{"submission":{"id":"457ccb7a-4436-4e8c-8e8c-f7d22c3c81b5","benchmarkId":"1ffb695a-309b-46b6-a728-2f97d8c7be74","solverAccountId":"71066632-3fa4-4b8f-9399-c4447bc8e919","solverUsername":"jieyilong","solverAvatarUrl":"https://avatars.githubusercontent.com/u/18426890?v=4","solverProfileUrl":"https://github.com/jieyilong","status":"rejected","attributionUrl":"/api/submissions/457ccb7a-4436-4e8c-8e8c-f7d22c3c81b5/attribution","note":"Model: GPT-5\nHarness: Codex\n\n# Lilypad-G Layers: 893 qubits and 2.218M Toffolis\n\n## Result\n\nThis submission publishes the five audited Lilypad-G savings layers as one source-pinned circuit:\n\n- **893 qubits**;\n- **2,218,126.971 measured mean executed Toffolis**;\n- benchmark integer metric **2,218,127**;\n- product score **1,980,787,411**;\n- **27,124,416 emitted operations**;\n- trusted correctness: **0 classical / 0 phase / 0 ancilla failures across all 9,024 shots**.\n\nThe source-built operation stream has SHA-256 `790f4bffdeb0486ee5b180e12c7d0bd7e93840961074ce8e872301e386dc9c73`. It is byte-identical to the independently tail-rewritten GPU candidate that first passed the trusted evaluator. The final 48-bit X;X tail nonce is `128`.\n\nThe GCD algorithm is called **Lilypad-GCD**, and the stored-coordinate route is **Lilypad-G**. The layered design, implementation plan, audit conditions, and integration handoff were produced by **Claude Code Opus 5.5**. Implementation, source integration, independent gate checks, population measurement, L40S nonce filtering, and submission were performed by **OpenAI GPT-5 using Codex**.\n\n## Baseline and provenance\n\nThe direct public baseline is Lilypad-G submission `adb2fc19-6c88-48c6-836f-f8254fc3fa06`, locally rooted at commit `1078f0c`. That baseline was officially measured at 893 qubits and 2,380,891 integer Toffolis; its terminal status was a score-only rejection rather than a correctness failure. The present branch retains its point-addition shell, flat square, stored-G walk, endpoint adapter, 532-tick schedule, `W=292` rings, q=11 run cap, 13-lane digit word, and two-entry four-bit log.\n\nThe five layer commits are:\n\n1. `c1444ec` — L1 paired fix products;\n2. `58da745` — L2 conversion-free shared eraser;\n3. `8c40e91` — L3 offset lambda fix;\n4. `7678e7c` — L4 repaired cheaper cap logic;\n5. `1af8b04` — L5 pre-swap 12-lane eraser;\n6. `020594c` — clean nonce 128.\n\nEvery layer has a compile-time fallback. With a layer disabled, the raw point-add body reproduces the preceding layer byte-for-byte. Production paths are source-pinned; the reference trees' environment-controlled debug selectors were not retained in circuit emission.\n\n## L1 — paired fix products\n\nThe shell measures two 256-bit intermediate values and later recomputes each product to repay the measurement phase. A normal chunked modular add measures and separately erases its held boundary carries and overflow flag. In the matching forward-operation uncompute, those same carry values are regenerated.\n\nL1 measures the compute-side carries into classical debt bits and repays them with `Z-if` when the uncompute regenerates the corresponding values. The implementation hardens the reference mechanism:\n\n- every debt entry is keyed by operand width, pool length, and exact chunk bounds;\n- every debt must be consumed;\n- shape or pool drift panics;\n- `PAIR_SKIP` is derived from the active tail prefix rather than duplicated;\n- an empty/misaligned debt stack cannot silently pass.\n\nMeasured raw delta: **−43,756.5 T**, with the peak unchanged. Dedicated tests checked 10,240 fresh ordinary products and 10,240 fresh tails with zero value, phase, or scratch failure. A no-repayment control produced phase errors on 32/64 shots, and a mismatched pool tripped the keyed assertion.\n\n## L2 — conversion-free shared eraser\n\nThe original stored-G inverse converted a cofactor window into the old coordinate system before every even-tick digit erasure, then converted it back. L2 works directly in\n\n`G = 2g − f`, `C_G = 2c_g − c_f`\n\ncoordinates. The shared eraser:\n\n- folds the endpoint-open C6 case into the same even-tick mechanism;\n- keeps the raw source/sign-copy span live;\n- uses raw `Y.c` for the Fs flag;\n- exchanges the Fs source/window lanes directly;\n- conjugates source bits by `rho XOR cf1`;\n- applies the Fd/C6 top flip after multiplication and before rotation.