{"submission_id":"87c1c3a4-2dc4-40f9-8028-2ebdd830180e","submission_revision_id":"00d70337-4f15-4930-8507-6c7c3572b2e2","revision_version":1,"submission_status":"submitted","submitted_at":"2026-10-15T05:51:12.446165Z","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":"2026-10-15T05:51:12.446165+00:00","domain_payload":null,"industry_domain":" Boolean circuit synthesis","task_short_name":"formally_verified_compact_substitution_circuit_01","operating_system":"Linux","task_description":"Implement and formally verify a compact Boolean substitution circuit\n\nA hardware team has a fixed eight-bit 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 eight 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 64 AND gates and no more than 400 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 64 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","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 64 AND gates and at most 400 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":"10568cdc-bad7-45bd-af72-048233d430ec","filename":"sbox_circuit_inputs.zip","category":"input_materials","content_type":"application/x-zip-compressed","size_bytes":4329},{"file_id":"960622c8-9002-48f8-8dd7-8ab246da3df6","filename":"sbox_circuit_reference.zip","category":"reference_output","content_type":"application/x-zip-compressed","size_bytes":50815},{"file_id":"9ab39c5a-243a-4ad7-a4e7-862f89987ec8","filename":"sbox_circuit_evidence.zip","category":"difficulty_self_test_evidence","content_type":"application/x-zip-compressed","size_bytes":65415}],"deep_review":{"overall_verdict":"Accept","review_text":"**Overall Verdict:** Accept — The task is complete, objectively evaluable, and supported by a compliant reference circuit and coherent formal-proof evidence.\n\n**Completeness Check:**\n\n- Instruction: Complete — Deliverables, permitted gates, wire ordering, budgets, theorem interfaces, and prohibited proof shortcuts are explicit.\n- Inputs: Complete — The 256-entry truth table matches the fixed Lean table; duplicate input copies agree.\n- Toolchain: Complete — Lean 4.19.0, a pinned Mathlib revision, and standard-library Python provide a documented Linux workflow.\n- Reference output: Complete — Independent checks confirm 64 AND gates, 316 total gates, exact outputs for all 256 inputs, and identical ordered Lean and JSON circuit data. Supporting proof modules and build logs are included.\n- Rubric: Complete — The 20/30/50 allocation clearly distinguishes functional correctness, budget compliance, and complete formal verification.\n\n**File and Task Reachability:**\n\nAttachment classification: `reachable`. All three archives, `sbox_circuit_inputs.zip`, `sbox_circuit_reference.zip`, and `sbox_circuit_evidence.zip`, match their manifest sizes and contain 4, 38, and 54 readable members respectively. No unsafe paths, encrypted members, or corrupt entries were found. Contents are ASCII or UTF-8 text with parseable structured data.\n\nInspected materials include `task.txt`, `circuit_format.txt`, `truth_table.json`, `CircuitSpec.lean`, reference `circuit.json`, `Core.lean`, `Cases00.lean` through `Cases07.lean`, `Solution.lean`, checking instructions, license and source records, verification scripts and logs, and trial circuits, proof candidates, synthesis sources, and grading evidence. All 256 reference traces agree with independently computed gate values. Reference answers are packaged separately from solver inputs.\n\nTask classification: `reachable`. A single-machine workflow supports synthesis, exhaustive comparison, circuit-data comparison, Lean compilation, and theorem-type and axiom inspection. Uploaded code was inspected but not executed. Lean was unavailable for an independent rebuild; submitted logs report successful checking with only permitted standard logical axioms. No attachment remained unreadable.\n\nThe self-test’s selected circuit independently reproduces all outputs but exceeds the total-gate budget, consistent with its reported 20/100 score. Its unfinished proof is explicitly identified.\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. MIT-licensed BearSSL components are documented, but the target is a different composed function. Neither public-benchmark identity nor material AI fabrication is established. External provenance was not independently verified because approved external search was unavailable.\n\n**Recommended Changes:**\n\nThe fixed specification, compliant reference, and transparent self-test evidence support acceptance. No changes are required.","reviewed_at":"2026-10-15T05:56:05.506125Z"},"claim":null}