{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CW7IEQO26EPOTDLXFRJSG6LGCI","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":"aa1a43623f017f59f36312abd5700b5a21e0b4ba0910ae6f69fd22c1ea70e1bc","cross_cats_sorted":["math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-15T16:30:26Z","title_canon_sha256":"d30617cc40f9ab47edbb194129759b77c3f008a97e622d7c37857c830cfb8897"},"schema_version":"1.0","source":{"id":"1010.3210","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3210","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3210v3","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3210","created_at":"2026-05-18T04:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"CW7IEQO26EPO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CW7IEQO26EPOTDLX","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CW7IEQO2","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:13728784b59d264f9f3b05f00dda3b548fe40012f97348e0d07ca1ef92d115a0","target":"graph","created_at":"2026-05-18T04:09:45Z","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":"Motivated by DeWitt's viewpoint of covariant field theory, we define a general notion of non-local classical observable that applies to many physical lagrangian systems (with bosonic and fermionic variables), by using methods that are now standard in algebraic geometry. We review the (standard) methods of local functional calculus, as they are presented by Beilinson and Drinfeld, and relate them to our construction. We partially explain the relation of these with the Vinogradov's secondary calculus. The methods present here are all necessary to understand mathematically properly and with simpl","authors_text":"Frederic Paugam","cross_cats":["math.AG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-15T16:30:26Z","title":"Histories and observables in covariant field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3210","kind":"arxiv","version":3},"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":"sha256:5d43d04d709e3fca96c4ab21e6d4f2255ff1e5cbbe141fcdcd6beb53a027d96d","target":"record","created_at":"2026-05-18T04:09:45Z","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":"aa1a43623f017f59f36312abd5700b5a21e0b4ba0910ae6f69fd22c1ea70e1bc","cross_cats_sorted":["math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-15T16:30:26Z","title_canon_sha256":"d30617cc40f9ab47edbb194129759b77c3f008a97e622d7c37857c830cfb8897"},"schema_version":"1.0","source":{"id":"1010.3210","kind":"arxiv","version":3}},"canonical_sha256":"15be8241daf11ee98d772c5323796612221a5ba7cc4302c37ab8609027994f6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15be8241daf11ee98d772c5323796612221a5ba7cc4302c37ab8609027994f6b","first_computed_at":"2026-05-18T04:09:45.857976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:45.857976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y6hP1i/gBVVqGEojO0KoOFgqfU76Z721E5bTwAb6a4cVUN085J+TnOuR5ONZz5rtiEi61IB5ljIZ7VrFXkY0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:45.858428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3210","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d43d04d709e3fca96c4ab21e6d4f2255ff1e5cbbe141fcdcd6beb53a027d96d","sha256:13728784b59d264f9f3b05f00dda3b548fe40012f97348e0d07ca1ef92d115a0"],"state_sha256":"cfe5427833e2005828c268ee9c65c5aa9d5afdb270819ddc8be50d0e7b913b32"}