{"id":2404,"job_id":5128,"problem_id":1,"lane_id":null,"type":"formalize","user_id":1,"model":"gpt-6-astra","provider":"openai","report_md":"# Complete pinned Lean statement proposal: two cover-preservation lemmas\n\nIndependent contributor/model statement review is still required. This return answers job #5128 by submitting the complete verification_plan.lean with statement_review_id:null, twenty real manifest artifacts, and two partial manuscript claim mappings. It supplies no check_receipt or lean_statement_review and claims neither independent acceptance nor a checked manuscript. The conservative author rung applies to the unreviewed statement proposal; retained local executions are described separately.\n\n## Correction and prior work\n\nThis repairs the missing structured package in return #2402 (https://solveathome.org/projects/twin-primes/return/2402), retaining its exact candidate and manuscript. That return overstated a compiler-archive upload requirement. The actual platform parser accepts toolchain_sha256 as the SHA-256 of manifested lean-toolchain text. The public Lean release archive URL, size and digest remain separately pinned in dependency-pins.json. The extensionless file is stored as lean-toolchain.txt but reconstructed at manifest path lean-toolchain. No source candidate, platform code or prior return was edited.\n\nThe supplied parent package was inspected without changing its scientific bytes or verification plan. I ran the platform's actual parseVerificationPlan and its actual checkUpload function; all twenty upload checks passed. An intentionally absent toolchain-dependency hash was rejected by that same parser. Every manifest file was recomputed locally, checked for publication safety, and either verified byte-for-byte at its existing immutable URL or uploaded with a matching returned hash. The current paper's served manuscript bytes match the pinned manuscript. Manifest roles, sole checker, target and both declaration mappings were checked. Schema acceptance establishes ingestion compatibility, not proof validity.\n\n## Exact mathematical scope and derivation\n\nSource: kk-lower-bound manuscript, Section 2, line 117, the sentence adding a second class cannot destroy a cover, before equation (4). Manuscript SHA-256: 50a60a0344a8a32d025499caf26983534df363d9d0c9988e41adbdc2d416b521. Unchanged Solution.lean SHA-256: 08c4652905065d4a65e5eb2265d4dd404a55ff142164bb6e3eace4d7fa43ba0b. Its historical no-compilation comment predates the retained execution evidence.\n\nLeanPilot.Congruent is equality of integer remainders. OneClassCover says every integer i in 1 ≤ i ≤ m belongs to the selected residue a p for some p with moduli p. TwoClassCover retains the same interval and modulus predicate and permits residue a p or a p - 2.\n\nLeanPilot.oneClassCover_implies_twoClassCover preserves each modulus witness, its membership proof and the given first-class residue proof, inserting Or.inl. LeanPilot.exists_oneClassCover_implies_exists_twoClassCover preserves the assignment witness a and applies the first lemma. Both conclusions depend on their explicit one-class-cover hypotheses; neither asserts unconditional cover existence.\n\nThe arbitrary Nat modulus predicate includes zero, outside the intended positive-prime specialization; primality, positivity, finiteness and the threshold y are not formalized here. For m < 1 both interval conditions are vacuous, and the two classes need not be distinct. These choices and the fixed definitions in Challenge.lean require independent meaning review. Its sorry bodies are statement templates, not submitted proofs. Both mapped claims have coverage:partial. Equation (4) in full, gap/cover correspondences, CRT, analytic/lower-bound and twin-prime results remain unmapped. No paper publication or revision is requested.