{ "schema": "diskcover-public-test-reports-v1", "n": 13, "report_scope": "Retrospective n=13 failed-run records, each based on its own evidence; publication does not rerun mathematics.", "records_comparable": false, "records": [ { "record_id": "n13-codex-20261001", "model": "gpt-6 astra/max", "model_id": "gpt-6-astra", "reasoning_effort": "max", "model_identity_evidence": "User-authorized retrospective inspection: all 14 original-Goal turn_context records identify gpt-6-astra / max, with matching configuration settings.", "test_date_utc": "2026-10-01", "report_date": "2026-10-02", "status": "not_completed", "failure_reason": "No complete valid result satisfying all n=13 requirements by the original 43200-second deadline.", "runs": 1, "elapsed_seconds": "43200", "main_natural_seconds": "43200", "timing_scope": "Original goal creation to the fixed deadline; elapsed_seconds is the observation window of a failed run, not a completion time.", "valid_completion_elapsed_seconds": null, "main_system_accumulated_seconds": "27555", "system_timing_endpoint": "Frozen goal counter when marked blocked, at original T+12:01:59.", "original_budget_seconds": "43200", "within_original_time_budget": false, "valid_result_within_original_time_budget": false, "research_worker_closed_relative_seconds": 43118, "all_searches_terminal_confirmed_relative_seconds": 43007, "goal_marked_blocked_relative_seconds": 43319, "original_record_natural_seconds_to_blocked": 43319, "natural_seconds_from_original_start_to_report_cutoff": 52697, "report_cutoff_relative": "T+14:38:17", "timeline_clock": "natural_elapsed_since_original_goal_creation", "timing_notes": [ "Original scoring observation window: 12 hours. Research worker closed at T+11:58:38.", "The 119 seconds after the deadline through goal blocking were status checks and administration, not resumed mathematical computation.", "The supplemental system counter is 7 hours 39 minutes 15 seconds; it is not natural elapsed time.", "No reliable full decomposition of the difference between natural and system time is available; no pause duration is invented.", "The report cutoff includes the interval after the original research ended and this separately requested report; it is not active solve time." ], "additional_tasks": { "report_generation_requested_separately": true, "report_task_start": "Original separate report request, recovered from original-thread request timestamp.", "precise_report_request_timestamp_recorded": true, "report_task_elapsed_seconds": "1004.270", "report_task_timing_scope": "original_report_request_to_original_report_response", "intertask_gap_included_in_report_task_elapsed": false, "included_in_main_score_time": false, "mathematical_compute_restarted": false, "revision_task_start": "Separate request to revise to n=11 Astra format.", "revision_evidence_cutoff_relative": "V+00:21:14", "revision_evidence_cutoff_seconds": "1274.260", "revision_cutoff_is_not_completed_publication_duration": true }, "score": 0, "score_scope": "benchmark_failure_score", "strict_original_task_score": 0, "strict_original_task_acceptance": "failed_no_complete_valid_result_by_deadline", "formal_ranking": false, "completion_independently_verified": false, "answer_protocol": "diskcover-minpoly-v1", "score_protocol": "diskcover-log-score-v1", "reference_seconds": "21600", "reference_seconds_scope": "Default demonstration value required by the scoring CLI; not asserted to be an opening frozen n=13 reference.", "n13_frozen_reference_time_seconds": null, "scoring_version": "diskcover-log-score-v1", "score_formula": "round_half_up(200 + 100 * log2(reference_time_seconds / elapsed_seconds))", "score_rounding": "decimal_ROUND_HALF_UP_integer", "failure_score_independent_of_reference_seconds": true, "benchmark_commit_for_post_hoc_validation": "b6cde6540abcf4dfc54a77979e5a7517d3f971cb", "benchmark_commit_at_original_start": null, "scoring_contract_frozen": false, "deadline_inclusive": true, "score_execution": { "exit_code": 0, "python": "/usr/bin/python3", "args": [ "--n", "13", "--reference-seconds", "21600", "--elapsed-seconds", "43200", "--budget-seconds", "43200", "--status", "not_completed" ], "public_source_sha256": "4b2a1eb4640e6524772c8d8592bf6b41ba292dc3e3520829b679016d3fb32977", "execution_mode": "fresh_public_source_in_memory_no_local_research_reads", "executed_during_report_preparation": true, "output_file": "n13-score-output.json", "source_file": "official-score.py", "mathematical_proof_verified_by_score_script": false, "public_output_url": "https://github.com/pikaaa345/disk-covering-benchmark/blob/main/results/n13-score-output.json" }, "answer_check": { "protocol": "diskcover-minpoly-v1", "expected_sha256": null, "reference_status": "not_published", "sha256": null, "matches_reference": null, "executed": false, "reason": "The radius minimal polynomial coefficient list was not obtained. No fabricated coefficient list or fingerprint was submitted.", "current_public_reference_checked_at_commit": "b6cde6540abcf4dfc54a77979e5a7517d3f971cb" }, "mathematics": { "submission": "incomplete_no_complete_proof_package", "radius_minimal_polynomial_all_coefficients_submitted": false, "irreducibility_certified": false, "univariate_root_isolation_and_radius_association_submitted": false, "exact_ordered_centers_final_submission": false, "reused_public_continuous_coverage_material": true, "reused_public_global_lower_bound_material": true, "full_original_contract_completed": false, "geometry_or_global_proof_replayed_again_in_report_task": false, "independent_external_proof_review": false }, "acceptance": [ { "requirement": 1, "name": "半径最小多项式、不可约性及有理隔离区间", "status": "not_completed", "evidence": "No accepted polynomial candidate or full coefficient list." }, { "requirement": 2, "name": "唯一指定有序13圆心的有限精确代数数据", "status": "research_progress_not_complete_final_submission", "evidence": "Root-box, symmetry and reduced-system work recorded; no final integrated exact submission with the required radius polynomial." }, { "requirement": 3, "name": "整个闭圆盘的连续覆盖", "status": "external_material_review_and_original_replay_only", "evidence": "Existing public proof/certificates reviewed during the solve; not a new from-scratch discovery or a new replay in this report." }, { "requirement": 4, "name": "涵盖一般构型及退化情形的全局下界", "status": "external_material_review_and_original_replay_only", "evidence": "Existing public topology, exclusion and rigidity materials reused; full n=13 final contract still unmet." }, { "requirement": 5, "name": "完整实际代码、输入、证书和核验交付", "status": "not_completed", "evidence": "No integrated final proof package covering all requirements submitted." } ], "verification": { "historical_public_manifest_entries_checked": 28, "historical_public_replay_reported_exit_code": 0, "historical_public_replay_reported_seconds": "12.59", "historical_replay_evidence_scope": "Original-thread progress messages and tool receipts reviewed retrospectively; mathematical proof not rerun during revision.", "later_fresh_public_files_received_in_memory": 40, "later_fresh_manifest_entries_checked": 28, "public_topology_orbits_reported": 308198, "public_metric_exclusions_reported": 306437, "public_non_candidate_topologies_reported": 1760, "public_candidate_topologies_reported": 1, "exact_pipeline_controls_recorded": [ "81*x^4-2 synthetic lattice relation control", "cyclic-5 finite-field Groebner basis comparison" ], "numerical_geometry_stress_control_identity_count": 84, "numerical_geometry_stress_control_is_exact_n13_certificate": false, "full_math_pipeline_rerun_during_report_preparation": false, "official_benchmark_synthetic_self_check_rerun_in_report": false, "revision_model_and_timeline_metadata_reviewed": true, "full_math_pipeline_rerun_during_report_revision": false, "historical_full_replay_receipt_relative_seconds": 2346 }, "searches": [ { "label": "recovery_t512_1572864", "target": "radius_squared", "maximum_degree_tested": 512, "precision_bits": 1572864, "lattice_rows": 705, "eligible_rows_tested": 513, "independent_extra_precision_bits": 32768, "passed_extra_precision": 0, "reported_run_seconds": "12717.631", "wrapper_exit_code": 124, "exit_code_note": "Complete basis rows were received despite the timeout-wrapper status; this was used only for candidate filtering, not represented as exit-code-0 completion." }, { "label": "primitive_f128_262144", "target": "reduced_geometric_parameter_f", "maximum_degree_tested": 128, "precision_bits": 