Research proof index

OptionT companion to QueryImpl.simulateQ_liftM_eq_of_query: simulating an OracleComp-computation oa lifted into OptionT (OracleComp spec₂') (the shape produced by an OptionT-monadic verifier's let _ ← liftM (queryHelper) binds) agrees, at the run (Option) level, with some-mapping the simulation of oa through a per-query-bridged handler...

Three-layer simulation collapse: if a "reduction" red : QueryImpl spec₁ (StateT σ (OracleComp spec₂)) followed by an inner cached impl : QueryImpl spec₂ (StateT τ n) agrees per-query with a single "combined" handler combined : QueryImpl spec₁ (StateT (σ × τ) n) up to the natural reassociation α × σ × τ ≃ (α × σ) × τ, then the agreement extends to...

Interval form of sin_div_error_pointwise_bound: integrating the pointwise bound over [-1, 1] controls the windowed error integral by (D / π) · vol (Ioc (-1) 1).

Pointwise bound on the sin-div windowed error term: scaling by the normalized sinc kernel and a mean-value estimate on g (x - u) - g x gives a bound D / π that is independent of the height T.

Singleton bound for arbitrary codes

If G is generated by a set s, then the slash action by elements in G is uniquely determined by the slash action by elements in s. See slashaction_generators' for a version where s is a set of elements in G.