Research proof index

Completing an occurrence resamples the focused answer as a fresh query i: any event on that answer marginalizes the resampled suffix away.

Cache preimage bound: if the initial cache contains at most one preimage of a target value v₀, then the probability that simulateQ cachingOracle oa creates a fresh cache entry equal to v₀ is at most n / |C|, where n is the total query bound. Each cache miss is a fresh uniform draw, so a union bound over the at most n misses gives the resul...

Two events have equal probabilities when their predicates agree on the support of the first computation and the two computations share an evaluation distribution.

A fixed guarded fork is the corresponding component of the dynamic semantic fork.

Multi-key hidden-target first-fire bound. Drawing n independent hidden targets from oa (each outcome of mass at most ε) and probing each by q adaptive reads fires with probability at most n · q · ε. Proved by induction on n: the head key's contribution is the single-target bound probEvent_hiddenReadMany_le (≤ q · ε), the tail's is the...

Probability that the k-th log entry's output is HEq to a fixed value u₀ : spec.Range t₀. Unlike probEvent_log_entry_eq_le which matches the full sigma entry, this only constrains the output component. The bound uses hrange to get 1/|Range default|.