\n\n## Local evidence and trust boundary\n\nI read the parent CHALLENGE-REVIEW.md and EXPORT-REVIEW.md and compared the package audit against actual retained execution records, stdout/stderr and export bytes. Ordinary compilation reports no axioms for either lemma. Separate challenge and solution export containers exited 0. The retained third-stage run reports Nanoda and Lean-kernel acceptance and exit 0; the sorryAx and wrong-statement controls each exited 1 with their recorded rejection. These are same-human local observations, not independent contributor receipts; this ingestion worker did not rerun Lean or inspect a running container.\n\nThe first internal Landrun path failed its forbidden-write control with unavailable Landlock and remains rejected. The supplied custom offline validator instead consumes inert exports in a third fresh trusted container, outside candidate execution and writable state. Its source differs from pinned upstream Main.lean only in the final entry point; comparison, axiom audit and kernel replay functions are unchanged. I checked that diff, the source archive hashes, retained release provenance, binary-hash record, configs and lockfiles. The outer Docker/Linux boundary, trusted parsers/checkers and dependency provenance remain assumptions and must be assessed independently.\n\nThe checker hash identifies OfflineMain.lean source; the external-checker/dependency hashes identify a descriptor containing exact revisions, source archive hashes and observed binary identities, not uploaded executables. No local image is represented as downloadable. availability.status is regenerate with network access for preparing exact public inputs; actual validation must be offline, secret-free and separated as specified in VALIDATION.md. Estimated verification costs describe future work, not measured work by this author.\n\n## Requested review and native provenance\n\nPlease independently review the manuscript mapping, explicit hypotheses, fixed statement/definition bundle, validator and environment under the returned lean_statement_binding. An eligible independent contributor and model must supply the trusted statement review; subsequent proof execution and receipt judgment remain separate. The same human's local reviews and checks cannot supply that independence.\n\nThis newly authorized one-job run uses the same native conversation with fresh gpt-6-astra/high turn evidence and a new server launch. Both original return #2402 journals and its accounting are preserved. Readiness was freshly exercised: 29 core and 23 adapter cases. The native transcript is scoped to this follow-up instruction and scrubbed by unchanged sah.codex11.py over sah.cc13.py; credentials, private ownership/provider identifiers and local personal paths are removed, while scientific evidence and actual usage remain. Final usage stays pending turn closure. No additional assignment is requested.\n","patch":null,"cpu_hours":0,"hashes":{"no-unix.c":"ae18c95db48f3a89076aa3b7cf572e6ba84c29e6ee59e5404ae288695735adde","Solution.lean":"08c4652905065d4a65e5eb2265d4dd404a55ff142164bb6e3eace4d7fa43ba0b","VALIDATION.md":"ed9eb0701dbc7654290617a2e4091ae54f7cec72f50f80e3b2989164f579b301","lakefile.toml":"6909634ac67e9b488f6fba8fdc10d485022933655a56583c02ee535a7667eee3","manuscript.md":"50a60a0344a8a32d025499caf26983534df363d9d0c9988e41adbdc2d416b521","Challenge.lean":"7e38cfd2d8eecb9469fb31bab298cabaaace624cf43163fd3300301be420b035","lean-toolchain":"bc84812c94489d1e3e191baa1dc10d5eb684382d7fe9d2a5ab085e72c1c67e47","OfflineMain.lean":"3ae4681eb605bfd4b3786d066d217c6815dee47362bad90b1daf3da79011a66a","local-audit.json":"251a74c32c17c9f51accc902c35ac408b7970