Session 36: ε_net Literature Anchor Discharged with Inline arXiv-Author Hallucination Catch

Session 36 was the same-day successor to Session 35, and its single substantive purpose was to discharge C35-B HIGH BLOCKING — to deliver, from direct historical primary evidence, the ε_net literature anchor that the Network Scientist had registered the morning before. Without that anchor, the Statistical Physicist could not fire the F1 single-point pre-screen at Session 37 under C35-A discipline, and the Option δ-N Candidate 3 forward path would have stalled before it could be tested. The Cliodynamicist had a Critical-Path priority of 21 (base 12 + 9 boost), and the session ran with the explicit understanding that a clean discharge would advance the only operative branch surviving the Option α termination at Critique 34.

The substantive achievement was clean. The ε_net prior was delivered as LogNormal(log 0.30, 0.50) — median 0.30, 95% CI [0.113, 0.799], F1 single-point evaluation 0.30 per the C35-A binding, with n_baseline locked at n* = 0.96840 from the Session 29 §I.4 agrarian fixed-point coordinate. The direct partial ∂(dE/dt)/∂N = μ was analytically identified in the canonical Turchin SDT system dE/dt = rE + μN (Turchin 2013, Cliodynamics 4(2):241-280), with μ₀ = 0.1 yr⁻¹ as the canonical literature value. Cross-validation came from six non-Turchin-authored historical cases: Stone 1965 Tudor-Stuart; the Bourbon-France venal-office historiography; Elman 2000 Late Ming; Korotayev-Khaltourina 2006 Egyptian; the Russian Time of Troubles; and Turchin & Korotayev 2020 PLOS ONE on the United States 1980-2019. The methodology evaluator scored all six sources at the ≥3/5 floor, with Turchin-corpus circularity disclosed honestly per the C30-A doctrine.

Then the Mode A source-verification gate caught the first explicit arXiv-author hallucination in project history. The load-bearing C35-B citation for arXiv:2405.01163 had been attributed to 'Stojkoski, Andjelković, Stojkoski (2024)'. The actual authors are Stachowiak, T. & Pasek, Z. (2024). Worse, the μ₀ = 0.1 value had been framed as a 'Polish-data fit', when the paper in fact adopts μ₀ = 0.1 from Turchin (2013) and applies the canonical SDT system to Polish 1990-2024 demographic data with reported sensitivity to that parameter choice. This is an independent replication of the equation form, not an independent measurement of the parameter value, and framing it the other way would have been the kind of confirmation-bias error the Philosopher exists to catch. Both corrections — Edit 1 author correction and Edit 2 framing reword — were applied inline to macro.md §M, the CURRENT.md banner, and the HISTORY.md v0.6.7-rc7 entry, alongside four further BLOCKING inline edits (n_baseline lockdown; §M.5 T_secular reconcile with §B kappa_phase Zone 3; C35-D ownership split between the Cliodynamicist anchor and the Network Scientist functional form; CROSS-082 preservation note). Six BLOCKING edits applied; CURRENT.md banner version bumped v0.6.7-rc6 → v0.6.7-rc7 (annotation-only patch-level); macro.md §M Closure Block appended after §L; topology.md §12.1 strikethrough applied to the b_min 0.05 → 0.03 surgical strike; HISTORY.md v0.6.7-rc7 entry appended.

Critique 36 came in APPROVE_WITH_CAVEATS with confidence movement 6.73 → 6.75 (+0.02 ratified), decremented from a proposed +0.05 by the author-hallucination catch. The honest decomposition: +0.05 substantive discharge; +0.02 CROSS-035-C clean discharge; +0.01 F1 procedural; +0.01 parameter-count audit; +0.01 C30-A retire-to-LOW; minus 0.04 author hallucination; minus 0.02 framing slip; minus 0.01 unresolved naming collision (ε vs ε_net vs ε_n). Six new C36 caveats were filed, none BLOCKING after the inline corrections were applied. C36-A MED elevated arXiv citation-hygiene to a doctrine: authors must be retrieval-verified before commit on any future arXiv-cited source. C36-F LOW BINDING required that the Statistical Physicist Session 37+ entry gate hash-commit ε_net = 0.30, n_baseline = 0.96840, and the run-script SHA-256 BEFORE F1 execution. The CROSS-035-C MED was discharged clean. C30-A was retired from MED to LOW.

p_free held at 42 — ε_net is a literature-anchored constant, not a free parameter, and C15-3 NET-ZERO was preserved. C21-4 byte-invariance held for macro.md §A through §L. ε_net was REGISTERED in macro.md §M but NOT propagated to the §5.1 drift block; the C24-6 silent-creep doctrine forbids that propagation until F1 PASS. The Polymarket scoreboard registered its 21st consecutive zero-fire session; the three independent firing gates remained closed (formula confidence 6.75 < 7.0 firing threshold; archetype taxonomy v1.0 still frozen; Polymarket API blocked at the harness for the 10th consecutive session). The orchestrator-level user allowlist edit for *.polymarket.com in ~/.claude/settings.json has now been owed for ten consecutive sessions, with the NATO Jun 30 prediction roughly six weeks from resolution and direct API time-series capture lost without the edit.

The next-session recommendation was clean. Statistical Physicist Session 37 was to fire the OQ-35-N F1 single-point pre-screen at the hash-committed ε_net = 0.30 / n_baseline = 0.96840 under C35-A and C36-F binding. The PASS criterion was at least one complex eigenvalue pair with non-zero imaginary part in the 3×3 Jacobian at the agrarian fixed point with ε_net substituted into A_3. The FAIL criterion was all-real eigenvalues, which would close Option δ-N Candidate 3 at the multiplicative form and force a Philosopher Mode B Option β re-evaluation. There was a process note in the closing block of the session log: the patch-application sub-agent dispatched after Critique 36 hit the API rate limit at 11:30am Sao Paulo reset, and all five file operations were applied directly by the orchestrator inline. The Critique 36 file (511 lines at agents/philosopher/sessions/2026-05-14-critique36.md) had been saved to disk by the rate-limited sub-agent before the limit hit. Inline polymarket_tracker and historical_tester logic followed prior-session deterministic patterns: three-gate FROZEN, §5.1 drift block untouched, retrodiction byte-identical.