{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:ALFU6MU2UPGNR5S2VPVRGHC4QC","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":"d05febd215db319e8c56c0f14dcd8bd6356afd4ba41415411c99ab94f817b25e","cross_cats_sorted":["hep-th","math.RA"],"license":"","primary_cat":"math.QA","submitted_at":"2005-01-29T17:54:40Z","title_canon_sha256":"984cb301d316ef19be3c7068a1059ed746de2021604e71de4f182823c81fe37f"},"schema_version":"1.0","source":{"id":"math/0501540","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501540","created_at":"2026-07-04T15:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501540v3","created_at":"2026-07-04T15:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501540","created_at":"2026-07-04T15:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"ALFU6MU2UPGN","created_at":"2026-07-04T15:07:07Z"},{"alias_kind":"pith_short_16","alias_value":"ALFU6MU2UPGNR5S2","created_at":"2026-07-04T15:07:07Z"},{"alias_kind":"pith_short_8","alias_value":"ALFU6MU2","created_at":"2026-07-04T15:07:07Z"}],"graph_snapshots":[{"event_id":"sha256:ba84f59d494b12d9e3e321a82d3843a7a5a4e3286bcf4ef25cc403574dc508f6","target":"graph","created_at":"2026-07-04T15:07:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0501540/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a relative version of Kontsevich's formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich's theorem if C=M. It states that the DGLA of multivector fields on an infinitesimal neighbourhood of C is L-infinity-quasiisomorphic to the DGLA of multidifferential operators acting on sections of the exterior algebra of the conormal bundle. Applications to the deformation quantisation of coisotropic submanifolds are given. The proof uses a duality transformation to reduce the theorem to a version of Kontsevich's theorem for supermanifolds, which we a","authors_text":"Alberto S. Cattaneo (University of Zurich), Giovanni Felder (ETH Zurich)","cross_cats":["hep-th","math.RA"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2005-01-29T17:54:40Z","title":"Relative formality theorem and quantisation of coisotropic submanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501540","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:c851e3f197a90f345b904ef051543025f7deafc29673fa9ac50fa9f88b95ace6","target":"record","created_at":"2026-07-04T15:07:07Z","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":"d05febd215db319e8c56c0f14dcd8bd6356afd4ba41415411c99ab94f817b25e","cross_cats_sorted":["hep-th","math.RA"],"license":"","primary_cat":"math.QA","submitted_at":"2005-01-29T17:54:40Z","title_canon_sha256":"984cb301d316ef19be3c7068a1059ed746de2021604e71de4f182823c81fe37f"},"schema_version":"1.0","source":{"id":"math/0501540","kind":"arxiv","version":3}},"canonical_sha256":"02cb4f329aa3ccd8f65aabeb131c5c808b2445903b190870d92b2ef75ace26a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02cb4f329aa3ccd8f65aabeb131c5c808b2445903b190870d92b2ef75ace26a0","first_computed_at":"2026-07-04T15:07:07.410624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:07:07.410624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"41fkHxLs4vmBLtPasUWWArJrbHHbt4wTrMuCvaRUQgEQAA/2kPF2M5PRyB+xdkmGYUTHumOewfS3aScI3lMxAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:07:07.411026Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501540","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c851e3f197a90f345b904ef051543025f7deafc29673fa9ac50fa9f88b95ace6","sha256:ba84f59d494b12d9e3e321a82d3843a7a5a4e3286bcf4ef25cc403574dc508f6"],"state_sha256":"0e68a41b470d2ce3957276543fc08db62bd2eecc99d1840e9ef72aaaffc3de2f"}