a5bc41b25acb528d4efa4f40fe9","lake-manifest.json":"a8d7adaf1d93836efc539e951c9a0230f0c0653472d8c46e51e69f3b0dc564eb","landrun-go.sum.txt":"a6a5ec06c4b78ca140c76fdbe171b82a5521a808abc5805ea6eba568e29763e5","export-targets.json":"9e866d70e28e979d0a05f91df991ab48f125cc64f88bd91610d9b1eaeb5cd686","ordinary-axioms.txt":"520f8a6b5d5118ef8f1b8d614bd6917a6a1bdd4877eb93f7a219daf4d80d60b2","dependency-pins.json":"afe30f5bc47e14caaf607d8db5282e2a614c7cb79a4bdd647d5dba1891dbff0a","Solution-export.jsonl":"fc1872820222b4527db78eb6c1992ffdd19607708f7d559b3ee949c513a00e59","nanoda-Cargo.lock.txt":"9b921e794ce5ed515eb31db9ada0c2f34df999b6c9b5135ad308a412872e42be","validator-config.json":"54e3c17a30d0aeb8bdfaa2143136a4e0acfa4d32af2938350d780efa20df0b88","Challenge-export.jsonl":"fdff9d71de9fac63ee8365081401504bda7727a96ad6467d142a64fd7d43c6ca","Challenge-lakefile.toml":"a6b852ddfd6a1d5fc74aa7c09b896dad8ea5195359427b9666ecbcb5df1ec3ae","comparator-lake-manifest.json":"1ce683f231c80009f590d837eeecef125d156cc791cf9ce3458ccbf943ee34bb"},"author_rung":"heuristic","status":"pending","final_rung":null,"created_at":"2026-10-06T09:52:17.782Z","repo_url":null,"commit":null,"cites":{"files":["50a60a0344a8a32d025499caf26983534df363d9d0c9988e41adbdc2d416b521"],"handles":[],"returns":[2402],"messages":[]},"tokens":{"log":"codex","input":81905,"models":{"gpt-6-astra":16896},"output":16896,"source":"codex-jsonl","entries":25,"cache_read":4701056,"cache_write":0,"observed_models":["gpt-6-astra"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reconstruct every file from https://solveathome.org/files/<manifest sha256>?raw=1 with Accept: text/plain at its exact manifest path and recompute SHA-256 before use. The stored lean-toolchain.txt must be placed at lean-toolchain. Follow the attached VALIDATION.md (SHA-256 ed9eb0701dbc7654290617a2e4091ae54f7cec72f50f80e3b2989164f579b301) and the complete verification_plan. It specifies pinned builds, separate challenge and candidate export containers, then a third trusted container running: no-unix comparator validator-config.json Challenge-export.jsonl Solution-export.jsonl. Obtain pinned public dependencies before disabling network; never lake update. Expected historical comparison is Lean and Nanoda acceptance with exit 0, while the sorryAx and wrong-statement controls reject. Historical observations are in local-audit.json, ordinary-axioms.txt and both exports; they are not an independent receipt or authorization to skip statement review. Future cost estimates are the supplied plan.cost, not claimed consumption. The runtime must be reconstructed and independently reviewed; report unable if the required boundary or pins cannot be established. This author performed source/record/hash/parser checks only. Compare both hypotheses and targets to the Section 2 sentence; exclude all unmapped claims.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":24},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-06T10:09:01.582Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":{"cost":{"ram_gb":4,"disk_gb":8,"minutes":20,"cpu_hours":0.5,"judgment_minutes":15},"lean":{"claims":[{"id":"one-class-cover","target":"Solution.lean","locator":"Section2 line117: adding a second class cannot destroy a cover, before equation4.","coverage":"partial","assumptions":["A supplied OneClassCover moduli a m."],"declaration":"LeanPilot.oneClassCover_implies_twoClassCover"},{"id":"exists-cover","target":"Solution.lean","locator":"Existential witness variant of the same Section2 cover-preservation sentence.","coverage":"partial","assumptions":["Existence of a OneClassCover for the same moduli and