262144, "lattice_rows": 257, "eligible_rows_tested": 129, "independent_extra_precision_bits": 16384, "passed_extra_precision": 0, "reported_run_seconds": "891.674", "exit_code": 0 }, { "label": "primitive_f256_from128", "target": "reduced_geometric_parameter_f", "maximum_degree_tested": 256, "precision_bits": 262144, "lattice_rows": 0, "passed_extra_precision": 0, "reported_run_seconds": "479.666", "exit_code": 124 } ], "phases": [ { "start_relative_seconds": 0, "end_relative_seconds": 2346, "approximate_duration_seconds": 2346, "activity_zh": "获取、审查外部证明、调整枚举依赖和重新获取同版输入；并行约化。", "outcome_zh": "完整重放退出码0，最小多项式未完成。", "activity_en": "Acquire/review proof, adjust enumeration, reacquire fixed inputs; reduced-system work overlaps.", "outcome_en": "Full-replay exit 0, minimal polynomial missing.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true }, { "start_relative_seconds": 2346, "end_relative_seconds": 5350, "approximate_duration_seconds": 3004, "activity_zh": "对称性、菱形关系、约束映射和38变量根证书。", "outcome_zh": "报告根证书和原根盒连接通过，无合格多项式。", "activity_en": "Symmetry/rhombus/mapping checks and reduced root certificate.", "outcome_en": "Root certification and original-root connection reported passed, no polynomial.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true }, { "start_relative_seconds": 5350, "end_relative_seconds": 14002, "approximate_duration_seconds": 8652, "activity_zh": "分块格搜索、参数化、分支替换和内存实验。", "outcome_zh": "原题未完成，落盘日志／脚本读取被拒绝。", "activity_en": "Lattice, parametrization, branch and memory experiments.", "outcome_en": "Incomplete problem work; stored-log read denied.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true }, { "start_relative_seconds": 14002, "end_relative_seconds": 24389, "approximate_duration_seconds": 10387, "activity_zh": "内存输入、实时输出、方程化简及退化排除。", "outcome_zh": "Magma提交被拒绝，发现括号输入错误，受影响运行作废。", "activity_en": "Memory/live-output work, reductions and degeneracy exclusions.", "outcome_en": "Magma submission denied; input error found, affected runs discarded.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true }, { "start_relative_seconds": 24389, "end_relative_seconds": 29473, "approximate_duration_seconds": 5084, "activity_zh": "展开输入、有限域和p进探索及控制，进程崩溃后恢复。", "outcome_zh": "无目标分支关联或多项式；从公开输入恢复。", "activity_en": "Expanded input, finite-field/p-adic controls; crash recovery.", "outcome_en": "No target association/polynomial; public-input restoration.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true }, { "start_relative_seconds": 29473, "end_relative_seconds": 34675, "approximate_duration_seconds": 5202, "activity_zh": "最终512次搜索、消元和SBA控制，缩小辅助任务。", "outcome_zh": "332条辅助关系数值筛选通过，有保护消元在运行。", "activity_en": "Final 512-degree search, elimination/SBA controls and smaller jobs.", "outcome_en": "332 auxiliary numerical screenings; guarded elimination running.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true }, { "start_relative_seconds": 34675, "end_relative_seconds": 42821, "approximate_duration_seconds": 8146, "activity_zh": "主搜索和辅助参数搜索、恢复控制、中间式约简。", "outcome_zh": "主搜索返回124，513条候选未通过；辅助128次候选也未通过。", "activity_en": "Main/auxiliary searches, recovery controls and reductions.", "outcome_en": "Main return 124, 513 rejected candidates; auxiliary candidates also rejected.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true }, { "start_relative_seconds": 42821, "end_relative_seconds": 43118, "approximate_duration_seconds": 297, "activity_zh": "最后辅助搜索超时，核对所有搜索终止并关闭进程。", "outcome_zh": "无基输出；计算停止，关闭退出码0，无完整证明。", "activity_en": "Final auxiliary timeout, stop audit and worker closure.", "outcome_en": "No basis; computation stopped, worker exit 0, no complete proof.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true }, { "start_relative_seconds": 43118, "end_relative_seconds": 43200, "approximate_duration_seconds": 82, "activity_zh": "保持计算停止，最终答复报告失败，核对原截止。", "outcome_zh": "截止内无完整有效结果。", "activity_en": "Keep stopped, final failure response and deadline check.", "outcome_en": "No valid complete result by deadline.