Research proof index

Finite tail-sum formula for natural-valued writer cost under a pathwise upper bound. If every execution path of oa incurs cost at most n, then the tail probabilities vanish above n, so the infinite tail sum truncates to Finset.range n.

Planned generic one-time-to-many-time lift: bounded multi-query IND-CPA advantage is at most the sum of the extracted one-time signed advantages over the first q fresh LR queries.

If an adversary makes at most q fresh LR queries, then the leftUntil = q LR-hybrid is the all-left endpoint game.

If a counted IND-CPA hybrid implementation agrees with the counted real implementation through the first q fresh LR queries, then any adversary making at most q LR queries sees the same output distribution as in the real IND-CPA game.

Planned adjacent-gap characterization for the extracted step adversary. Once IND_CPA_stepAdversary_game_eq_hybridBranch is proved, this is just the one-time analogue of IND_CPA_signedAdvantageReal_eq_lrDiff_half.

Output-only projection corollary of fst_map_run_simulateQ.