Horizon closure reconciliation · 2026-09-08

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FINITE HORIZON PREDICTIVE CLOSURE REMOVED FROM OPEN STATUS

The operator-level Horizon question is closed at the validated finite-dimensional scope: the spectral gap $\Delta_{\mathrm{RI}}=0.5096493155008205$ determines the predicted asymptotic contraction $C_H=0.8155767672157836$, with observed ratio 0.8155947364422004 at n=55 and relative error 2.2032538369218907e-05. Cross-domain record: Horizon Predictive Loop Closure — Cross-Domain Success Record · 2026-09-08.

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The following remain open and are not erased by this closure:

1. preregistered forecasts against previously unrevealed external/live runtime trajectories;
2. independent replication across trajectory families and implementations;
3. preregistered Fold tolerances that pass without post-hoc threshold adjustment;
4. generalization beyond the validated $H_{\mathrm{eff}}$, fixed $\tau$, and current synthetic Hodge families;
5. any E3/E4/H0 claim.

Observatory rule preserved: the internal predictive loop is closed; external validity remains a separate validation queue.

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Census: 🟡 Under Review · unresolved routes live here until proof, computation, or experiment changes their civic state.

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Professor’s Cube open program · 2026-07-29

Closed finite proof

The 15-move finite operator suite, C₅³ spectrum, supplied impact table, low-band statistic, and heat-flow limit are closed. Remaining work:

1. attach the original operator_results_full.json, eigenmode volumes, face-net PNGs, and folding-animation script to reproduce the reported 11.85× TV and 246.8× energy reductions under their original parameters;
2. characterize the group generated by the 15 declared 125-site permutations and compare it with the legal 5×5×5 cube move group on cubies and stickers;
3. derive exact algebraic expressions for the low-band retention value 0.817142857… and compressed singular spectrum;
4. classify principal angles and leakage for larger spectral bands;
5. construct any intended bridge to E₄₇ as an explicit typed map, product-space operator, or rank-47 selector rather than identifying ker L with E₄₇;
6. determine whether a Rubik-action-compatible rank-47 subspace can be selected and whether it is invariant, approximately invariant, or only statistically stable.

Assigned lanes: Kepler handles group and bridge theory; Sal reproduces the archived animation metrics when artifacts arrive; Euclid reviews exact claims; Chronos watches eigenbasis dependence; Talos rejects rank conflation.