observational-equivalence

Exact finite mathematics of how rulebooks with identical present behavior become distinguishable under whole-rule failures and continuation probes, with dual natural/isolation observers, exact reconstruction, universal Pareto-frontier representation, sharp resource-cost laws, and reproducible verification — Shunyaya Rule Continuation Geometry.

Mathematics that can be rebuilt — a finite mathematical framework for reconstructing theorem systems under failures, with a universal continuation classification by canonical normal forms, constructive distinguishing continuations, bounded-width algorithms, and reproducible verification — Shunyaya Theorem Reproducibility Framework.