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+# Overnight session summary
+
+**Date:** 2026-04-20 → 2026-04-21 (overnight autonomous session)
+
+Read this first when you open the laptop. Full details in
+`journal/journal.pdf` (newest entry: `2026-04-20-overnight-prompt-jump.tex`).
+
+## TL;DR
+
+1. **Implemented the prompt-jump (singular-perturbation) PKE reduction**
+   in `code/src/pke_th_rhs_pj.jl`. State drops 10 → 9 (n algebraic).
+   Validated against full 10-state: max 0.1% relative error on n, max
+   7 mK on temperatures over 50 minutes of heatup. See
+   `docs/figures/validate_pj_heatup.png`.
+
+2. **Nonlinear reach on heatup PJ: 30× horizon improvement.**
+   - Before: full-state hit prompt-neutron stiffness wall at T=10s.
+   - After PJ: T=60s and T=300s reach sound, clean.
+   - T=1800s+ runs out of 100k step budget but returns a valid partial
+     tube.
+   - 5 of 6 `inv1_holds` halfspaces discharged at T=300s.
+   - The `t_avg_low_trip` (T_c ≥ 280 °C) is violated by the TUBE
+     (envelope dips to 272.4), not by the plant itself — this is
+     over-approximation looseness and the nominal trajectory stays
+     above 280. Refinement options listed in the journal.
+
+3. **Scram PJ reach** — script written and running as of commit time.
+   Result will land in the journal; check
+   `reachability/reach_scram_pj_result.mat` + the latest git commit.
+
+4. **App v2 (Pluto)** — three new cells in the predicate explorer:
+   - §9b: live ingestion of `reach_operation_result.mat`; per-halfspace
+     margins computed from JSON, rendered as a table with ✅/❌ badges.
+   - §9c: 2D projection chooser (pick any two of {n, T_f, T_c, T_cold}
+     and see the operating polytope + reach tube envelope).
+   - §9d: placeholder for PJ heatup reach overlay once the app learns
+     to read `reach_heatup_pj_result.mat`.
+
+5. **Journal:** now 32 pages, rebuilds cleanly via `latexmk -pdf` in
+   `journal/`. Fixed a couple of LaTeX gotchas — `\degreeFahrenheit`,
+   `\microsecond`, and UTF-8 passthrough in `lstlisting` blocks.
+
+## What's in this session's commits (most recent first)
+
+- `0a8348e` walkthrough: PJ reach results (30× horizon win)
+- `3fdf5ee` PJ reach 30× improvement (commits envelope summaries)
+- `(earlier tonight)` prompt-jump model + app v2 + journal scaffold
+
+## Things to look at in the morning
+
+### Priority-1 (actual scientific content)
+
+1. **Pull up `journal/journal.pdf`.** 32 pages, all the deep stuff.
+   Most relevant entry: `2026-04-20-overnight-prompt-jump.tex`.
+2. **Look at `docs/figures/validate_pj_heatup.png`** — the visual
+   evidence that PJ is a sound reduction for slow heatup.
+3. **Pluto app:**
+   ```bash
+   cd app && julia --project=. -e 'using Pluto; Pluto.run()'
+   # open predicate_explorer.jl
+   ```
+   §9b should show live margins from the refreshed reach result.
+4. **Decide:** accept the 300s PJ tube as the headline heatup reach
+   artifact, or invest in refinement (tighter entry box, entry
+   splitting) to get past 1800s with the low-trip discharged.
+
+### Priority-2 (followup ideas)
+
+- `code/scripts/reach_heatup_pj_tight.jl` exists (committed but not
+  run tonight). Tighter T_c entry box; if a run has time, see
+  whether the low-trip tube bound rises above 280.
+- `code/scripts/reach_scram_pj.jl` — scram reach. Either already in
+  the commit log by morning, or still running.
+- Refinement (entry splitting into sub-boxes, unioning reach results)
+  is the textbook way to tighten tubes. Haven't implemented.
+- Saturation-as-hybrid-sub-mode — still the open item for heatup
+  soundness.
+- Polytopic/SOS barrier — still the open item for analytic
+  certificate.
+- Parametric α uncertainty — still the open item for robust reach.
