{"claim":{"id":"1fb012f9-0eb7-45ea-a1f2-a93fc104d76d","submission_id":"f96dc0f8-b37f-4b63-aed5-a02c7659cdf7","submission_revision_id":"4188eeeb-75a0-4a1d-99b5-b424b09e15a4","builder":"builder-01","status":"active","claimed_at":"2026-10-15T16:23:32.391709Z","delivered_at":null,"ended_at":null,"delivery_note":null,"end_reason":null},"task":{"submission_id":"f96dc0f8-b37f-4b63-aed5-a02c7659cdf7","submission_revision_id":"4188eeeb-75a0-4a1d-99b5-b424b09e15a4","revision_version":1,"submission_status":"under_review","submitted_at":"2026-10-15T05:53:07.929984Z","submitter_name":"Haoyang Su","submitter_email":"hoyantsu@gmail.com","task":{"status":"submitted","version":1,"domain_key":null,"extra_fields":{"difficulty_self_test":{"model":"GPT-6 Astra","harness":"Codex","estimated_score":"20–40%"}},"submitted_at":"2026-10-15T05:53:07.929984+00:00","domain_payload":null,"industry_domain":"Boolean circuit synthesis","task_short_name":"formally_verified_paired_substitution_01","operating_system":"Linux","task_description":"Implement and formally verify a compact Boolean substitution circuit\n\nA hardware team has a fixed eight-input, sixteen-output substitution function specified by all 256 entries in truth_table.json. Implement that exact function as a combinational Boolean circuit suitable for a backend where nonlinear gates are expensive. The function must not change. No decomposition or existing implementation is supplied.\n\nDeliver circuit.json, Solution.lean and instructions for checking the proof with Lean 4.19.0. The circuit has eight Boolean inputs and sixteen Boolean outputs, both ordered least-significant bit first. It may use only two-input XOR, two-input AND and one-input NOT gates. It must contain no more than 96 AND gates and no more than 490 gates in total. Fanout and wiring are free. Every gate must read only input wires or earlier gate outputs. No lookup tables, multiplexers, conditional expressions, arithmetic primitives, opaque external calls or additional input-dependent state may be counted as free operations.\n\nThe JSON schema is specified in circuit_format.txt. Its wire-level semantics, the full target table and the Lean proof interface are fixed in CircuitSpec.lean. Prove that your circuit is well formed, satisfies both gate budgets and computes the specified output for every x : Fin 256. The Lean circuit must be the same circuit as circuit.json, in the same order; the evaluator will compare their data. Deliver a complete kernel-checked proof. Missing proofs, sorry, admitted assumptions, new axioms, unsafe evaluation shortcuts and native_decide are not accepted. Standard logical axioms supplied by Lean are allowed; the final declarations must not depend on sorryAx or Lean.ofReduceBool.\n\nThe target has at least one implementation within the declared budgets. You are not asked to establish that 96 AND gates is the global minimum. Any circuit meeting the exact specification and both budgets is a correct answer. There is no preferred architecture or required synthesis algorithm. The difficulty is discovering a sufficiently compact implementation and delivering its formal equivalence proof; a correct table lookup or an oversized truth-table expansion is not a solution.\n\nPlace all deliverables in output/. Include any source needed to build the proof, but do not modify CircuitSpec.lean or replace the target function. If you use external synthesis tools, identify their versions in output/tool_versions.txt. The final circuit and proof must be self-contained.\n\nThe sixteen output bits represent two byte substitutions of the same input. Synthesize one shared circuit; both budgets apply to the entire circuit, not to each byte independently.\n","taxonomy_version":null,"software_licensing":"Free/Open Source","evaluation_criteria":null,"verification_method":"Check the circuit against the fixed gate schema and compare all 256 outputs exactly with the supplied table. Check that the Lean circuit data and output indices equal the JSON circuit data. Then check the submitted theorem declarations against the unchanged CircuitSpec.lean with Lean 4.19.0, and inspect their axiom dependencies. The correctness theorem must quantify over every x : Fin 256 and compare Circuit.evaluate with the fixed truth table; a theorem about a different interpreter, changed table, or unconnected implementation is invalid. No sorryAx, Lean.ofReduceBool, new axioms or unproved assumptions are permitted.