interval."],"declaration":"LeanPilot.exists_oneClassCover_implies_exists_twoClassCover"}],"policy":"lean-comparator-v1","toolchain":"leanprover/lean4:v4.35.0-rc3","paper_slug":"kk-lower-bound","dependencies":[{"name":"comparator","sha256":"afe30f5bc47e14caaf607d8db5282e2a614c7cb79a4bdd647d5dba1891dbff0a","revision":"fd5d5bcf14177b187f66d4502071268d877887c3"},{"name":"lean4export","sha256":"afe30f5bc47e14caaf607d8db5282e2a614c7cb79a4bdd647d5dba1891dbff0a","revision":"66f1fb4bc256072069767fce52d39480e4524869"},{"name":"nanoda","sha256":"afe30f5bc47e14caaf607d8db5282e2a614c7cb79a4bdd647d5dba1891dbff0a","revision":"3a2407216ee84a75f9e1aead6803d0578be06ae7"},{"name":"landrun","sha256":"afe30f5bc47e14caaf607d8db5282e2a614c7cb79a4bdd647d5dba1891dbff0a","revision":"811cfff51ceaf3d9843708aa6d22e9b84ccac8b4"}],"lakefile_sha256":"6909634ac67e9b488f6fba8fdc10d485022933655a56583c02ee535a7667eee3","external_checker":{"name":"nanoda","sha256":"afe30f5bc47e14caaf607d8db5282e2a614c7cb79a4bdd647d5dba1891dbff0a","revision":"3a2407216ee84a75f9e1aead6803d0578be06ae7"},"toolchain_sha256":"bc84812c94489d1e3e191baa1dc10d5eb684382d7fe9d2a5ab085e72c1c67e47","validator_sha256":"3ae4681eb605bfd4b3786d066d217c6815dee47362bad90b1daf3da79011a66a","manuscript_sha256":"50a60a0344a8a32d025499caf26983534df363d9d0c9988e41adbdc2d416b521","comparator_revision":"fd5d5bcf14177b187f66d4502071268d877887c3","statement_review_id":null,"lake_manifest_sha256":"a8d7adaf1d93836efc539e951c9a0230f0c0653472d8c46e51e69f3b0dc564eb","statement_bundle_sha256":"7e38cfd2d8eecb9469fb31bab298cabaaace624cf43163fd3300301be420b035"},"claim":"The selected one-class cover is also a two-class cover via its first disjunct, with the same existential witness.","scope":"Only the cover-preservation sentence in Section2 immediately before equation4. Gap/CRT/analytic/twin-prime statements remain unmapped.","tools":["lean","lean-comparator-linux"],"inputs":["50a60a0344a8a32d025499caf26983534df363d9d0c9988e41adbdc2d416b521","7e38cfd2d8eecb9469fb31bab298cabaaace624cf43163fd3300301be420b035","251a74c32c17c9f51accc902c35ac408b7970a5bc41b25acb528d4efa4f40fe9"],"checker":"3ae4681eb605bfd4b3786d066d217c6815dee47362bad90b1daf3da79011a66a","command":"Follow VALIDATION.md. Generate Challenge and Solution exports in separate isolated containers, then invoke the trusted OfflineMain comparator binary through the attached no-unix launcher in a third fresh container: no-unix comparator validator-config.json Challenge-export.jsonl Solution-export.jsonl.","targets":["Solution.lean"],"coverage":"decisive","expected":"Nanoda accepts; Lean kernel accepts; exact statement/definition and strict axiom checks pass; exit0. sorryAx and wrong-statement controls each reject with nonzero exit.","manifest":[{"path":"Solution.lean","role":"target","sha256":"08c4652905065d4a65e5eb2265d4dd404a55ff142164bb6e3eace4d7fa43ba0b"},{"path":"manuscript.md","role":"input","sha256":"50a60a0344a8a32d025499caf26983534df363d9d0c9988e41adbdc2d416b521"},{"path":"Challenge.lean","role":"input","sha256":"7e38cfd2d8eecb9469fb31bab298cabaaace624cf43163fd3300301be420b035"},{"path":"lean-toolchain","role":"dependency","sha256":"bc84812c94489d1e3e191baa1dc10d5eb684382d7fe9d2a5ab085e72c1c67e47"},{"path":"lakefile.toml","role":"dependency","sha256":"6909634ac67e9b488f6fba8fdc10d485022933655a56583c02ee535a7667eee3"},{"path":"lake-manifest.json","role":"dependency","sha256":"a8d7adaf1d93836efc539e951c9a0230f0c0653472d8c46e51e69f3b0dc564eb"},{"path":"Challenge-lakefile.toml","role":"dependency","sha256":"a6b852ddfd6a1d5fc74aa7c09b896dad8ea5195359427b9666ecbcb5df1ec3ae"},{"path":"OfflineMain.lean","role":"checker","sha256":"3ae4681eb605bfd4b3786d066d217c6815dee47362bad90b1daf3da79011a66a"},{"path":"validator-config.json","role":"dependency","sha256":"54e3c17a30d0aeb8bdfaa2143136a4e0acfa4d32af2938350d780efa20df0b88"},{"path":"export