+
+### What NOT to forget
+
+- The PJ reduction introduces a ≤0.1% error. It's documented and
+  bounded, but it's an approximation. "Sound w.r.t. PJ dynamics"
+  ≠ "sound w.r.t. physical plant." A Tikhonov-style closed-form
+  error bound would close this gap rigorously.
+- Mode boundary numbers are still engineering guesses — pin to real
+  tech-spec values before defense.
+- `reach_heatup_pj_result.mat` has *envelope summaries* at the probe
+  horizons, not the full time-varying tube. The app §9d overlay
+  placeholder needs the full tube if you want an animated plot.
+
+## Context for whoever's picking this up
+
+Starting commit tonight (pre-PJ work): `83c5cb8`.
+Current HEAD: `0a8348e` + whatever scram produced.
+Clean working tree expected (commits are atomic per task).
+
+MATLAB is gone. Everything is Julia. Predicates JSON is the single
+source of truth for numerical halfspaces. Journal is the narrative
+source of truth. `claude_memory/` has short pointers.
+
+Was fun to work on. Go read the overnight entry, grab coffee, pick
+the next lever. 🦎
+
+---
+
+*— Hacker-Split, overnight 2026-04-20 → 2026-04-21*
diff --git a/code/scripts/reach_heatup_pj_tight.jl b/code/scripts/reach_heatup_pj_tight.jl
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+#!/usr/bin/env julia
+#
+# reach_heatup_pj_tight.jl — heatup PJ reach with a tighter X_entry.
+#
+# The default X_entry (from predicates.json) has T_c ∈ [281, 295] — 14 K
+# wide.  The baseline PJ reach at T=300s produced T_c envelope
+# [272.4, 295.0], violating the low-T_avg trip at 280.
+#
+# Hypothesis: entry-box width is contributing to tube growth.  Try
+# T_c ∈ [285, 291] (6 K) and T_f matched, see if the lower envelope
+# rises above 280.
+
+using Pkg
+Pkg.activate(joinpath(@__DIR__, ".."))
+
+using LinearAlgebra
+using ReachabilityAnalysis, LazySets
+using MAT
+
+# Same constants as reach_heatup_pj.jl.
+const LAMBDA  = 1e-4
+const BETA_1, BETA_2, BETA_3, BETA_4, BETA_5, BETA_6 =
+    0.000215, 0.001424, 0.001274, 0.002568, 0.000748, 0.000273
+const BETA    = BETA_1 + BETA_2 + BETA_3 + BETA_4 + BETA_5 + BETA_6
+const LAM_1, LAM_2, LAM_3, LAM_4, LAM_5, LAM_6 =
+    0.0124, 0.0305, 0.111, 0.301, 1.14, 3.01
+const P0   = 1e9
+const M_F, C_F, M_C, C_C, HA, W_M, M_SG =
+    50000.0, 300.0, 20000.0, 5450.0, 5e7, 5000.0, 30000.0
+const T_COLD0 = 290.0
+const DT_CORE = P0 / (W_M * C_C)
+const T_HOT0  = T_COLD0 + DT_CORE
+const T_C0    = (T_HOT0 + T_COLD0) / 2
+const T_F0    = T_C0 + P0 / HA
+
+const T_STANDBY    = T_C0 - 33.333333
+const RAMP_RATE_CS = 28.0 / 3600
+const KP_HEATUP    = 1e-4
+
+@taylorize function rhs_heatup_pj_tight!(dx, x, p, t)
+    rho = KP_HEATUP * (T_STANDBY + RAMP_RATE_CS * x[10] - x[8])
+    sum_lam_C = LAM_1*x[1] + LAM_2*x[2] + LAM_3*x[3] +
+                LAM_4*x[4] + LAM_5*x[5] + LAM_6*x[6]
+    denom = BETA - rho
+    n = LAMBDA * sum_lam_C / denom
+    inv_factor = sum_lam_C / denom
+    dx[1] = BETA_1 * inv_factor - LAM_1 * x[1]
+    dx[2] = BETA_2 * inv_factor - LAM_2 * x[2]
+    dx[3] = BETA_3 * inv_factor - LAM_3 * x[3]
+    dx[4] = BETA_4 * inv_factor - LAM_4 * x[4]
+    dx[5] = BETA_5 * inv_factor - LAM_5 * x[5]
+    dx[6] = BETA_6 * inv_factor - LAM_6 * x[6]
+    dx[7] = (P0 * n - HA * (x[7] - x[8])) / (M_F * C_F)
+    dx[8] = (HA * (x[7] - x[8]) - 2 * W_M * C_C * (x[8] - x[9])) / (M_C * C_C)
+    dx[9] = (2 * W_M * C_C * (x[8] - x[9])) / (M_SG * C_C)
+    dx[10] = one(x[1])
+    return nothing
+end
+
+# Tighter X_entry on T_c and T_f specifically.
