correct
— steam dump pulls heat through secondary, cascades into cold-leg
and T_avg. The reach tube accurately captures this coupling.

Thesis-relevant finding: without modeled disturbance bounds, reach
tubes are over-optimistic. Quantifies how much of the prior
"all 6 halfspaces" result came from Q_sg=0 simplification vs.
actual controller robustness.

Results saved to results/reach_heatup_pj_with_steam_dump.mat.
Journal entry updated with the per-horizon table + decision box on
what this means for thesis claims.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

journal/entries/2026-04-21-polytopic-sos-tikhonov.tex

@@ -209,10 +209,46 @@ amplifies slow precursor modes under large disturbance, so horizons
 $> 3$~\unit{\second} blow up).  A proper zonotope-generator
 propagator would fix this; deferred.}
 
-\apass{Heatup with steam-dump $Q_{\mathrm{sg}}$ demand (user's point 3)
+\textbf{Heatup with steam-dump $Q_{\mathrm{sg}}$ demand (user's morning
-queued; a one-line change to \texttt{main\_mode\_sweep.jl}'s
+point 3) --- landed this session.}  Built
-\texttt{Q\_heat} lambda plus a corresponding disturbance bound in
+\texttt{code/configs/heatup/with\_steam\_dump.toml} +
-\texttt{reach\_heatup\_pj.jl}.}
+\texttt{code/scripts/reach/reach\_heatup\_pj\_sd.jl}: 11-state RHS
+(9 physics + $x_{10} = Q_{\mathrm{sg}}$ as augmented bounded parameter
+with $\dot x_{10} = 0$, $x_{11} = t$).  Entry box on $Q_{\mathrm{sg}}$:
+$[0,\ 0.05 P_0]$ (steam dump to atmosphere, conservative).
+
+Results from the tight X\_entry + steam-dump run:
+\begin{lstlisting}[style=terminal]
+--- Probe T = 60.0 s ---
+  TMJets: 7042 reach-sets in 393.6 s
+  T_c envelope:   [270.97, 291.0] °C
+  Low-T_avg trip (T_c >= 280): × loose
+
+--- Probe T = 300.0 s ---
+  Max-steps budget exhausted (100,000 reach-sets, 5403 s wall)
+  T_c envelope:   [219.4, 316.28] °C
+  Low-T_avg trip: × loose
+\end{lstlisting}
+
+\textbf{Steam-dump disturbance costs the low-$T_{\mathrm{avg}}$ trip
+discharge even at 60~\unit{\second}.}  Without the dump
+($Q_{\mathrm{sg}} = 0$ exact), the tight-entry run cleared all six
+halfspaces at 300~\unit{\second} with T\_c $\in [281.05, 291.0]$.  With
+the dump in $[0, 5\%]$, T\_c lower bound drops to 270.97~$^\circ$C ---
+physically consistent: steam dump pulls heat from secondary, cools
+cold-leg, cascades into T\_avg.
+
+At 300~\unit{\second} with the dump, step budget exhausts (100k sets
+in 90~\unit{\minute} wall) and the envelope blows out.  Bigger budget
+or entry-box refinement would likely recover; deferred.
+
+\begin{decision}
+The steam-dump result is pedagogically useful for the thesis: it
+shows quantitatively how much of the safety margin comes from
+``plant is isolated'' modeling vs.\ realistic operational
+assumptions.  Without accurate disturbance bounds the reach tube
+is over-optimistic.
+\end{decision}
 
 \apass{The reach tube plots (Dane's point 4) for the heatup PJ tight
 entry revealed a controller-reference mismatch: with