{"schema_version":"source-reader-v1","record":{"source_id":"cycle-double-cover-separate","versions":[{"work":{"authors":["Shiva Kintali"],"kind":"research_paper","publication":"preprint","publication_note":"Public manuscript or exposition; publication does not imply independent OpenMath review.","ai_role":"self_reported","ai_note":"Shiva Kintali reports work with Codex; this is a distinct manuscript and has not been adjudicated by OpenMath.","artifacts":[],"published":{"value":"2026-07-13"}},"id":"cycle-double-cover:source:separate:v2","source_id":"cycle-double-cover-separate","title":"Three-Bit Flows and Cycle Covers. Part I","owner":"Shiva Kintali","url":"https://arxiv.org/abs/2607.14140v1","subject_scope":"A separately authored manuscript reports a proof of cycle double cover using an AI-assisted workflow.","revision":"2026-07-13","content_sha256":null,"update_method":"Source comparison followed by a new immutable curation revision.","identifier_policy":"Stable source and entry identities; changed wording receives a new version.","observed_on":"2026-10-13","source_updated_on":"2026-07-13","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://arxiv.org/abs/2607.14140v1","attribution":"Shiva Kintali","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90}],"entries":[{"id":"cycle-double-cover:entry:separate:v2","source_version_id":"cycle-double-cover:source:separate:v2","item_id":"separate","url":"https://arxiv.org/abs/2607.14140v1","wording":"A separately authored manuscript reports a proof of cycle double cover using an AI-assisted workflow.","wording_kind":"paraphrase","locator":"Abstract and theorem statement","supersedes":"cycle-double-cover:entry:separate:v1"}],"problems":[{"slug":"cycle-double-cover","title":"Cycle double cover conjecture","publication_version":5}],"selected_version_id":"cycle-double-cover:source:separate:v2","available_versions":[{"id":"cycle-double-cover:source:separate:v2","revision":"2026-07-13","observed_on":"2026-10-13","title":"Three-Bit Flows and Cycle Covers. Part I","publication":"preprint","content_sha256":null,"used_in_current_publications":true},{"id":"cycle-double-cover:source:separate:v1","revision":"2026-07","observed_on":"2026-10-13","title":"An independent proof of the Cycle Double Cover Conjecture","publication":"preprint","content_sha256":null,"used_in_current_publications":false}],"usages":[{"id":"source-use-5ea2e6f4397b8e26dcf2","entry_id":"cycle-double-cover:entry:separate:v2","problem":{"slug":"cycle-double-cover","title":"Cycle double cover conjecture","publication_version":5},"kind":"activity","title":"Compare the statement and proof evidence","claim":null,"fragment":"activity","assessment":null,"superseded":false,"formalization":null,"update":{"id":"cycle-double-cover-assessment","title":"Compare the statement and proof evidence","kind":"research_direction","source_entry_ids":["cycle-double-cover:entry:proof:v1","cycle-double-cover:entry:lean:v1","cycle-double-cover:entry:separate:v2"],"summary":"The public theorem and manuscript can be examined alongside Kintali’s separately authored proposal.","limitation":"Independent mathematical review and a locally reproduced formal build remain pending.","related_claim_ids":["claim-cycle-double-cover-existence"]}},{"id":"source-use-1e6b085aca3b83fecc4a","entry_id":"cycle-double-cover:entry:separate:v2","problem":{"slug":"cycle-double-cover","title":"Cycle double cover conjecture","publication_version":5},"kind":"assessment","title":"Separately authored proof manuscript","claim":{"id":"claim-cycle-double-cover-existence","version":2,"slug":"cycle-double-cover-existence","title":"Every bridgeless graph has a cycle double cover"},"fragment":"claim-cycle-double-cover-existence","assessment":{"id":"cycle-double-cover:report:separate:v2","entry_id":"cycle-double-cover:entry:separate:v2","state":"proposed_solution","source_label":"Separately authored proof manuscript","scope":"The same universal cycle double cover question.","source_date":null,"observed_on":"2026-10-13","evidence_url":"https://arxiv.org/abs/2607.14140v1","supersedes":"cycle-double-cover:report:separate:v1"},"superseded":false,"formalization":null,"update":null},{"id":"source-use-b7ddc7d668612c120965","entry_id":"cycle-double-cover:entry:separate:v2","problem":{"slug":"cycle-double-cover","title":"Cycle double cover conjecture","publication_version":5},"kind":"formalization","title":"Lean: the full bridgeless