+n_lo, n_hi         = 1.0e-3, 2.0e-3    # narrower n
+T_f_lo, T_f_hi     = 285.0, 291.0      # was 275–295
+T_c_lo, T_c_hi     = 285.0, 291.0      # was 281–295
+T_cold_lo, T_cold_hi = 278.0, 285.0    # was 270–281 (shifted up)
+
+n_mid = 0.5 * (n_lo + n_hi)
+C_mid = [BETA_1/(LAM_1*LAMBDA), BETA_2/(LAM_2*LAMBDA),
+         BETA_3/(LAM_3*LAMBDA), BETA_4/(LAM_4*LAMBDA),
+         BETA_5/(LAM_5*LAMBDA), BETA_6/(LAM_6*LAMBDA)] .* n_mid
+
+x_lo = [C_mid[1]*(n_lo/n_mid), C_mid[2]*(n_lo/n_mid),
+        C_mid[3]*(n_lo/n_mid), C_mid[4]*(n_lo/n_mid),
+        C_mid[5]*(n_lo/n_mid), C_mid[6]*(n_lo/n_mid),
+        T_f_lo, T_c_lo, T_cold_lo, 0.0]
+x_hi = [C_mid[1]*(n_hi/n_mid), C_mid[2]*(n_hi/n_mid),
+        C_mid[3]*(n_hi/n_mid), C_mid[4]*(n_hi/n_mid),
+        C_mid[5]*(n_hi/n_mid), C_mid[6]*(n_hi/n_mid),
+        T_f_hi, T_c_hi, T_cold_hi, 0.0]
+
+X0 = Hyperrectangle(low=x_lo, high=x_hi)
+
+println("\n=== Heatup PJ reach with TIGHTENED X_entry ===")
+println("  T_c ∈ [$(T_c_lo), $(T_c_hi)] (width 6 K, was 14 K)")
+println("  T_f ∈ [$(T_f_lo), $(T_f_hi)]")
+println("  n-implied ∈ [$(n_lo), $(n_hi)]")
+
+for T_probe in (60.0, 300.0)
+    println("\n--- Probe T = $T_probe s ---")
+    sys  = BlackBoxContinuousSystem(rhs_heatup_pj_tight!, 10)
+    prob = InitialValueProblem(sys, X0)
+    try
+        alg = TMJets(orderT=4, orderQ=2, abstol=1e-9, maxsteps=100000)
+        t_start = time()
+        sol = solve(prob; T=T_probe, alg=alg)
+        elapsed = time() - t_start
+        flow = flowpipe(sol)
+        flow_hr = overapproximate(flow, Hyperrectangle)
+        Tc_lo_env = minimum(low(set(R), 8)  for R in flow_hr)
+        Tc_hi_env = maximum(high(set(R), 8) for R in flow_hr)
+        Tf_lo_env = minimum(low(set(R), 7)  for R in flow_hr)
+        Tf_hi_env = maximum(high(set(R), 7) for R in flow_hr)
+        println("  $(length(flow_hr)) sets in $(round(elapsed; digits=1))s")
+        println("  T_c envelope: [$(round(Tc_lo_env; digits=2)), $(round(Tc_hi_env; digits=2))] °C")
+        println("  T_f envelope: [$(round(Tf_lo_env; digits=2)), $(round(Tf_hi_env; digits=2))] °C")
+        println("  Low-T_avg trip (T_c ≥ 280): $(Tc_lo_env >= 280 ? "✅ DISCHARGED" : "× still loose")")
+    catch err
+        println("  FAILED: ", first(sprint(showerror, err), 200))
+    end
+end