{
 "_doc": "The lab's current claim and limits for one result, copied word for word from the line of its current-claims list named here. A value that is replaced by an object with sha256_of_value and bytes is committed by its hash instead of printed, for the reason it states. Nothing here is typed by hand.",
 "portfolio_id": "inference-limits:encoder-within-3-bits",
 "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.",
 "limits": "The certificate ships dominance_foil — a theorem PROVING the unconditional claim FALSE — plus a worked counter-case (W=64, g=32) where the dense competitor wins 64 bits to 128. Two fixtures have dense_over_ours_x below 1.0. An earlier wording overstated what the Lean proof shows about a lower bound and is no longer used: the lower-bound half assumes the encoding is one-to-one, and the upper half is the identity map, a counting tautology. Bit counts were NOT independently re-derived this pass beyond the axiom audit. A3 2026-09-09: two defects, both closed here. (1) The registered command named scripts/gen_marquee_axioms.py, which mentions prior_art_dominance_cert.json ZERO times and emits an axiom receipt; the producer is experiments/gen_prior_art_dominance_report.py, which mentions it eight times and was run in this pass, regenerating the certificate with no diff. (2) The 1.79x and 2.36x figures were attributed to \"the sparse fixtures\". They are measured.dense_over_ours_geomean_x and sack_over_ours_geomean_x over all FIVE committed fixtures, two of which the certificate itself labels regime \"dense\" and on which dense_over_ours_x is 0.996 and 0.992 -- our encoder loses there, which is exactly what the Lean dominance_foil says. Recomputed in this pass over the three sparse fixtures only (1.58, 2.612, 4.531 and 3.16, 2.612, 2.265): both geometric means are 2.654. Still open, per the grader: the accounting is payload-only and header-inclusive deployed accounting has not been done, so \"the deployed sparse-gap encoder\" has been narrowed to \"the modeled Elias-Fano sparse-gap payload\". A3 also added a `make top40-gates` target that runs this list's four checks, with check_top40_commands.py --strict: nothing in the repository called that script before, and without --strict it prints a failure and exits 0. CORRECTED 2026-09-02 (peer review S02, reports/PEER_REVIEW_2026-09.md): the entry cited only `python3 scripts/gen_marquee_axioms.py`, which writes reports/proof_axioms_marquee.txt and never this certificate; the producer of prior_art_dominance_cert.json is experiments/gen_prior_art_dominance_report.py, which exits 1 in a fresh checkout until rustcheck is built (`cargo build --release`) and then regenerates the certificate with zero semantic differences. The marquee axiom gate is environment-dependent: in a fresh worktree it reports every corpus without a .lake build as an unresolved footprint and exits 1; see reports/PEER_REVIEW_2026-09.md structural findings for its state after every enumerated corpus was built. STATUS 2026-09-02 (S04, kit gate 4): the command's first half regenerates the certificate byte-identically (rustcheck built), but its second half, scripts/gen_marquee_axioms.py, exits 1 in this checkout because the marquee audit reports every unbuilt library as UNRESOLVED (164 lines after five build rounds; zero disallowed axioms among 442 resolved; whether the prior-art corpus itself resolved is read from the receipt section, not assumed). run_status is therefore BLOCKED until the marquee gate is green from a fresh clone; the certificate itself is REPRODUCED (out/run_receipts.json rank 7: failed, exit 1, 20.3 s).",
 "lab_commit": "9d619007982bf311b1d3b64c929b835bbceb1f97",
 "differs_from_sealed": false,
 "source": {
  "list": "the lab's current claims",
  "line": 78,
  "sha256": "03cbc720dc0c135b24ba7e8060eb92541f7b5759dcd151d4e2c8afa2e47afadb"
 },
 "result_receipt": "/receipts/inference-limits/results/encoder-within-3-bits.json",
 "vendored_utc": "2026-10-06T02:09:30Z"
}