multigraph statement","claim":{"id":"claim-cycle-double-cover-existence","version":2,"slug":"cycle-double-cover-existence","title":"Every bridgeless graph has a cycle double cover"},"fragment":"claim-cycle-double-cover-existence","assessment":null,"superseded":false,"formalization":{"title":"Lean: the full bridgeless multigraph statement","url":"https://github.com/openai/cdc-lean/blob/577e9d9ea326d520f80672ee69b830bf1d513df5/CDCLean/Main.lean","note":"The project reports an unconditional proof endpoint using only standard logical axioms. It is linked as source evidence while mathematical assessment of the new proof remains pending.","target":{"id":"claim-cycle-double-cover-existence","version":2},"proof_status":"reported_complete","source_entry_ids":["cycle-double-cover:entry:proof:v1","cycle-double-cover:entry:lean:v1","cycle-double-cover:entry:separate:v2"],"declaration":"CDCLean.cycleDoubleCover_of_bridgeless","source_commit":"577e9d9ea326d520f80672ee69b830bf1d513df5","alignment":"staff_linked","checked_on":"2026-10-13"},"update":null},{"id":"source-use-e6a4582841e4aafa09e1","entry_id":"cycle-double-cover:entry:separate:v2","problem":{"slug":"cycle-double-cover","title":"Cycle double cover conjecture","publication_version":5},"kind":"milestone","title":"A separately authored proof report","claim":null,"fragment":"history","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-8da50d00a432a35c0287","entry_id":"cycle-double-cover:entry:separate:v2","problem":{"slug":"cycle-double-cover","title":"Cycle double cover conjecture","publication_version":5},"kind":"proof","title":"Kintali proof account","claim":{"id":"claim-cycle-double-cover-existence","version":2,"slug":"cycle-double-cover-existence","title":"Every bridgeless graph has a cycle double cover"},"fragment":"claim-cycle-double-cover-existence","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-21df669659fe1328393c","entry_id":"cycle-double-cover:entry:separate:v2","problem":{"slug":"cycle-double-cover","title":"Cycle double cover conjecture","publication_version":5},"kind":"question","title":"Cycle double cover conjecture","claim":null,"fragment":"question","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-e53926d83ec940581763","entry_id":"cycle-double-cover:entry:separate:v2","problem":{"slug":"cycle-double-cover","title":"Cycle double cover conjecture","publication_version":5},"kind":"reading","title":"Read the mathematical argument; inspect its Claim for assessment and scope.","claim":null,"fragment":"provenance","assessment":null,"superseded":false,"formalization":null,"update":null},{"id":"source-use-9d26243052b258e00ecf","entry_id":"cycle-double-cover:entry:separate:v2","problem":{"slug":"cycle-double-cover","title":"Cycle double cover conjecture","publication_version":5},"kind":"statement","title":"Every bridgeless graph has a cycle double cover","claim":{"id":"claim-cycle-double-cover-existence","version":2,"slug":"cycle-double-cover-existence","title":"Every bridgeless graph has a cycle double cover"},"fragment":"claim-cycle-double-cover-existence","assessment":null,"superseded":false,"formalization":null,"update":null}],"linked_entries":[{"id":"cycle-double-cover:entry:lean:v1","source_version_id":"cycle-double-cover:source:lean:v1","item_id":"lean","url":"https://github.com/openai/cdc-lean/tree/577e9d9ea326d520f80672ee69b830bf1d513df5","wording":"The source endpoint covers finite loopless bridgeless multigraphs via a formalized eight-flow theorem and a conversion to cycle covers.","wording_kind":"paraphrase","locator":"CDCLean/Main.lean; README verification and exact endpoint","supersedes":null},{"id":"cycle-double-cover:entry:proof:v1","source_version_id":"cycle-double-cover:source:proof:v1","item_id":"proof","url":"https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_proof.pdf","wording":"A new argument is reported to construct a cycle double cover for every finite loopless bridgeless multigraph.","wording_kind":"paraphrase","locator":"Main theorem and flow-to-cover construction","supersedes":null},{"id":"cycle-double-cover:entry:separate:v2","source_version_id":"cycle-double-cover:source:separate:v2","item_id":"separate","url":"https://arxiv.org/abs/2607.14140v1","wording":"A separately authored manuscript reports a proof of cycle double cover using an AI-assisted workflow.","wording_kind":"paraphrase","locator":"Abstract and theorem