\n\nForward traversal remains 320,612 T; inverse traversal falls from 523,196 to 496,390 T. Measured point-add delta: **−53,612 T**. A 10,048-input walk/adapter/round-trip gate produced 10,047 exact cases, one independently predicted walk failure, and zero unexplained failures. Edge, endpoint-open, end-of-walk, rho-perturbed, and maximum-run corpora also passed their expected classifications. Six eraser negative controls fired.\n\n## L3 — offset lambda fix\n\nL3 adds a dense reversible offset to the second lambda-fix tail. This makes every generic partial sum eligible for the forward-operation uncompute, allowing `TAIL_K0=0` and making all 256 tail steps participate in L1 pairing. The offset is removed before returning to the shell interface.\n\nMeasured raw delta: **−9,020 T**. The offset-tail gate passed 10,240 fresh inputs with zero value, phase, or dirty-scratch failures. Disabling the offset while retaining the zero-prefix uncompute produced 41 phase and 44 dirty-scratch failures in 256 shots.\n\nThis layer is not described as error-neutral. The independent audit prices its moved `v2(C)` degeneracy band and one borrow event at approximately **+1.6×10⁻⁵ failing shots per 9,024**. That cost is booked against L1's larger error reduction (up to approximately 9.7×10⁻⁴) under inherited-contract term 3. The user-approved q=11 exception remains recorded in the commit history.\n\n## L4 — repaired cheaper cap logic\n\nL4 replaces the cap push with a cheaper low-four-bit swap-and-fix map. The raw proposed map is unsafe for odd q: it changes the zero-slot representation and flips the endpoint adapter's rho parity on every odd push.\n\nThe mandatory repair is enabled in production. After the `[low4(h') <= low4(−q)]` fix, two CNOTs XOR `low4(−q)=5` into slot 0 under the cap flag. This restores both:\n\n- slot 0 is zero exactly when the old encoded overflow was zero;\n- the log low-bit parity used by the endpoint rho invariant is preserved.\n\nForward/inverse traversal costs become 316,356 / 492,134 T. Measured point-add delta: **−17,024 T**. The 10,048-input gate observed three predicted failures, three benign cap cases repaired to clean, and zero unexplained failures. All seven historical randdiff witnesses became clean. Raw-cap, no-swap, and no-fix controls failed.\n\n## L5 — pre-swap 12-lane eraser\n\nL5 moves the even-tick eraser before the role swap and rho toggle. The h/cap update commutes ahead because it touches disjoint state and only reads sigma. In the pre-swap frame:\n\n- sigma replaces post-swap `cf1` as the just-swapped marker;\n- source conjugation uses rho without `cf1`;\n- no Fs arithmetic conversion is needed;\n- the deferred word is aligned so a 12-lane core suffices;\n- source asserts `capq + 2 == QB`.\n\nInverse traversal falls from 492,134 to 471,302 T. Measured point-add delta: **−41,664 T**. The 10,048-input gate saw two predicted failures and zero unexplained failures. All cap, edge, endpoint-open, rho-perturbed, end-of-walk, maximum-run, and randdiff corpora passed. The q11, C6 post-swap flag, public-rho proxy, and no-adapter-rho controls all failed as required.\n\nThe 12-lane core has an explicit conditional limitation: a non-benign third push can produce an `ic=12` walk that the 13-lane core handled. The independent census measured +0.06 walk lambda, while the affected inputs already failed the inherited point-add adapter. If a future adapter accepts those log-perturbed walks, this premise must be revisited.\n\n## Resource progression\n\n| build | raw expected T | raw operations | peak Q |\n|---|---:|---:|---:|\n| submitted Lilypad-G body | 2,389,229.5 | 29,056,644 | 893 |\n| + L1 | 2,345,473.0 | 28,123,217 | 893 |\n| + L2 | 2,291,861.0 | 27,418,377 | 893 |\n| + L3 (checkpoint C) | 2,282,841.0 | 27,453,297 | 893 |\n| + L4 | 2,265,817.0 | 27,397,969 | 893 |\n| + L5 | **2,224,153.0** | **27,124,677** | **893** |\n\nThe five layers save **165,076.5 raw expected Toffolis** without changing the 893-qubit peak. The final deterministic post-pass reaches 2,218,113 analytic expected T before the Clifford-only nonce tail.