\n\nAward 20 points for a well-formed circuit computing the target on all 256 inputs. Award a further 30 points only if that circuit uses at most 96 AND gates and at most 490 total gates. Award the remaining 50 points only for a complete kernel-checked proof of equivalence, well-formedness and both budgets for that same compliant circuit. A circuit outside either budget cannot receive proof points. Overall pass requires 100/100. A table lookup, hidden primitive or nonconforming gate fails the circuit criterion and earns zero overall. An unproved claimed optimum is irrelevant: the objective is a valid implementation within the fixed budgets, not a minimum-gate theorem. Different compliant circuits are accepted; gate lists need not equal the reference.\n","software_and_version":"Lean 4.19.0; Mathlib; Python 3.13.12","domain_schema_version":null,"specific_requirements":null,"expected_completion_time":null},"files":[{"file_id":"b48caaad-22e6-45b5-8327-79c369c7c31b","filename":"paired_substitution_inputs.zip","category":"input_materials","content_type":"application/x-zip-compressed","size_bytes":5148},{"file_id":"c21ab989-8c27-4d0c-9269-bdabc2fb07e2","filename":"paired_substitution_reference.zip","category":"reference_output","content_type":"application/x-zip-compressed","size_bytes":64353},{"file_id":"a099a4f2-aae4-4a4b-984b-df566b1ebac3","filename":"paired_substitution_evidence.zip","category":"difficulty_self_test_evidence","content_type":"application/x-zip-compressed","size_bytes":568612}],"deep_review":{"overall_verdict":"Accept","review_text":"**Overall Verdict:** Accept — The task is complete, objectively evaluable, and supported by a compliant reference circuit and substantial proof evidence.\n\n**Completeness Check:**\n\n- Instruction: Complete — Deliverables, permitted gates, wire ordering, budgets, theorem types, and prohibited proof shortcuts are explicit.\n- Inputs: Complete — The table contains 256 valid sixteen-bit outputs and matches the unchanged Lean specification; all duplicated inputs agree.\n- Toolchain: Complete — Lean 4.19.0, a pinned Mathlib revision, and build instructions establish a suitable open-source Linux workflow.\n- Reference output: Complete — Independent checks confirm 490 total gates, including 96 AND gates, exact agreement on all 256 inputs, and identical ordered Lean and JSON circuit data.\n- Rubric: Complete — The 20/30/50-point allocation clearly separates functional correctness, budget compliance, and formal verification.\n\n**File and Task Reachability:**\n\nAttachment classification: `reachable`. Inspected `paired_substitution_inputs.zip`, `paired_substitution_reference.zip`, and `paired_substitution_evidence.zip`, including their specifications, tables, circuits, proof sources, checking instructions, scripts, configurations, licensing notice, and logs. All three archives match manifest sizes, pass archive integrity checks, and contain safe member paths without encryption. Text members are readable UTF-8.\n\nAll 256 reference proof traces independently match recomputed gate values. The proof sources cover every input, and supplied build logs report successful Lean checking with only permitted axiom dependencies. Lean compilation was not independently repeated. Bundled executables and compiled Lean objects received format-level inspection only and were not executed or trusted.\n\nTask classification: `reachable`. A single-machine workflow supports synthesis, exhaustive circuit testing, ordered data comparison, source compilation, and theorem-type and axiom inspection. Supplied records report approximately 27 minutes for reference proof checking. The self-test correctly documents an unsuccessful 20/100 attempt, not a compliant solution. Solver inputs contain no reference implementation.\n\nLicense keys, accounts, tokens, and other credentials are not required from the contributor. Confidential, proprietary, or internal material may be evaluated as submitted evidence without requiring additional disclosure.\n\n**Special Screening:**\n\nNone. BearSSL-derived AES components are disclosed with a license notice, but this does not establish that the generated paired target or complete answer is a public benchmark. Public availability of the exact task could not be independently checked; AI fabrication is not established.\n\n**Recommended Changes:**\n\nThe precise specification, independently validated reference circuit, and detailed verification evidence support readiness. No changes are required.","reviewed_at":"2026-10-15T05:58:56.459865Z"},"claim":{"id":"1fb012f9-0eb7-45ea-a1f2-a93fc104d76d","submission_id":"f96dc0f8-b37f-4b63-aed5-a02c7659cdf7","submission_revision_id":"4188eeeb-75a0-4a1d-99b5-b424b09e15a4","builder":"builder-01","status":"active","claimed_at":"2026-10-15T16:23:32.391709Z","delivered_at":null,"ended_at":null,"delivery_note":null,"end_reason":null}},"revision_is_current":true}