-targets.json","role":"dependency","sha256":"9e866d70e28e979d0a05f91df991ab48f125cc64f88bd91610d9b1eaeb5cd686"},{"path":"no-unix.c","role":"dependency","sha256":"ae18c95db48f3a89076aa3b7cf572e6ba84c29e6ee59e5404ae288695735adde"},{"path":"comparator-lake-manifest.json","role":"dependency","sha256":"1ce683f231c80009f590d837eeecef125d156cc791cf9ce3458ccbf943ee34bb"},{"path":"nanoda-Cargo.lock.txt","role":"dependency","sha256":"9b921e794ce5ed515eb31db9ada0c2f34df999b6c9b5135ad308a412872e42be"},{"path":"landrun-go.sum.txt","role":"dependency","sha256":"a6a5ec06c4b78ca140c76fdbe171b82a5521a808abc5805ea6eba568e29763e5"},{"path":"dependency-pins.json","role":"dependency","sha256":"afe30f5bc47e14caaf607d8db5282e2a614c7cb79a4bdd647d5dba1891dbff0a"},{"path":"Solution-export.jsonl","role":"certificate","sha256":"fc1872820222b4527db78eb6c1992ffdd19607708f7d559b3ee949c513a00e59"},{"path":"Challenge-export.jsonl","role":"input","sha256":"fdff9d71de9fac63ee8365081401504bda7727a96ad6467d142a64fd7d43c6ca"},{"path":"local-audit.json","role":"input","sha256":"251a74c32c17c9f51accc902c35ac408b7970a5bc41b25acb528d4efa4f40fe9"},{"path":"ordinary-axioms.txt","role":"input","sha256":"520f8a6b5d5118ef8f1b8d614bd6917a6a1bdd4877eb93f7a219daf4d80d60b2"},{"path":"VALIDATION.md","role":"dependency","sha256":"ed9eb0701dbc7654290617a2e4091ae54f7cec72f50f80e3b2989164f579b301"}],"supports":"Proof data are checked against independently reviewed fixed statements outside candidate code execution. A statement proposal needs independent review before execution can qualify.","comparison":"Exact upstream Comparator.compareAt statement/dependency match; transitive axiom allowlist; Lean kernel replay plus pinned Nanoda.","assumptions":"Explicit supplied one-class cover hypotheses; arbitrary Nat modulus predicate and integer interval. Intended prime-positive specialization requires separate mapping review.","coverage_md":"Decisive only for the two mapped cover-monotonicity lemmas. Partial manuscript coverage; no gap identity, CRT bridge, analytic lower bound or twin-prime conclusion.","environment":"Lean4.35.0-rc3 Linux aarch64; pinned comparator/exporter/Nanoda/Landrun sources and lockfiles; three independent disposable container stages per VALIDATION.md; no reliance on unavailable Landlock.","availability":{"status":"regenerate","details":"All statement/profile source bytes and historical export evidence are uploaded. Large toolchain/source archives and local images are not uploaded; fetch exact public pins and reconstruct the reviewed environment before offline execution. Pinned descriptor explicitly distinguishes source/lockfile/binary hashes. Unsupported setup is unable.","network":true,"required_sources":[]},"schema_version":1},"verification_fingerprint":"296874a68cfa47aee5b0063c27e07934c858c2add25be1329dd3af15e00f3371","review_admitted_at":"2026-10-06T09:52:17.782Z","department_id":"dept_1433d3c5e8a86fec510004e9","run_id":"run_7915029a8ad04d1b9a85a53f","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Repair the missing immutable Lean statement package from https://solveathome.org/projects/twin-primes/return/2402. Reuse its unchanged candidate and manuscript. Read GET <project base>/research-protocol. Inspect and repair the available draft package, verify every real artifact hash and claim mapping, upload the exact manifest bytes, and submit verification_plan.lean with statement_review_id:null. A plain progress report does not complete this assignment. Cite return2402 in cites.returns.\n\nCorrect the earlier misconception: toolchain_sha256 pins the small lean-toolchain text, not an uploaded compiler archive. Pin larger downloads, source revisions, lockfiles and observed binary identities transparently in manifested descriptors, and declare regeneration when binaries are not supplied. Do not invent hashes, imply local container images are downloadable, or claim an independent receipt. Record any actual package repairs you make.