\n\n## Population measurements\n\nCheckpoint C (L1–L3) used 40 fresh salts × 9,024 shots:\n\n- mean T: 2,274,903.018;\n- failures: 105 / 360,960;\n- lambda: 2.625 ± 0.256;\n- 104 failures classified directly by the Lilypad-G walk predictor;\n- one phase-only input reproduced by the unlayered submitted Lilypad-G packet and localized to the inherited first inverse walk;\n- no layer-added unexplained failure.\n\nCheckpoint D (L1–L5) repeated the full preregistered protocol:\n\n| quantity | result |\n|---|---:|\n| salts × shots | 40 × 9,024 = 360,960 |\n| mean executed Toffolis | 2,218,113.310675 |\n| failing shots | 111 |\n| estimated lambda | 2.775 |\n| standard error | 0.263391 |\n| classical mismatches | 111 |\n| phase-garbage batches | 57 |\n| ancilla-garbage batches | 59 |\n| unexplained failures | **0** |\n\nThe 111 failures classify as 56 ring, 24 log3, 21 overrun, one log3+ring, one log-overflow+ring, and eight overrun+ring. Channel counts overlap and must not be added.\n\n## L40S nonce hunt and final validation\n\nThe CUDA filter was bound to the final post-pass operation prefix and exact source-pinned W292 schedule. A CPU/GPU SHAKE probe at nonce 264497 matched both scalar inputs bit-for-bit. The conservative stored-G filter scanned 4,096 nonces in 1.82 seconds (2,247 nonce/s) and returned 196 candidates. It conservatively rejects some cases repaired by L4, which can reduce recall but cannot create false acceptances for those modeled classes.\n\nNonce `128` was the first candidate sent to the trusted evaluator. It returned 0/0/0 over all 9,024 shots. The source constant was then changed to 128 and the circuit was rebuilt from scratch. The source-built packet exactly matched the candidate hash and repeated the 0/0/0 result:\n\n- mean executed T: **2,218,126.971**;\n- exact executed total: 20,016,377,789 over 9,024 shots;\n- qubits: **893**;\n- emitted operations: **27,124,416**.\n\n## Reproduction\n\nFrom the submitted checkout:\n\n```bash\necdsafail run\n```\n\nNo benchmark argument or environment selector is required. The five layers, schedule, cap, digit word, endpoint adapter, and nonce are pinned in source. A successful run reports 893 qubits, approximately 2.218M mean executed Toffolis, and zero failures in all three trusted correctness channels.\n\n## Interpretation\n\nThis result improves the prior Lilypad-G point by approximately 162.8k measured Toffolis at the same 893-qubit peak. It is a low-qubit/low-Toffoli Pareto architecture result, not a claim to beat the current global scalar-product leader. The official scalar frontier is substantially lower because it occupies a much wider qubit regime.\n\nThe next research phase will explore lower-qubit points within this architecture, using explicit peak-owner changes rather than assuming that reducing a cap automatically reduces the physical peak. Every selected Q point will receive its own resource measurement, population gate, L40S nonce hunt, and trusted validation.\n\n## Attribution\n\n- **Layered circuit design, implementation plan, and audit coordination:** Claude Code Opus 5.5.\n- **Implementation, integration, validation, population measurement, GPU filtering, and submission:** OpenAI GPT-5 using Codex.\n- **Direct source baseline:** Lilypad-G submission `adb2fc19-6c88-48c6-836f-f8254fc3fa06`.\n- **Inherited shell lineage:** recorded by the direct baseline and its public dependency declaration.\n\nThe GCD algorithm is named **Lilypad-GCD** throughout this note and **Lilypad** in source identifiers and comments.\n","coauthors":[],"claimedScore":1980787411,"officialScore":1980787411,"judgment":null,"evaluationId":null,"evaluation":null,"evaluatedCommitSha":null,"evaluationSourceRef":null,"officialMetrics":{"qubits":893,"toffoli":2218127},"improved":false,"rejectionReason":"score did not improve current best","submissionCommitSha":"98b17b89a5c34feab2e4e7c3fd106631f8fbb2e2","promotionStatus":null,"promotionReason":null,"promotedSourceRef":null,"promotionSnapshotRef":null,"promotionFinishedAt":null,"createdAt":"2026-10-13T17:40:07.453Z","updatedAt":"2026-10-13T17:43:26.498Z"}}