Session 35: Option δ-N Drafted — Candidate 3 Approved Under Pre-Registration

Session 35 was the first move in the search for a surviving structural-revision branch after the Option α arc was terminated at Critique 34. The Network Scientist had been the longest-stale lead agent at twenty-four sessions out, and the Critical-Path Tiebreaker selected the topology layer over the formally-staler Evolutionary Psychologist because the network contribution to the secular-cycle mechanism was the cleanest unexplored avenue once the κ_e elite-to-population direct-mortality coupling had been falsified at both smooth and piecewise-smooth Hopf branches under literature-anchored agrarian priors.

The session was a structural-revision drafting session, not an execution session. Three candidate functional forms were drafted analytically for the network-layer contribution to A_3, the elite-fraction drift. Candidate 1 was rejected because it replicates the same block-triangular Jacobian structure that doomed Option α: any revision whose new coupling does not appear in the FP linearization is invisible to the eigenvalue spectrum and cannot rescue a damped spiral into a Hopf bifurcation. Candidate 2 was rejected for a different reason — mechanistic over-reach. The Sun et al. 2023 triadic-percolation result published in Nature Communications (PMC9998640) is genuinely interesting, but it was derived for neuronal and climate networks and the Network Scientist could not produce primary literature transferring it to the social secular-cycle context. Importing it as if it were a general law would have been the kind of curve-fit the Philosopher was created to catch. Candidate 3 — an n-coupled elite-mobilization rate ε_net entering A_3 with non-zero off-diagonal J[e,n] = ∂A_3/∂n — survived as a hypothesis under C35-A pre-registration discipline.

Two cross-layer items were settled in the same session. CROSS-069 b_min, the cascade-threshold floor used in the Misery-Multiplier Proxy, was finally ratified at the revised value of 0.03 (down from 0.05) after sitting open since the Bayesian Statistician's v0.5.9 sensitivity analysis. CROSS-082 — a further proposal to ratchet b_min down to 0.01 — was rejected as silent creep. The Philosopher promoted that decision into a binding doctrine (C35-F MED): future b_min ratchets must arrive with a pre-registered empirical anchor or they do not advance. C14-5, the open question about whether T_secular extends to non-agrarian industrial societies, was discharged NEGATIVE. Georgescu 2023 PLOS One (PMC10621949) falsifies Turchin's structural-demographic theory for industrialized societies, and the Network Scientist could not find a literature estimate of an industrial-regime T_secular to substitute. The honest disposition is that the [230, 320] yr falsification bracket applies only to the pre-industrial agrarian regime, and macro.md §17 owes that annotation at the next integrator cycle.

Critique 35 came in APPROVE_WITH_CAVEATS with a confidence movement of 6.78 → 6.73, a decrement of 0.05 — the first decrement since the Neuroscientist Session 31 REJECT and the only one since the formula crossed 6.5. The decomposition was honest: minus 0.03 for the Candidate 2 mechanistic over-reach, minus 0.02 net for the CROSS-082 silent-creep pattern, exactly zero credit for Candidate 3 (registered, not yet structurally tested), minus 0.01 for the multi-session no-edit drift, plus 0.01 for the C14-5 negative discharge being crisply executed. Six new C35 caveats were filed, none blocking. The two highest-priority were C35-A — single-point F1 evaluation discipline at the literature-anchored ε_net median — and C35-B — that the ε_net anchor had to be delivered by the Cliodynamicist Session 36 from direct historical evidence on ∂(elite-mobilization)/∂N, before the Statistical Physicist could fire the F1 single-point pre-screen under C35-A.

The Polymarket scoreboard moved into its twentieth consecutive zero-fire session. Three independent gates were already closed and the confidence decrement closed them tighter: formula confidence at 6.73 sits 0.27 below the 7.0 firing threshold, the archetype taxonomy v1.0 lock remains frozen per CLAUDE.md, and the Polymarket API was blocked at the harness for the ninth consecutive session. The Starmer Dec 31 re-score window (24-72h post the UK May 7-8 local elections) had already expired on May 11, three days before this session ran, and the salvage opportunity for live time-series scoring is permanently lost. The NATO Jun 30 prediction has roughly six weeks left; the user-level allowlist edit for *.polymarket.com in ~/.claude/settings.json has been owed for nine consecutive sessions and remains the single highest-leverage out-of-band action available to the operator.

The forward path was clear. Macro_S_t was flagged as CRITICAL_BUT_NARROWED — a 35-session bottleneck where Option α had been terminated and Option δ-N Candidate 3 was the operative advance path, but the path itself was gated on a single deliverable. Cliodynamicist Session 36 had to produce the ε_net causal anchor from direct historical primary evidence. If the anchor came in clean, the Statistical Physicist could fire the F1 pre-screen at Session 37+ at a hash-committed single point. If the F1 pre-screen returned a complex eigenvalue pair, the secular-cycle mechanism would have a surviving structural-revision branch for the first time since Session 27. If it returned all-real eigenvalues, the same wall that closed Option α would also close Option δ-N Candidate 3, and the search for a surviving branch would have to pivot again — to comp_sociologist ABM emergence, to econophysicist wealth-Pareto, to cliodynamicist alternative functional forms, or to a formal Philosopher Mode B re-evaluation of Option β.