{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EUDJGJOJVLU6VLCA2ZFPZI4WOF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f11755aa3c5f9b40aa7b17c2844c346b4cf02e5c4a51adcd1ce5a6345af90bf3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-04T14:16:34Z","title_canon_sha256":"6eeaf6b7910ef61e47bb8d65d69f5579aaa632d5026b74924b7cc3114950d84c"},"schema_version":"1.0","source":{"id":"1304.1371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1371","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1371v1","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1371","created_at":"2026-05-18T03:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"EUDJGJOJVLU6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EUDJGJOJVLU6VLCA","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EUDJGJOJ","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:3c72a929d2102836c9913ae4ca1ac6c171426698ec9a02d9f1cfe87b49193f3a","target":"graph","created_at":"2026-05-18T03:28:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Combining the Batchelor theorem and the Serre-Swan theorem, we come to that, given a smooth manifold $X$, a graded commutative $C^\\infty(X)$-algebra $\\cA$ is isomorphic to the structure ring of a graded manifold with a body $X$ iff it is the exterior algebra of some projective $C^\\infty(X)$-module of finite rank. In particular, it follows that odd fields in field theory on a smooth manifold $X$ can be represented by graded functions on some graded manifold with body $X$.","authors_text":"G. Sardanashvily","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-04T14:16:34Z","title":"Remark on the Serre-Swan theorem for graded manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1371","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:87839576a8710947868ae542dc4d8f811918126afd024f6539931abea7a4351c","target":"record","created_at":"2026-05-18T03:28:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f11755aa3c5f9b40aa7b17c2844c346b4cf02e5c4a51adcd1ce5a6345af90bf3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-04-04T14:16:34Z","title_canon_sha256":"6eeaf6b7910ef61e47bb8d65d69f5579aaa632d5026b74924b7cc3114950d84c"},"schema_version":"1.0","source":{"id":"1304.1371","kind":"arxiv","version":1}},"canonical_sha256":"25069325c9aae9eaac40d64afca396715f8c213d547e27f6d697eb65ae518b7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25069325c9aae9eaac40d64afca396715f8c213d547e27f6d697eb65ae518b7f","first_computed_at":"2026-05-18T03:28:56.973093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:56.973093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8t+yzdEr/5DhqjDYtimPERuKwX4VxcVyUjnrq9OkOAuNZTXJcN63N+Jsc2jRixxnw40lV65roh1vqH/61z9CBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:56.973779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87839576a8710947868ae542dc4d8f811918126afd024f6539931abea7a4351c","sha256:3c72a929d2102836c9913ae4ca1ac6c171426698ec9a02d9f1cfe87b49193f3a"],"state_sha256":"c214fbc16446e14057d990f3269b0b60a63aececc4c54e48e7296e6f1e70cffb"}