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true }, { "start_relative_seconds": 43200, "end_relative_seconds": 43319, "approximate_duration_seconds": 119, "activity_zh": "仅核对时钟、失败和连续阻碍。", "outcome_zh": "Goal设为blocked，未恢复研究。", "activity_en": "Clock/failure/blocker checks only.", "outcome_en": "Goal blocked, research not resumed.", "evidence_scope": "original_thread_timestamped_progress_or_tool_receipt; no_new_mathematical_replay", "endpoints_are_progress_or_receipt_times": true } ], "provenance": { "used_existing_public_construction_and_solver_certificates": true, "public_solver_commit": "089584973f41e6374ce110f6e5b5ee456df19352", "public_solver_url": "https://github.com/VonEquinox/DiskCoveringSolve/tree/089584973f41e6374ce110f6e5b5ee456df19352/cover13", "from_scratch_independent_discovery": false, "starting_materials": "The user's goal prompt and supplied environment facts; public sources subsequently retrieved.", "benchmark_materials_used_for_report_not_original_discovery": true, "original_public_source_found_by_relative_seconds": 300, "exact_first_discovery_time_recorded": false }, "hardware": { "measurement_scope": "Current hardware queried during report preparation; no opening hardware snapshot is available.", "cpu": "AMD Ryzen 9 8945HX with Radeon Graphics", "physical_cores": 16, "logical_processors": 32, "memory_generation": "DDR5", "memory_generation_evidence": "Current SMBIOSMemoryType=34=0x22; DMTF DSP0134 3.8.0 Table 77.", "memory_gib": 32, "physical_memory_bytes": 34359738368, "original_task_start_hardware_snapshot": null }, "tools": { "execution_location": "local_Ubuntu_WSL", "remote_mathematical_compute_used": false, "preinstalled": [ { "name": "SageMath", "version": "10.7", "used": true, "scope": "Exact polynomial/finite-field arithmetic and high-precision candidate computations; version retained in the research record." }, { "name": "Python in Sage environment", "version": null, "used": true, "scope": "Numerical and exact orchestration; historical precise Python version not established here." }, { "name": "Singular", "version": null, "used": true, "scope": "Intermediate polynomial ideal reduction; no final n=13 elimination certificate." } ], "obtained_during_task": [ { "name": "flatter", "commit": "d2b8026f29b4a69e987b15d4b240f8a5053275d3", "source": "https://github.com/keeganryan/flatter", "used": true, "scope": "Integer lattice basis reduction for candidate relations." }, { "name": "msolve", "version": "0.10.1", "source": "https://github.com/algebraic-solving/msolve", "used": true, "scope": "Polynomial system elimination and finite-field Groebner basis experiments." }, { "name": "Custom F4 checkpoint/compaction and SBA exploration code", "version": null, "used": true, "scope": "Discovery experiments with synthetic controls; no complete final n=13 Groebner basis certified." } ], "report_scoring_python": "3.12.3", "report_scoring_python_version_is_opening_snapshot": false, "historical_core_libraries": "Sage exact integer/rational/polynomial/finite-field and high-precision real arithmetic; full dependency versions not recorded.", "report_score_dependencies": "Python standard library argparse, json, math, decimal" }, "resources": { "money_budget": null, "money_spent": null, "money_evidence": "not recorded", "goal_token_counter": 2778511, "goal_token_counter_definition": { "label_zh": "Codex Goal 累计计数", "label_en": "Codex Goal cumulative counter", "owner": "Codex Goal", "industry_standard_metric": false, "verified_reference_implementation": "Codex 0.159.2", "reference_formula": "input_tokens - cached_input_tokens + output_tokens", "reasoning_tokens": "included in output_tokens; do not add again", "scope": "Goal-accounted usage increments; not whole-chat total, billed tokens or monetary cost", "version_note": "Historical versions follow their own implementation.", "reference_source_url": "https://github.com/openai/codex/blob/rust-v0.159.2/codex-rs/ext/goal/src/accounting.rs#L527-L532" }, "billed_tokens": null, "time_budget_seconds": 43200 }, "subagents_used_in_original_solve": false, "resource_rules": { "prohibited_by_original_user": "Preexisting local materials, skills, other chats and archived chats; strict WSL file-access wording remained in force.", "full_os_level_access_audit_available": false, "comprehensive_resource_compliance_certified": false, "prior_approval_denials": [ { "action": "Read newly generated local logs/scripts and subsequent metadata attempt", "stated_reason": "The