{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IHPVFME2QGBZJER377OBM2KP4X","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":"bb4f6aab0ecc68c941452818815eb984f52d875dc55980fb60c60ba2982fadc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-12-26T13:53:22Z","title_canon_sha256":"1023309b17b380f01c7656e5b95508bf3911dfc5418671c53b57b8e0af902982"},"schema_version":"1.0","source":{"id":"1712.09268","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09268","created_at":"2026-07-05T00:24:34Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09268v3","created_at":"2026-07-05T00:24:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09268","created_at":"2026-07-05T00:24:34Z"},{"alias_kind":"pith_short_12","alias_value":"IHPVFME2QGBZ","created_at":"2026-07-05T00:24:34Z"},{"alias_kind":"pith_short_16","alias_value":"IHPVFME2QGBZJER3","created_at":"2026-07-05T00:24:34Z"},{"alias_kind":"pith_short_8","alias_value":"IHPVFME2","created_at":"2026-07-05T00:24:34Z"}],"graph_snapshots":[{"event_id":"sha256:ef5be8930fc48171ef44bbb71832bba71bf524c8b7cf901bfd656d2b12689da1","target":"graph","created_at":"2026-07-05T00:24:34Z","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/1712.09268/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new category of differential graded multi-oriented props whose representations (called homotopy algebras with branes) in a graded vector space require a choice of a collection of $k$ linear subspaces in that space, $k$ being the number of extra directions (if $k=0$ this structure recovers an ordinary prop); symplectic vector spaces equipped with $k$ Lagrangian subspaces play a distinguished role in this theory.\n  Manin triples is a classical example of an algebraic structure (concretely, a Lie bialgebra structure) given in terms of a vector space and its subspace; in the context","authors_text":"Sergei Merkulov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-12-26T13:53:22Z","title":"Multi-oriented props and homotopy algebras with branes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09268","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":"sha256:58319722b3e6fd21d5f7a2a8ac46066a2bdcef769a2e8bf953e09cca49ee0829","target":"record","created_at":"2026-07-05T00:24:34Z","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":"bb4f6aab0ecc68c941452818815eb984f52d875dc55980fb60c60ba2982fadc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-12-26T13:53:22Z","title_canon_sha256":"1023309b17b380f01c7656e5b95508bf3911dfc5418671c53b57b8e0af902982"},"schema_version":"1.0","source":{"id":"1712.09268","kind":"arxiv","version":3}},"canonical_sha256":"41df52b09a818394923bffdc16694fe5c522d8aa1fecc90afa4b3cdd7e024dbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41df52b09a818394923bffdc16694fe5c522d8aa1fecc90afa4b3cdd7e024dbf","first_computed_at":"2026-07-05T00:24:34.620646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:24:34.620646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IyYQAxe+rZJWnBeJRnEN828kLbKSrubWbq8vEbTKlIQq6TbEg6orJ4QBTEx3Er8p81neWpDj7ZPL+84K/tVAAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:24:34.621001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09268","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58319722b3e6fd21d5f7a2a8ac46066a2bdcef769a2e8bf953e09cca49ee0829","sha256:ef5be8930fc48171ef44bbb71832bba71bf524c8b7cf901bfd656d2b12689da1"],"state_sha256":"a5c086f2be52367567040246613a0d5b3c0a4a37b34b633bb1b2bbfe1df35018"}