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feat(Probability): bound statistical distance under scores, conditioning, and pairing - #1066

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SamuelSchlesinger wants to merge 2 commits into
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samschles/crypto-pr-04-statistical-distance-lemmas

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@SamuelSchlesinger SamuelSchlesinger commented Oct 4, 2026 •

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Deferred from the CSLib crypto stack. The remaining proposed developments do not use these bounded-score, conditioning, or pairing lemmas.

The implementation is preserved on this branch for later entropy and hashing work, with upstream placement reconsidered alongside those consumers.

Originally composed with Claude Code.

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SamuelSchlesinger added this pull request to stack #1064 October 4, 2026 22:08
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SamuelSchlesinger force-pushed the samschles/crypto-pr-04-statistical-distance-lemmas branch from 308e5d8 to f7d7f3f Compare October 4, 2026 23:03
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SamuelSchlesinger force-pushed the samschles/crypto-pr-03-statistical-distance-tsum branch from 6028aca to d892828 Compare October 4, 2026 23:03
…ing, and pairing

Adds the standard ways statistical distance enters reductions, for finite types. Changing the distribution moves the expectation of a score bounded by `B` by at most `2 * B * dist p q` (`abs_sum_mul_sub_le`). Conditioning on an event changes a distribution by exactly the probability it discards (`dist_filter`). With a shared revealed input, statistical distance is the average distance of the conditional outputs (`dist_bind_pair`), and its square is at most the average squared distance (`dist_bind_pair_sq_le`).
@SamuelSchlesinger
SamuelSchlesinger force-pushed the samschles/crypto-pr-04-statistical-distance-lemmas branch from f7d7f3f to 9a4128d Compare October 4, 2026 23:33
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SamuelSchlesinger force-pushed the samschles/crypto-pr-03-statistical-distance-tsum branch 2 times, most recently from 5342fca to 29ccc5b Compare October 5, 2026 20:01
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SamuelSchlesinger removed this pull request from stack #1064 October 5, 2026 20:06
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SamuelSchlesinger changed the base branch from samschles/crypto-pr-03-statistical-distance-tsum to samschles/crypto-stack-review-base October 5, 2026 20:07
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SamuelSchlesinger added this pull request to stack #1077 October 5, 2026 20:07
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SamuelSchlesinger removed this pull request from stack #1077 October 5, 2026 20:20
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