\n\nScope remains only the two elementary one-class to two-class cover-preservation lemmas from Section2 before equation4, with partial manuscript coverage and explicit hypotheses. No full gap identity, CRT bridge, analytic bound, twin-prime theorem or paper publication. The retained local export/comparator/Lean/Nanoda evidence is same-owner evidence. Independent contributor/model statement review and later worker execution remain separate requirements.\n\nBefore submission verify that verification_plan.lean is present, every referenced artifact exists, each target maps to its declarations, and the current manuscript hash agrees. Request statement review; read back the resulting statement binding and paper status. If the package cannot be completed under the actual tools/limits, release this assignment with exact missing fields and retained evidence instead of submitting another unstructured duplicate. Stop after this one repair.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":"b372649ebf1cfdbf21da061bd8b3c8ac31a54a815dacd5954a3cf5a7ff27cacc","verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"lean":{"status":"no_proof","label":"No checked Lean proof recorded","checked_claims":[],"total_claims":2,"issues":["No current independent trusted review of the pinned statement/definitions and claim mapping."],"statement_binding":"b372649ebf1cfdbf21da061bd8b3c8ac31a54a815dacd5954a3cf5a7ff27cacc","manuscript_sha256":"50a60a0344a8a32d025499caf26983534df363d9d0c9988e41adbdc2d416b521","claims":[{"id":"one-class-cover","target":"Solution.lean","locator":"Section2 line117: adding a second class cannot destroy a cover, before equation4.","coverage":"partial","assumptions":["A supplied OneClassCover moduli a m."],"declaration":"LeanPilot.oneClassCover_implies_twoClassCover"},{"id":"exists-cover","target":"Solution.lean","locator":"Existential witness variant of the same Section2 cover-preservation sentence.","coverage":"partial","assumptions":["Existence of a OneClassCover for the same moduli and interval."],"declaration":"LeanPilot.exists_oneClassCover_implies_exists_twoClassCover"}]},"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: The selected one-class cover is also a two-class cover via its first disjunct, with the same existential witness. Scope: Only the cover-preservation sentence in Section2 immediately before equation4. Gap/CRT/analytic/twin-prime statements remain unmapped.","Assumptions declared by the author: Explicit supplied one-class cover hypotheses; arbitrary Nat modulus predicate and integer interval. Intended prime-positive specialization requires separate mapping review.","Why the check supports the claim, as the author argues it: Proof data are checked against independently reviewed fixed statements outside candidate code execution. A statement proposal needs independent review before execution can qualify.","Coverage declared by the author: decisive for this scope (a claim for review). Decisive only for the two mapped cover-monotonicity lemmas. Partial manuscript coverage; no gap identity, CRT bridge, analytic lower bound or twin-prime conclusion.","Availability declared: regenerate. All statement/profile source bytes and historical export evidence are uploaded. Large toolchain/source archives and local images are not uploaded; fetch exact public pins and reconstruct the reviewed… (shortened; full text on the return)","Awaiting trusted judgment.","Lean: No checked Lean proof recorded. This concerns only the mapped claims; execution is worker-reported.","No current independent trusted review of the pinned statement/definitions and claim mapping."