{ "schema": "diskcover-public-test-reports-v1", "n": 11, "report_scope": "Historical source-based reports and an independently reviewed failed DeepSeek submission; mathematical answer data withheld. Existing global proofs were not rerun; the DeepSeek exact counterexample was replayed.", "records_comparable": false, "records": [ { "record_id": "n11-astra-20260930", "model": "gpt-6 astra/max", "test_date_utc": "2026-09-30", "status": "historical_demo_not_formal_pass", "elapsed_seconds": "20895.189", "main_natural_seconds": "20069.011", "main_system_accumulated_seconds": "17881", "followup_natural_seconds": "826.178", "followup_system_accumulated_seconds": null, "timing_scope": "sum_of_main_and_independent_required_followup_natural_intervals_excluding_gap", "original_budget_seconds": "3600", "within_original_budget": false, "hardware": { "cpu": "AMD Ryzen 9 8945HX with Radeon Graphics", "memory_generation": "DDR5", "memory_gib": 32, "memory_bytes": 34359738368, "snapshot_scope": "queried_during_original_sol_report_preparation_not_at_task_start", "astra_scope": "shared_publisher_machine_reference_from_sol_report_no_separate_astra_snapshot" }, "prompt_artifacts": [ { "kind": "main", "original_text_url": "reports/n11-astra-main-prompt.original.txt", "sha256": "d761c10aed4fd064342bdef7775b2e533de7c519cd63b09d7a2351a34f5c19cf" }, { "kind": "followup", "original_text_url": "reports/n11-astra-followup-prompt.original.txt", "sha256": "52d9329a252304ebae2cad738fa157dc0243a1f10ba84dab968b19ded71e1e30" } ], "phases": [ { "start_relative_seconds": "0", "end_relative_seconds": "3252.612", "duration_seconds": "3252.612", "activity_zh": "经典资料、候选重建与独立下界探索；找到网上已有的完整最优性证明材料", "activity_en": "Background research, candidate reconstruction and independent lower bounds; find an existing complete optimality proof package online", "outcome_zh": "得到候选与粗下界，尚未匹配；阶段末找到外部完整证明材料，全局证明并非模型独立发现。", "outcome_en": "A candidate and coarse bounds were available but did not match; an external complete proof package was found at the end. Its global proof was not independently discovered by the model.", "evidence_scope": "reconstructed_progress_intervals" }, { "start_relative_seconds": "3252.612", "end_relative_seconds": "7437.363", "duration_seconds": "4184.751", "activity_zh": "获取、审查并重放外部已有的全盘覆盖与全局最优性证明", "activity_en": "Acquire, review and replay the existing external full-disk coverage and global optimality proof", "outcome_zh": "复用 DiskCoveringSolve 的证明、输入和验证代码，两轮全量重放通过；并行代数探索，仍缺显式一元多项式。", "outcome_en": "Reuse the DiskCoveringSolve proof, inputs and verification code; two full replays passed. Algebraic work ran alongside replay, but an explicit univariate polynomial was still missing.", "evidence_scope": "reconstructed_progress_intervals" }, { "start_relative_seconds": "7437.363", "end_relative_seconds": "11127.284", "duration_seconds": "3689.921", "activity_zh": "几何降维、三变量与多变量消元尝试", "activity_en": "Geometric reduction and elimination attempts", "outcome_zh": "几何降维取得新方程；若干消元及整数关系搜索未成功。", "outcome_en": "Geometric reduction produced new equations; several elimination and integer-relation searches failed.", "evidence_scope": "reconstructed_progress_intervals" }, { "start_relative_seconds": "11127.284", "end_relative_seconds": "12024.037", "duration_seconds": "896.753", "activity_zh": "清除退化分支，取得有限域消元结果", "activity_en": "Remove degenerate branches and obtain finite-field elimination data", "outcome_zh": "清除退化分支后有限域消元成功，确定待恢复的数据规模。", "outcome_en": "Removing degenerate branches