docs(S3): record Session 4 Rung-2 continuous entropy bound landing

continuous_entropy_le_ln_bma Qed-closed at 37713fb (+193 LOC).
Updates §3.6.2 pending → Session 4 landed; Session 5+ items listed.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: hyperpolymath

docs/handover/AI-WORK-007.md

@@ -678,11 +678,23 @@ continuous Boltzmann theorem):
     rewrites via `ln_Rinv` + `ln_mult`, sums, and collapses using
     `prob_dist_sum_one` + `finSum_const_1`.  Jensen is **not** used —
     the tangent-line route is direct and sidesteps the Jensen step.
-- **Session 4+ (pending):** Rung-2 (Riemann) / Rung-3 (Lebesgue;
-  needs `coq-mathcomp-analysis`) / Rung-4 (full Boltzmann
-  collision operator + H-functional monotonicity, research-grade).
-  Equality case of Rung-1 (uniform distribution as the unique
-  maximiser) also open.
+- **Session 4 (landed, commit `37713fb`, +193 LOC):** §8
+  `ContinuousEntropySection` — Rung-2 continuous entropy bound via
+  Coquelicot `RInt_le`.  Variables: `a b : R`, `Hab : a < b`,
+  pdf `f` with positivity + integrability + normalisation
+  hypotheses.  `continuous_entropy := -RInt (f x * ln (f x)) a b`.
+  **`continuous_entropy_le_ln_bma` Qed-closed** (`H_cont[f] ≤
+  ln(b-a)`).  Proof route: tangent-line `ln u ≤ u - 1` (from
+  `exp_ineq1_le` via `ln_exp`); pointwise bound on
+  `f(x) * (-ln(b-a) - ln f(x))`; `RInt_le`; `RInt_plus` /
+  `RInt_scal` / `RInt_const` linearity; normalisation (∫f = 1);
+  `lra`.  No Jensen needed — tangent-line route is direct.
+  Suite verified 35/35 after commit.
+- **Session 5+ (pending):** Rung-3 (Lebesgue; gated on
+  `coq-mathcomp-analysis` being installed — not in current Guix
+  env) / Rung-4 (full Boltzmann collision operator + H-functional
+  monotonicity, research-grade).  Equality case of Rung-1
+  (uniform distribution as the unique maximiser) also open.
 
 #### 3.6.3 S4 — n-dim Heisenberg / Cauchy-Schwarz ladder