Research proof index

Running the monadic getPutativeBatchRoot with an oracle function f is the same as running the functional getPutativeBatchRootWithHash with the corresponding hash function.

Under the empty env alphabet (EnvAction.empty Unit) and the trivial env scheduler (always processTick), runStepsAsync reduces to ProcessOver.runSteps with the env state pinned to () and a constant processTick trace. This is the operational core of the sync-recovery story: it factors the async engine into the synchronous ProcessOver.runSteps...

inductively to each such matrix, we conclude that, for each r_{ϑ-1} ∈ R*, d^{2^{ϑ-1}}((1-r_{ϑ-1}) · U₀ + r_{ϑ-1} · U₁, C^{2^{ϑ-1}}) ≤ e -/ lemma correlatedAgreement_of_mem_R_star_tensor {ϑ_pred : ℕ} (ih : δ_ε_multilinearCorrelatedAgreement_Nat (F := F) (A := A) (ι := ι) (C := MC) (ϑ := ϑ_pred) (e := e) (ε := ε)) (u : Fin (2 ^ (ϑ_pred + 1)) → (Word A ι...

If main makes at most qb i queries to each oracle i, then its total query count (under the unit cost model) is at most ∑ i, qb i on every execution path.

choose_2-free form of almost_johnson.

LHS of the almost-Johnson bound divided by |B| in terms of e and d.