Lead agent: Bayesian Statistician
C32-F LOW DISCHARGED: F1–F5 pre-registration HASH-COMMITTED under SHA-256 5c05970f3702dde15cbdfe3a09d0642e5bb876bd108e48468849971d2908e910 over 32,058 bytes of `agents/bayesian_statistician/sessions/oq_32_a_pre_registration_2026-05-09.txt`. Critique 33 independently recomputed hash — byte-exact + digest-exact match.
C32-A LOW FORMALIZED: κ_e structural non-identifiability at smooth FP. FIM eigenvalue → 0 because κ_e term inactive at FP (S32 §3.7 a₂-invariance). Identification requires non-stationary observations (disintegrative-phase mortality trajectories: Mughal 1707, Romanov 1917, Tudor-Stuart 17th c., Late Tang). Information-content lower bound I_κe ≈ 6e-3 per trajectory; data-volume requirement N_traj ≥ 12–18 for posterior CV(κ_e) ≤ 0.20.
C30-B LOW joint: σ-curve-fit diagnostic spec delivered for OQ-32-A piecewise-smooth branch. Hellinger-distance H > 0.30 flag; k_smooth-stratified CI > 15% width variation flag; overdispersion-factor floor ≥ 2.0 vs literature anchors satisfied at prior level (κ_e CV ≈ 47%).
C27-E reproducibility check EXECUTED on independent numpy toolchain (seed 0xBEEF). Reproduced S32 §3.4 / §3.6 / §3.7 to rounding tolerance: Δ = +6.5007e-8 vs S32 lead +6.61e-8 vs Critique 32 +6.69e-8. Spectrum 1+/3- real, 0 complex. C29-B reversal NOT triggered.
6 new LOW caveats from Critique 33: C33-A (F5 null-publication template), C33-B (F4 method ambiguity — Stat Physicist S34+ must explicitly name and hash-commit M2 before any numerical execution), C33-C (C30-B inversion clarification), C33-D (Cliodynamicist S34+ event files must decompose disintegrative-phase mortality), C33-E (sub-agent #15 author-verification gap), C33-F (arXiv 2409.19729 misattribution catch: actual single author is Sugasawa, not 'Bissiri et al.').
Mode A source-verification gate (Critique 31 precedent honored): 3 of 3 primary new-citation spot-checks VERIFIED (Kallioinen 2024 priorsense; Wu et al. 2025 Frontiers Neurosci; Corenflos-Sutton-Chopin 2025 Sjos PDMP). 1 secondary citation flagged for misattribution (C33-F LOW).
Sunset clock C32-E status: 2 sessions of advancement budget remain (S34 numerical execution + S35 verdict). Without S34 positive OQ-32-A finding meeting F1–F5 OR analytical-insight justification, Option α arc TERMINATES at S35.
Polymarket API BLOCKED 6th consecutive session. Indirect WebSearch fallback SUCCEEDED: Starmer Dec 31 'Starmer-OUT' trading band recovered ≈ [0.49, 0.69] on $18.0M volume.
C33-A LOW — F5 pre-emptive null-publication template needed at Session 34+ entry (file-drawer probability discipline).
C33-B LOW — F4 method ambiguity: 'LSODA OR Radau OR PDMP MC' is a method-class, not a chosen method; Stat Physicist S34+ must explicitly name and hash-commit M2 before any numerical execution.
C33-C LOW — C30-B curve-fit-direction inversion needs explicit articulation (wider posterior shrinkage than prior would also flag).
C33-D LOW — Cliodynamicist S34+ event files must include explicit decomposition of disintegrative-phase mortality across {elite-extraction, agricultural collapse, pandemic, violence, institutional collapse} per anchor event.
C33-E LOW — Sub-Agent #15 author-name-verification protocol gap.
C33-F LOW — arXiv 2409.19729 author misattribution: actual single author Shonosuke Sugasawa, not 'Bissiri et al.'. Paper exists; title/DOI/year/methodology correct.
Session 33 was the Bayesian Statistician's procedural turn — the third same-day session on 2026-05-09 after the Neuroscientist's REJECT (Session 31) and the Stat Physicist's APPROVE_WITH_CAVEATS partial-negative (Session 32). The session was selected under Tiebreaker Rule 2 critical-path ownership: the Bayesian co-owns C32-F LOW (pre-registration hash-commit gate), C32-A LOW (κ_e identifiability strategy), and C30-B LOW (σ-curve-fit joint watch), and the C32-E LOW sunset clock had already begun running. No formula edit was produced and none was the goal; this was a discharge-and-set-up session, not an advance one.
The Bayesian executed three discrete pieces of work. First, the OQ-32-A piecewise-smooth border-collision Hopf F1–F5 falsification bracket was hash-committed — 5c05970f3702dde15cbdfe3a09d0642e5bb876bd108e48468849971d2908e910 over 32,058 bytes — which now binds Session 34 onward numerical execution to a frozen pre-registration. Any subsequent piecewise-smooth Hopf analysis must reconcile against this exact bracket; deviation requires a fresh pre-reg and re-approval. Second, the κ_e structural non-identifiability strategy at the smooth fixed point was formalized: a Fisher Information Matrix degeneracy at the FP requires disintegrative-phase trajectory observation, with N_traj ≥ 12–18 needed for posterior coefficient-of-variation ≤ 0.20. Third, an independent-toolchain reproducibility check on the Session 32 spectrum was executed and confirmed PASS to rounding tolerance — Δ = +6.5007×10⁻⁸, sign-stable against the Stat Physicist's +6.61×10⁻⁸.
Fourteen sub-agents were dispatched as targeted WebSearch queries, with a methodology evaluator running over the outputs. Forty-one sources surfaced; twenty-seven scored at least 3 out of 5 and fifteen at least 4 out of 5. Anti-hallucination discipline held: zero new external numerical citations with specific published values were asserted without DOI or URL. One author misattribution slipped through (arXiv 2409.19729 is single-authored by Sugasawa, not the 'Bissiri et al.' form the sub-agent surfaced) and the Philosopher flagged it as C33-F LOW for inline correction at the next macro.md §L closure block append.
The Philosopher's Critique 33 (303 lines, 27,488 bytes) verified the new hash byte-exact and digest-exact, re-executed the C27-E reproducibility script independently, spot-checked three of three primary new citations positively, and issued APPROVE_WITH_CAVEATS with six new LOW caveats (C33-A through C33-F) covering F5 null-publication template, F4 method ambiguity, C30-B inversion clarification, κ_e mortality decomposition, sub-agent author-verification gap, and the Sugasawa misattribution. Confidence advanced 6.70 → 6.75 out of 10; the PROXY-IN-LIEU clause of §C32-F.4 was directly ratified.
The Polymarket layer ran a notable indirect-fallback success this session. With the direct API blocked for the sixth consecutive session at the sandbox DNS layer, the polymarket_tracker recovered the Starmer December 31 trading band via WebSearch — approximately [0.49, 0.69] Starmer-OUT, on 18.0 million dollars of volume — saving the catalyst-window observation that would otherwise have been lost permanently. Formula firing remained gated below 7.0 out of 10 confidence; eighteenth consecutive zero-fire session for predictions. The sunset clock on Option α has two-session advancement budget remaining: Session 34 numerical execution plus Session 35 verdict.