enabled finite-field elimination and established the recovery scale.", "evidence_scope": "reconstructed_progress_intervals" }, { "start_relative_seconds": "12024.037", "end_relative_seconds": "17352.345", "duration_seconds": "5328.308", "activity_zh": "参数化、唯一根盒与有理系数恢复尝试", "activity_en": "Parametrization, a unique-root box and rational coefficient recovery attempts", "outcome_zh": "根盒和重构论证推进；整体有理恢复失败，改为逐素数恢复。", "outcome_en": "Root-box and reconstruction arguments progressed; failed automatic recovery led to a prime-by-prime route.", "evidence_scope": "reconstructed_progress_intervals" }, { "start_relative_seconds": "17352.345", "end_relative_seconds": "18351.374", "duration_seconds": "999.029", "activity_zh": "逐次提升、根隔离及精确代入连接", "activity_en": "p-adic lifting, rational reconstruction, root isolation and exact substitution", "outcome_zh": "逐次提升恢复全部系数；精确代入和唯一根连接通过。", "outcome_en": "Successive lifting recovered the coefficients; exact substitution and the unique-root connection passed.", "evidence_scope": "reconstructed_progress_intervals" }, { "start_relative_seconds": "18351.374", "end_relative_seconds": "20069.011", "duration_seconds": "1717.637", "activity_zh": "独立验证器、证明说明与交付打包", "activity_en": "Integrate independent verifiers, complete the arguments and package delivery", "outcome_zh": "新增独立核验、分支检查及完整交付完成。", "outcome_en": "Independent checks, branch selection and complete delivery were finished.", "evidence_scope": "reconstructed_progress_intervals" } ], "source_report": { "filename": "cover11-work-report.md", "sha256": "d2aa68c72384dc0ffb9732e076e0446f68406d0d093c3f17b1aa9a8a78ec1592", "public_version": "answer_withheld_summary" }, "report_urls": { "zh": "record-n11-astra-20260930.zh.html", "en": "record-n11-astra-20260930.html" }, "external_work": { "source_repository": "VonEquinox/DiskCoveringSolve", "source_commit": "089584973f41e6374ce110f6e5b5ee456df19352", "source_url": "https://github.com/VonEquinox/DiskCoveringSolve/tree/089584973f41e6374ce110f6e5b5ee456df19352/cover11/proof_bundle", "proof_origin": "existing_external_work_obtained_online", "independently_discovered_global_proof": false, "reused_materials": [ "candidate_configuration_and_110_variable_KKT_root_certificate", "full_disk_coverage_proof_and_certificates", "general_configuration_Voronoi_reduction_and_exhaustive_enumeration", "stress_continuous_branch_and_local_lower_bound_certificates", "verification_code_and_inputs" ], "contribution_zh": "检索、审查与实际重放外部已有证明；补全显式半径多项式、圆心代数数据、认证连接及交付。", "contribution_en": "Find, review and replay the existing external proof; supply an explicit radius polynomial, algebraic center data, certified connections and delivery.", "timing_note_zh": "Astra 在 T+00:54:13 左右找到该来源；T+00:54:13—T+02:03:57 的约1小时9分45秒用于获取、审查与重放已有证明，并行进行代数探索，两轮全量重放通过。这是利用现成证明的复核阶段，不是从头发现全局证明的用时，也不是纯验证程序运行时间。主任务后续主要补足显式一元多项式及严格连接；最小多项式另有独立追加任务。", "timing_note_en": "Astra found the source at about T+00:54:13. The approximately 1 h 9 min 45 s interval T+00:54:13–T+02:03:57 covered acquisition, review and replay of the existing proof, alongside algebraic exploration; two full replays passed. This was verification of an existing proof, not discovery of a global proof from scratch or pure verifier runtime. Subsequent main-task work chiefly supplied the explicit univariate polynomial and certified connections; the minimal polynomial was handled in a separate follow-up.", "verification_scope": "historical_executed_replays; this website edit performs no new mathematical replay" } } ] }