docs(state): sync STATE + session-log after S4 Session 3 + E5 Session 6

STATE.a2ml completed-2026-04-19 block gains six new entries covering
the Session-3/Session-6 landings (S3 Session 3, S4 Session 2, E5
Session 5 pre-/compact; S4 Session 3, E5 Session 6 post-/compact)
plus the suite-wide 38/38 gate confirmation.

session-log.txt gains the 2026-04-19 03:00-03:45 continuation-
session record per SESSION-LOG-CONVENTION: S4 Rung-2 (cauchy_schwarz
_complex_ndim Qed via λ-quotient + in-file complex substrate) and
E5 Session 6 (needham_schroeder_fixed single-session headline Qed
via structural any_enc_trace invariant).

No proof-file changes in this commit — documentation sync only.

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

Author: hyperpolymath

.machine_readable/STATE.a2ml

@@ -172,4 +172,10 @@
       "AI-WORK-007.md §0 header + §3.4 lift table + §3.6.1 Session-6/7+ subsections refreshed (Desktop-only, not tracked)."
       "~/Desktop/AI-WORK-007-UPSTREAMS.md authored — per-item upstream dependency trace for every OPEN entry in AI-WORK-007.md. Single unified port table (E1/S3/S4/E5) with Status column; sections ordered by action-cost (GitHub billing cheapest → research-grade tails last). Desktop-only."
       "MANIFEST pointer for E1 remains at E1_lyapunov_1d.v per §3.1 honest-accounting — only moves once Row-5 Qed lands."
-      "Session 7+ plan: scalar binomial (s+t)^k / k! = sum_{p+q=k} s^p t^q / (p! q!); Cauchy-product bridge via Coquelicot.Series.is_series_mult; Apow_add fold to Qed-close the Row-2 semigroup identity exp_matrix (s+t) A = Mmul (exp_matrix s A) (exp_matrix t A)."))))
+      "S3 Session 3 — S3_h_theorem_ndim.v §§5-7 (+131 LOC): shannon_entropy_le_ln_n Qed-closed via ln_le_x_minus_1 helper (exp_ineq1_le unconstrained). Commit 1b85602."
+      "S4 Session 2 — S4_heisenberg_ndim.v §4 (+97 LOC): norm_triangle_ndim Qed-closed via abs_inner_le_sqrt_product corollary of Rung-1 CS. Commit 26de845."
+      "E5 Session 5 — E5_needham_schroeder_fix.v §7 (+108 LOC): enc_only_trace + enc_trace_knows_is_observed + enc_trace_unobserved_unreachable + singleton_enc_trace_recovery (arbitrary-length generalisation of Session-4 singleton). Commit 82a097a."
+      "S4 Session 3 — S4_heisenberg_ndim.v §§5-8 (+622 LOC): in-file complex-number substrate [C := mkC R R]; complex vectors + finSumC; sesquilinear cinner with conjugate symmetry + sesquilinearity + self-inner-is-real; Rung-2 headline cauchy_schwarz_complex_ndim Qed-closed via λ-quotient route. Commit 4adc4d8."
+      "E5 Session 6 — E5_needham_schroeder_fix.v §8 (+293 LOC): session_state record; single_session_trace wire shape; structural invariant any_enc_trace → every derived msg is mEnc-shaped; single_session_no_key_derivable; MANIFEST-expected headline needham_schroeder_fixed Qed-closed for the single-session scope. Commit a67e565."
+      "Suite-wide recompile — 38/38 Qed, no regressions. panic-attack assail on both new files — 0 weak points (1099 LOC S4, 1079 LOC E5). 0 banned constructs."
+      "Session 7+ plan: (E1) scalar binomial + Coquelicot Cauchy-product bridge → Apow_add fold for Row-2 semigroup exp_matrix Qed. (S4) abstract pre-Hilbert record + self-adjoint operators + commutator algebra + Heisenberg. (E5) multi-session composition with cross-session nonce/key leakage. (S3) Riemann-integral layer if Rung-2 headline attempted."))))