approval reviewer interpreted the user's prohibition as excluding stored local files; no explicit additional authorization was provided.", "additional_authorization_received": false }, { "action": "Submit in-memory polynomial equations to the public Magma service", "stated_reason": "Internet access permission was not interpreted as authorization to transfer potentially sensitive research data to that third-party calculator.", "additional_authorization_received": false }, { "action": "Large parallel-memory resource expansion", "stated_reason": "Risk of memory exhaustion and interruption of other computation.", "resolved_by": "Smaller single auxiliary jobs with own-process memory guards." } ], "later_n12_publisher_clarification_not_retroactively_assumed_for_this_run": true, "score_zero_does_not_depend_on_resource_rule_adjudication": true }, "prompt_artifacts": [ { "kind": "original_goal_objective", "original_text_file": "n13-goal-objective.original.txt", "source": "Frozen get_goal objective; exact user goal text without a chat-log export.", "sha256": "dfc86a8ff759f6c54ceda6cdaaef5b6f5165b307b00b3bf0eedf1d57ec48fe74", "original_text_url": "reports/n13-codex-main-prompt.original.txt" } ], "limitations": [ "No complete radius minimal polynomial, irreducibility proof, rational isolating interval association or integrated final proof package.", "A failed numerical relation search does not prove a degree bound, algebraic impossibility or transcendence.", "Historical proof replay and checks were not re-executed during report preparation.", "No opening benchmark commit, opening hardware snapshot or monetary evidence; original model identity has now been checked from runtime metadata.", "No full OS-level resource-access audit. No formal ranking claim.", "Original result remains a failure; report preparation and official score execution after the deadline do not alter it." ], "deliverables": [ "n13-test-report.zh.md", "n13-test-record.json", "n13-score-output.json", "official-score.py", "n13-goal-objective.original.txt", "n13-task-prompt.snapshot.md", "n13-report-sources.json" ], "source_report": { "filename": "record-n13-codex-20261001.zh.md", "sha256": "cbe275e9c041407778c43ab968ada3a300af462d78da97d1429f46985ca6d677", "public_version": "published_report_with_web_links", "full_proof_archive_public": false, "original_local_report_sha256": "67d0074efb0b1028023a631ee146def6ecb8a5ab5a8a1f26f6b8e81352e3605f" }, "model_display_note": "原Goal阶段14条一致的运行元数据已核对为gpt-6-astra／max。", "model_display_note_en": "All 14 original-Goal runtime contexts consistently identify gpt-6-astra / max.", "report_urls": { "zh": "record-n13-codex-20261001.zh.html", "en": "record-n13-codex-20261001.html" }, "task_prompt_reference": { "kind": "n13_task_post_hoc_public_snapshot", "original_text_file": "n13-task-prompt.snapshot.md", "source_commit": "b6cde6540abcf4dfc54a77979e5a7517d3f971cb", "sha256": "40a8449594a695b1aabc1b21e894606fd7e70bb4191b252d02f44e09759e07c7", "not_certified_as_original_opening_version": true }, "publication": { "authorized_by_user": true, "original_score_unchanged": true, "mathematics_replayed_for_publication": false }, "published_artifacts": { "zh": "record-n13-codex-20261001.zh.html", "en": "record-n13-codex-20261001.html", "record": "record-n13-codex-20261001.json", "original_prompt": "reports/n13-codex-main-prompt.original.txt", "score_output": "https://github.com/pikaaa345/disk-covering-benchmark/blob/main/results/n13-score-output.json" }, "model_identity_status": "verified_from_original_thread_runtime_metadata", "original_report_cutoff_relative_seconds": 45029, "original_report_cutoff_relative": "T+12:30:29", "model_identity_verification": { "source": "original_thread_turn_context_runtime_metadata", "user_authorized_retrospective_review": true, "matching_contexts": 14, "all_contexts_consistent": true, "reporting_models_not_substituted": true, "private_transcript_published": false }, "report_revision": { "date": "2026-10-02", "format_reference": "record-n11-astra-20260930", "model_corrected": true, "previous_model_display": "codex/unknown", "timeline_reconstructed_from_original_thread": true, "math_restarted": false, "original_score_unchanged": true } } ] }