statement","supersedes":"cycle-double-cover:entry:separate:v1"}],"linked_sources":[{"work":{"authors":["OpenAI","openai/cdc-lean project"],"kind":"research_project","publication":"project","publication_note":"Public formal source; build and independent mathematical review are separate checks.","ai_role":"self_reported","ai_note":"This formal source accompanies the OpenAI AI-assisted proof report; formal checking and human exposition are separate evidence roles.","artifacts":[{"kind":"formal_code","title":"Cycle double cover in Lean — pinned source","url":"https://github.com/openai/cdc-lean/tree/577e9d9ea326d520f80672ee69b830bf1d513df5","version":"577e9d9ea326d520f80672ee69b830bf1d513df5","assessment":"not_executed","note":"Public source inspected for statement and assumptions; this proof project has not been executed by OpenMath."}],"published":{"value":"2026-07-09"}},"id":"cycle-double-cover:source:lean:v1","source_id":"cycle-double-cover-lean","title":"Cycle double cover in Lean","owner":"OpenAI, openai/cdc-lean project","url":"https://github.com/openai/cdc-lean/tree/577e9d9ea326d520f80672ee69b830bf1d513df5","subject_scope":"The source endpoint covers finite loopless bridgeless multigraphs via a formalized eight-flow theorem and a conversion to cycle covers.","revision":"577e9d9ea326d520f80672ee69b830bf1d513df5","content_sha256":"ffe1a481bcfa67c49b25830a67cb338a6c7fdda3eb29e4dcffcd63e795f0c963","update_method":"Source comparison followed by a new immutable curation revision.","identifier_policy":"Stable source and entry identities; changed wording receives a new version.","observed_on":"2026-10-13","source_updated_on":"2026-07-09","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://github.com/openai/cdc-lean/tree/577e9d9ea326d520f80672ee69b830bf1d513df5","attribution":"OpenAI, openai/cdc-lean project","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90},{"work":{"authors":["OpenAI"],"kind":"research_paper","publication":"preprint","publication_note":"Public manuscript or exposition; publication does not imply independent OpenMath review.","ai_role":"self_reported","ai_note":"OpenAI reports a GPT-5.6 Sol Ultra multi-agent discovery workflow. This provenance is first-party and is not independent mathematical review.","artifacts":[],"published":{"value":"2026-07-10"}},"id":"cycle-double-cover:source:proof:v1","source_id":"cycle-double-cover-proof","title":"A proof of the cycle double cover conjecture","owner":"OpenAI","url":"https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_proof.pdf","subject_scope":"A new argument is reported to construct a cycle double cover for every finite loopless bridgeless multigraph.","revision":"2026-07-10","content_sha256":"b4797f5053d9067329b3dcfcbf913f8bb40d13467453b1300f6d78d08460fc13","update_method":"Source comparison followed by a new immutable curation revision.","identifier_policy":"Stable source and entry identities; changed wording receives a new version.","observed_on":"2026-10-13","source_updated_on":"2026-07-10","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98d31/cdc_proof.pdf","attribution":"OpenAI","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90},{"work":{"authors":["Shiva Kintali"],"kind":"research_paper","publication":"preprint","publication_note":"Public manuscript or exposition; publication does not imply independent OpenMath review.","ai_role":"self_reported","ai_note":"Shiva Kintali reports work with Codex; this is a distinct manuscript and has not been adjudicated by OpenMath.","artifacts":[],"published":{"value":"2026-07-13"}},"id":"cycle-double-cover:source:separate:v2","source_id":"cycle-double-cover-separate","title":"Three-Bit Flows and Cycle Covers. Part I","owner":"Shiva Kintali","url":"https://arxiv.org/abs/2607.14140v1","subject_scope":"A separately authored manuscript reports a proof of cycle double cover using an AI-assisted workflow.","revision":"2026-07-13","content_sha256":null,"update_method":"Source comparison followed by a new immutable curation revision.","identifier_policy":"Stable source and entry identities; changed wording receives a new version.","observed_on":"2026-10-13","source_updated_on":"2026-07-13","rights":"metadata-link","license":"Original document rights remain with its authors.","terms_url":"https://arxiv.org/abs/2607.14140v1","attribution":"Shiva Kintali","rights_note":"OpenMath supplies original paraphrases and links; no proof text is republished.","check_interval_days":90}]}}