{
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    "id": "encoder-within-3-bits",
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    "title": "Sparse-gap encoder within 3 bits per gap of the counting floor",
    "claim": "The modeled Elias-Fano sparse-gap payload sits within 3 bits per gap of the machine-checked counting floor floor(log2 C(W,g)), proven in Lean for all W and g. On the five committed fixtures the payload accounting gives geometric means of 1.792x against Falcon's dense bitmap and 2.364x against QUIC SACK ranges -- but those five include two DENSE-regime fixtures on which our encoder is slightly WORSE than the dense bitmap (0.996x and 0.992x). Over the three SPARSE-regime fixtures alone the geometric means are 2.654x and 2.654x. The 1.792x figure is a five-fixture number, not a sparse-fixture one.",
    "scope": "theory/lean/PriorArtCost.lean, 11 theorem/lemma declarations, axioms subset of {propext, Quot.sound}, mathlib-free. The DOMINANCE half is CONDITIONAL on a sparsity hypothesis g*(floor(log2 W)+3) <= W and is measured on 5 committed deterministic fixtures, not silicon.",
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    "claim": "The modeled Elias-Fano sparse-gap payload sits within 3 bits per gap of the machine-checked counting floor floor(log2 C(W,g)), proven in Lean for all W and g. On the five committed fixtures the payload accounting gives geometric means of 1.792x against Falcon's dense bitmap and 2.364x against QUIC SACK ranges -- but those five include two DENSE-regime fixtures on which our encoder is slightly WORSE than the dense bitmap (0.996x and 0.992x). Over the three SPARSE-regime fixtures alone the geometric means are 2.654x and 2.654x. The 1.792x figure is a five-fixture number, not a sparse-fixture one.",
    "class": "ASSERTING",
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    "witness_command": "cd rustcheck && cargo build --release --offline && cd - >/dev/null && python3 experiments/gen_prior_art_dominance_report.py",
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      "witness_command": "cd rustcheck && cargo build --release --offline && cd - >/dev/null && python3 experiments/gen_prior_art_dominance_report.py",
      "recorded_exit": 0,
      "recorded_assertion": "dense/ours geomean 1.792x | sack/ours geomean 2.364x | xlang agree True",
      "mutation": "truncated reorder_events_4.txt from 4097 lines to 11",
      "mutated_exit": 0,
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