Status: DESIGNED 2026-07-03, deliberately deferred. This document is the pre-commitment: when this experiment runs, its verdict on equilibration is FINAL. No post-hoc caveats. Depth is the last untested variable.
Phase 8 (docs/phase8_prereg.md, docs/phase8_results.md) measured equilibrated standing vs vote-count standing on the graph that today's pipeline actually produces: a depth-1 forest (one node per work unit, exactly 3 judge claims each, single epoch, no disputes). Result: +0.127, real (CI excludes 0) but below the pre-registered 0.25 bar → equilibration demoted to experimental kernel.
The standing objection: equilibration's distinctive machinery (propagation through deep contested trees, cross-claim coupling) had almost no structure to work with. Phase 8 measured its floor. This experiment measures it on the graph the architecture was designed for.
The substrate does not care whether debate structure arrived from live agents or was constructed directly: replay determinism guarantees structural equivalence. So we BUILD the mature graph by hand:
- Start from the phase 8 corpus (200 units, experiments/phase8/).
- Synthetic debate generation (LLM-driven, cached): for each of the ~60 highest-retrieval-traffic units, generate a debate tree of depth 3 to 5: targeted CONs against specific claims (via submit_con semantics), PRO rebuttals, counter-CONs, cross-unit co-parent edges where units genuinely relate. Target ≥2000 nodes total, mixed contested/uncontested regions, generated by Opus with instructions to argue both sides honestly (not to favor either arm).
- Build two standings over the SAME graph:
- C': recursive vote standing (net_score recursion over the explicit tree: posts + signed children, no geometry).
- D': full equilibration (geometric propagation + recursion). NOTE: phase 8's arm C used flat per-unit vote counts; at depth the fair no-geometry baseline is the tree recursion, which the ledger keeps anyway. This is pre-registered here to prevent later dispute.
- Contest protocol identical to phase 8 (same selected questions, same contestant, same blind dual grading, same guards, same stats), arms: B (plain rag), C' (tree-recursion re-rank), D' (equilibrated re-rank). Primary contrast D'−C', same decision rule: Holm p < 0.05 AND mean diff ≥ 0.25.
- The verdict is final in BOTH directions: D'−C' clears the bar → equilibration is re-promoted and the O(N²) scaling work is funded; it fails → equilibration is retired from the mint path permanently (may remain a research kernel, never a launch dependency).
- The synthetic-graph generator is committed before any contest call, with its prompts; graph statistics (depth histogram, contested-node fraction, CON share) are published with the results.
- No new caveats may be introduced after data collection. Any validity concern must be raised (and fixed) before the contest runs.
Graph generation ~$15 to $25 of Opus calls (cached, one-time); world build at 2000+ nodes will be slow under current O(N²) equilibrate (hours), acceptable for a one-shot offline build; contest + grading ≈ phase 8 (~350 bridge calls).