.machine_readable/session-log.txt

@@ -15,3 +15,6 @@
 
 [2026-04-19 01:00:00] Session started: Claude Opus 4.7 (1M context) — user ask walked from "for each item in AI-WORK-007.md look upstream and identify anything that needs doing; make a separate upstreams doc" through two table-shape revisions to "do all you can": author the upstreams trace, then land whatever concrete TRG-D-adjacent work is safely shippable in one sitting.
 [2026-04-19 01:50:00] Session ended: 2 commits on origin/main — (1) `58200ca` proof(E1): matrix monoid foundations (Session 6, Row-2 algebra), (2) `5baca9f` chore(proof-suite): refresh runner artefacts after E1 Session 6. (a) DESKTOP DOC AUTHORED: `~/Desktop/AI-WORK-007-UPSTREAMS.md` — per-item upstream dependency trace for every OPEN entry in AI-WORK-007.md, three revisions: initial per-section tables → collapsed E1/S3/S4/E5 ports into one unified table → added Status column (done/in-progress/blocked/substrate-gated/workaround/research-grade/queued) + reordered all sections by action-cost (GitHub billing 5-min first; passive waits + research-grade tails last). §7 summary + §8 close-condition matrix both re-ordered to match. (b) PROOF WORK — E1 Session 6 Row-2 algebraic foundation: `proofs/canonical-proof-suite/E1_lyapunov_ndim.v` extended with new §18 containing six Qed-closed lemmas — Mid_sym (Mid is symmetric), Mmul_Mid_r / Mmul_Mid_l (identity laws, discharged via Mvmul_Mid), finSum_swap (generalised Fubini for finSum over Fin.t m × Fin.t n, induction on m with IH + finSum_add-reversed), Mmul_assoc (matrix product associative, via finSum_ext + finSum_scale pulling A i l and C m j out of inner sums, then finSum_swap), Apow_add (Apow (p+q) A = Mmul (Apow p A) (Apow q A), induction on p using Mmul_Mid_l + Mmul_assoc). +137 LOC. No Coquelicot dependency at this layer — those arrive at the final Cauchy-product step only. No banned constructs; banned-token scan clean; panic-attack assail on E1_lyapunov_ndim.v reports 0 weak points. (c) GATE: canonical-proof-suite-runner.sh → 35/35 passing, 0 regressed, exit 0, E1 semantic-check verified. REPORT.a2ml + STATUS.adoc auto-regenerated and committed. (d) AI-WORK-007.md UPDATES: §0 header rewritten for Session 6 landing (file LOC+decls bumped E1 1376/78 → 1513/84, aggregate 3063 LOC / 147 decls); §3.4 lift table "Sessions 1-5 landed" → "Sessions 1-6 landed" with commit list; §3.6.1 Session-6 subsection added + Session 7+ subsection replaces former Session 6+ subsection (names Session 7+ work as scalar binomial expansion + Coquelicot.Series.is_series_mult Cauchy-product + Apow_add fold + Row 3/4/5). (e) NOT TOUCHED (honest accounting): §1 human billing blocker (Jonathan-only); E1 Row-2 FULL semigroup Qed (would have risked half-baked commit — the scalar binomial + is_series_mult bridge is Session 7+); S3 Rung-1 ln-tangent-line derivation; S4 Rungs 2-4; E5 Session 5 multi-event trace induction; `opam install coq-mathcomp-algebra coq-mathcomp-analysis` (not required for Row 2 — the Fin.t-function encoding is unaffected; deferred to when a foundation rewrite is genuinely wanted). (f) DISCOVERIES: none new — environment (Rocq 9.1.1 + Stdlib 9.0.0 + Coquelicot 3.4.4 + mathcomp-ssreflect/fingroup 2.5.0, no algebra/analysis) matches what AI-WORK-007 §3.6.1 already documented. (g) SIDE EFFECTS OUTSIDE 007: none. No upstream repos touched. Blockers: GitHub Actions billing (`~/Desktop/YOUR-ACTIONS-todo.md §1`) — unchanged; TRG-D remains single-blocker-gated on this item. Next actions: (i) Session 7 = scalar binomial identity `(s+t)^k / k! = sum_{p+q=k} s^p t^q / (p! q!)` via Stdlib Binomial or local induction; (ii) Session 8 = Cauchy-product bridge `Coquelicot.Series.is_series_mult` applied to the exp_entry Series, folded through Apow_add to yield the Row-2 Qed `exp_matrix (s+t) A = Mmul (exp_matrix s A) (exp_matrix t A)`; (iii) E5 Session 5 multi-event trace induction as the other concrete Claude-side lane. MANIFEST pointer stays at E1_lyapunov_1d.v per §3.1 honest-accounting — only moves once Row-5 Qed lands.
+
+[2026-04-19 03:00:00] Session started: Claude Opus 4.7 (1M context, continuation after /compact) — user directive: "S4 Rung 2, then E5 Session 6". Build in-file complex-number substrate + complex C^n Cauchy-Schwarz via λ-quotient route, then per-session state + NS-Lowe secrecy invariant.
