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feat(Crypto): add negligible bounds for security games - #1068

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@SamuelSchlesinger SamuelSchlesinger commented Oct 4, 2026 •

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Introduces Negligible as an abbreviation for Mathlib's SuperpolynomialDecay at natural security parameters. Adds the three facts used by the security-game and hybrid developments: zero is negligible, pointwise comparison preserves negligibility for nonnegative bounds, and polynomially bounded natural factors preserve negligible decay.

The polynomial-loss proof uses the eventual power bound from PolynomiallyBounded and Mathlib's existing decay lemmas. It also applies to signed error functions.

Depends on #1067.

Originally composed with Claude Code; revised with Codex to retain the API needed by the remaining crypto stack.

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SamuelSchlesinger added this pull request to stack #1064 October 4, 2026 22:18
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SamuelSchlesinger force-pushed the samschles/crypto-pr-06-negligible branch from f4bfd3d to 4e92e38 Compare October 4, 2026 23:03
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SamuelSchlesinger force-pushed the samschles/crypto-pr-06-negligible branch from 4e92e38 to 071133b Compare October 4, 2026 23:33
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SamuelSchlesinger removed this pull request from stack #1064 October 5, 2026 20:06
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SamuelSchlesinger added this pull request to stack #1077 October 5, 2026 20:07
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SamuelSchlesinger force-pushed the samschles/crypto-pr-06-negligible branch from 071133b to 3e46473 Compare October 5, 2026 20:19
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SamuelSchlesinger removed this pull request from stack #1077 October 5, 2026 20:20
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SamuelSchlesinger added this pull request to stack #1080 October 5, 2026 20:20
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SamuelSchlesinger removed this pull request from stack #1080 October 5, 2026 20:43
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SamuelSchlesinger changed the base branch from samschles/crypto-pr-05-polynomial-bound to samschles/crypto-stack-review-base-1067 October 5, 2026 20:43
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SamuelSchlesinger added this pull request to stack #1082 October 5, 2026 20:43
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SamuelSchlesinger force-pushed the samschles/crypto-pr-06-negligible branch from 3e46473 to 07cf73b Compare October 5, 2026 20:56
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SamuelSchlesinger removed this pull request from stack #1082 October 5, 2026 20:57
@SamuelSchlesinger SamuelSchlesinger changed the title feat(Crypto): define negligible functions feat(Crypto): add negligible bounds for security games Oct 5, 2026
@SamuelSchlesinger
SamuelSchlesinger changed the base branch from samschles/crypto-stack-review-base-1067 to samschles/crypto-pr-05-polynomial-bound October 5, 2026 20:57
@SamuelSchlesinger
SamuelSchlesinger added this pull request to stack #1084 October 5, 2026 20:57
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SamuelSchlesinger removed this pull request from stack #1084 October 5, 2026 21:02
@SamuelSchlesinger
SamuelSchlesinger added this pull request to stack #1085 October 5, 2026 21:03
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