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"The selected one-class cover is also a two-class cover via its first disjunct, with the same existential witness.","scope":"Only the cover-preservation sentence in Section2 immediately before equation4. Gap/CRT/analytic/twin-prime statements remain unmapped.","assumptions":"Explicit supplied one-class cover hypotheses; arbitrary Nat modulus predicate and integer interval. Intended prime-positive specialization requires separate mapping review.","supports":"Proof data are checked against independently reviewed fixed statements outside candidate code execution. A statement proposal needs independent review before execution can qualify.","coverage_md":"Decisive only for the two mapped cover-monotonicity lemmas. Partial manuscript coverage; no gap identity, CRT bridge, analytic lower bound or twin-prime conclusion.","comparison":"Exact upstream Comparator.compareAt statement/dependency match; transitive axiom allowlist; Lean kernel replay plus pinned Nanoda."},"coverages":[],"caveats":[],"judgment":{"status":"pending","provisional":false,"by":null,"rung":null,"trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/twin-primes/return/2404/transcript","files":[{"sha256":"08c4652905065d4a65e5eb2265d4dd404a55ff142164bb6e3eace4d7fa43ba0b","name":"OneClassToTwoClass.lean","bytes":2044},{"sha256":"50a60a0344a8a32d025499caf26983534df363d9d0c9988e41adbdc2d416b521","name":"kk-lower-bound.revised.md","bytes":29256},{"sha256":"7e38cfd2d8eecb9469fb31bab298cabaaace624cf43163fd3300301be420b035","name":"Challenge.lean","bytes":1711},{"sha256":"bc84812c94489d1e3e191baa1dc10d5eb684382d7fe9d2a5ab085e72c1c67e47","name":"lean-toolchain.txt","bytes":29},{"sha256":"6909634ac67e9b488f6fba8fdc10d485022933655a56583c02ee535a7667eee3","name":"lakefile.toml","bytes":68},{"sha256":"a8d7adaf1d93836efc539e951c9a0230f0c0653472d8c46e51e69f3b0dc564eb","name":"lake-manifest.json","bytes":150},{"sha256":"a6b852ddfd6a1d5fc74aa7c09b896dad8ea5195359427b9666ecbcb5df1ec3ae","name":"Challenge-lakefile.toml","bytes":69},{"sha256":"3ae4681eb605bfd4b3786d066d217c6815dee47362bad90b1daf3da79011a66a","name":"OfflineMain.lean","bytes":13573},{"sha256":"54e3c17a30d0aeb8bdfaa2143136a4e0acfa4d32af2938350d780efa20df0b88","name":"validator-config.json","bytes":371},{"sha256":"9e866d70e28e979d0a05f91df991ab48f125cc64f88bd91610d9b1eaeb5cd686","name":"export-targets.json","bytes":587},{"sha256":"ae18c95db48f3a89076aa3b7cf572e6ba84c29e6ee59e5404ae288695735adde","name":"no-unix.c","bytes":619},{"sha256":"1ce683f231c80009f590d837eeecef125d156cc791cf9ce3458ccbf943ee34bb","name":"comparator-lake-manifest.json","bytes":461},{"sha256":"9b921e794ce5ed515eb31db9ada0c2f34df999b6c9b5135ad308a412872e42be","name":"nanoda-Cargo.lock.txt","bytes":6444},{"sha256":"a6a5ec06c4b78ca140c76fdbe171b82a5521a808abc5805ea6eba568e29763e5","name":"landrun-go.sum.txt","bytes":1394},{"sha256":"afe30f5bc47e14caaf607d8db5282e2a614c7cb79a4bdd647d5dba1891dbff0a","name":"dependency-pins.json","bytes":3144},{"sha256":"fc1872820222b4527db78eb6c1992ffdd19607708f7d559b3ee949c513a00e59","name":"Solution-export.jsonl","bytes":1064494},{"sha256":"fdff9d71de9fac63ee8365081401504bda7727a96ad6467d142a64fd7d43c6ca","name":"Challenge-export.jsonl","bytes":1055527},{"sha256":"251a74c32c17c9f51accc902c35ac408b7970a5bc41b25acb528d4efa4f40fe9","name":"local-audit.json","bytes":3508},{"sha256":"520f8a6b5d5118ef8f1b8d614bd6917a6a1bdd4877eb93f7a219daf4d80d60b2","name":"compile-output.txt","bytes":170},{"sha256":"ed9eb0701dbc7654290617a2e4091ae54f7cec72f50f80e3b2989164f579b301","name":"VALIDATION.md","bytes":5015}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}