+[2026-04-19 03:45:00] Session ended: 2 commits on origin/main — (1) `4adc4d8` proof(S4): Rung-2 complex C^n Cauchy-Schwarz (Session 3, §§5-8 Qed), (2) `a67e565` proof(E5): Session 6 — single-session NS-Lowe secrecy + headline needham_schroeder_fixed Qed. (a) S4 SESSION 3: S4_heisenberg_ndim.v extended with §§5-8 (+622 LOC) containing an in-file complex-number substrate [C := mkC R R] against Stdlib.Reals+Lra+FunctionalExtensionality (no Coquelicot/mathcomp-analysis dep). §5: C record + Cadd/Copp/Csub/Cmul + Cconj + Cmodsq + C_of_R + full ring + conjugation laws + Cmul_conj_l / Cmul_conj_r (z*conj(z) = Cmodsq z) + Cmodsq_mul. §6: CVec n + finSumC with zero/ext/add/opp/scale-by-C/conj/CRe-projection/CIm-projection lemmas. §7: sesquilinear cinner with conjugate symmetry, sesquilinearity (cinner_scale_l conj-linear, cinner_scale_r linear), additivity + subtraction on both args, self-inner-is-real (cinner_self_CIm = 0, cinner_self_CRe = cnorm2), cnorm2_as_cinner, cnorm2_zero_iff_zero. §8: RUNG-2 HEADLINE `cauchy_schwarz_complex_ndim : Cmodsq (cinner x y) <= cnorm2 x * cnorm2 y` Qed-closed via λ-quotient route — auxiliary vector cs_auxvec i := λr·x i - (cinner y x)·y i with λr = cnorm2 y, its self-inner-product expanding algebraically to λr · (λr · cnorm2 x - Cmodsq (cinner x y)), non-negativity of the LHS + λr > 0 closing the headline. Edge case λr = 0 handled via cnorm2_zero_iff_zero → y = 0 → cinner x y = 0 directly. panic-attack assail → 0 weak points on 1099 LOC, 0 banned constructs. (b) E5 SESSION 6: E5_needham_schroeder_fix.v extended with §8 (+293 LOC). session_state record (ss_init/ss_resp/ss_na/ss_nb), single_session_trace defining the three-event wire shape of one honest Lowe-fixed execution, single_session_trace_is_enc_only bridging to Session 5's enc_only_trace, single_session_wire_messages explicit wire-message list, nb_not_on_wire (mNonce not mEnc-shaped), ns_lowe_single_session_secrecy + ns_lowe_single_session_initiator_nonce_secrecy + ns_lowe_single_session_full_secrecy (keyed versions routing through enc_trace_unobserved_unreachable). Structural invariant any_enc_trace + single_session_is_any_enc + knows_any_enc_trace_is_mEnc_shaped (avoids Session-5 circularity by showing every attacker-derived message on an any_enc trace is mEnc-shaped) + single_session_no_key_derivable (attacker cannot derive ANY mKey on a single-session trace). Keyless forms ns_lowe_responder_nonce_secret + ns_lowe_initiator_nonce_secret. HEADLINE `needham_schroeder_fixed : forall ses tr, single_session_trace ses tr -> ~ knows tr (mNonce (ss_na ses)) /\ ~ knows tr (mNonce (ss_nb ses))` Qed-closed for the single-session scope. panic-attack assail → 0 weak points on 1079 LOC, 0 banned constructs. Set Implicit Arguments (E5 line 53) forced @-explicit application at six call sites. (c) SUITE GATE: `coqc` on every file in proofs/canonical-proof-suite/ → 38/38 exit 0, no regressions. (d) STATE.a2ml completed-2026-04-19 block appended with Session-3/Session-6 entries; S3 Session 3 + S4 Session 2 + E5 Session 5 entries also promoted from the pre-/compact work window into the block. (e) NOT TOUCHED (honest accounting): MANIFEST pointer for S4 still at S4_heisenberg_discrete.v (Rung-4 operator Heisenberg remains out, so headline file still hasn't reached target Qed); MANIFEST entry for E5 can be revisited once multi-session composition lands (Session 7+); E1 Row-2 Qed (needs scalar binomial + Cauchy-product bridge, deferred); §1 human GitHub Actions billing blocker (Jonathan-only). (f) DISCOVERIES: none new — Stdlib.Reals `exp_ineq1_le` is unconstrained, `Rsqr_le_abs_0` + `sqrt_pow2` work unmodified, `Req_dec` available for the real-valued λr=0 case-split. Blockers: unchanged. Next actions: (i) S4 Session 4 = abstract pre-Hilbert record + self-adjoint operators + commutator algebra + Heisenberg headline; (ii) E5 Session 7 = multi-session composition with cross-session nonce/key leakage; (iii) E1 Session 7 = scalar binomial + Coquelicot Cauchy-product bridge → Apow_add fold for Row-2 semigroup exp_matrix Qed. MANIFEST pointers stay intact per §3.1 honest-accounting — no pointer move until each file's final headline theorem Qed-closes.