[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"1lnwZiLThi":3},"# Proximity Prize — IRS reduction threshold\n\nThis repository defines two Lean challenges around the ABF26 reduction-error\nthreshold for one fixed interleaved Reed–Solomon profile. Each track includes\nan editable baseline candidate.\n\nLet\n\n```text\nepsilon* = 2^-128\nq(delta) = (1 - delta)^128\nb = B / 100\n```\n\nThe score is the spot-check quantity induced by a certified threshold radius.\nIt is not `-log2(WSS)` and is not a full-protocol security claim.\n\n## Challenges\n\n| Track | Certificate | Score |\n|:--|:--|:--|\n| `irs-reduction-threshold-lower` | At `delta = P/Q`, `certifiedGammaError(delta) \u003C= epsilon*` and `q(delta) \u003C= 2^-b` | maximize `B` |\n| `irs-reduction-threshold-upper` | For every admissible `delta >= delta* = i/2^18`, `winningSetDensity(delta) > epsilon*`, and `2^-b \u003C= q(delta*)` | minimize `B` |\n\nThe lower certificate is\n`ProximityPrize.Benchmark.ProtocolClaim B P Q`. It uses ArkLib's certified\ncombination-round error for the executable IRS straight-line extractor. Since\nArkLib proves `winningSetDensity \u003C= certifiedGammaError`, this is a\nconservative safe point.\n\nThe upper certificate is\n`ProximityPrize.Benchmark.Upper.ProtocolClaimUpper B i`. It certifies an entire\nunsafe suffix because no monotonicity theorem for `winningSetDensity` is\nassumed. The index is verified metadata; the leaderboard compares `B` only.\n\nThe protected definitions are in\n[`TargetLower.lean`](ProximityPrize/Benchmark/TargetLower.lean) and\n[`TargetUpper.lean`](ProximityPrize/Benchmark/TargetUpper.lean).\n\n## Included baselines\n\n| Track | Score | Claim metadata |\n|:--|--:|:--|\n| lower | `53.00` bits | radius `1/4` |\n| upper | `128.00` bits | unsafe index `131072`, hence radius `1/2` |\n\nThese are editable starting points, not authoritative leaderboard results. The\nlower baseline certifies the extractor-error target at radius `1/4`; the upper\nbaseline certifies that winning-set soundness exceeds the target throughout\nthe required half-radius suffix.\n\n## Candidate layout\n\nLower submissions use:\n\n```text\nProximityPrize/SubmissionLower/\n  Solution.lean\n  score.txt          # canonical non-negative centibits B\n  radius.txt         # exact P/Q\n```\n\nand export:\n\n```lean\ntheorem ProximityPrize.Benchmark.candidate :\n    ProximityPrize.Benchmark.ProtocolClaim B P Q := by\n  ...\n```\n\nUpper submissions use:\n\n```text\nProximityPrize/SubmissionUpper/\n  Solution.lean\n  score.txt          # canonical non-negative centibits B\n  unsafe-index.txt   # i, from 1 through 131072\n```\n\nand export:\n\n```lean\ntheorem ProximityPrize.Benchmark.Upper.candidate :\n    ProximityPrize.Benchmark.Upper.ProtocolClaimUpper B i := by\n  ...\n```\n\nEach challenge stands alone: a candidate may import only its own protected\ntarget and flat helper `.lean` files beside `Solution.lean` in the same\nsubmission root. Cross-challenge imports and subdirectories are rejected. The\nbenchmark binds the scalar files to the exact theorem type and permits only\n`propext`, `Classical.choice`, and `Quot.sound` in the candidate's axiom\nclosure.\n\n## Run\n\nBuild the pinned verifier tools and protected targets:\n\n```sh\n./setup.sh\n```\n\nThen run the track whose submission root you created:\n\n```sh\n./benchmark.sh lower\n./benchmark.sh upper\n```\n\nOn a machine without the trusted Linux sandbox, an explicitly unranked smoke\ntest is available with `BENCHMARK_INSECURE_LOCAL=1`.\n\nYukon exposes both score directions from [`benchmark.json`](benchmark.json):\n\n```sh\nyukon switch irs-reduction-threshold-lower\nyukon run\n\nyukon switch irs-reduction-threshold-upper\nyukon run\n```\n\nLocal artifacts are diagnostic only. Ranked results require the independent\nverifier to accept the exact commit and return the matching score plus exact\nradius or unsafe index. The repository-side identities are:\n\n```text\nproximity-prize-reduction-lower @ irs-reduction-threshold-v10\nproximity-prize-reduction-upper @ irs-reduction-threshold-v10\n```\n\nThose verifier profiles must be registered before either workflow can issue an\nauthoritative leaderboard score.\n",1789317493465]