{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FP6HD7DFZLUEXMD76D4RV6AUFG","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":"4692ce94a72a3dc41cca807df168ccb55f7944d5d6483302b99caf016ab4c48a","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-03-18T18:22:49Z","title_canon_sha256":"784689a2eb4f997bc6097491107deadc3db71c42ba23e8480f6a1e68adedd4c7"},"schema_version":"1.0","source":{"id":"0903.3215","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3215","created_at":"2026-05-18T04:26:33Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3215v3","created_at":"2026-05-18T04:26:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3215","created_at":"2026-05-18T04:26:33Z"},{"alias_kind":"pith_short_12","alias_value":"FP6HD7DFZLUE","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FP6HD7DFZLUEXMD7","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FP6HD7DF","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:72237d7388ef320e880b71a301a78e9890013481f30f9d89ce6713fa05bc1ba5","target":"graph","created_at":"2026-05-18T04:26:33Z","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":"We study the algebra of local functionals equipped with a Poisson bracket. We discuss the underlying algebraic structures related to a version of the Courant-Dorfman algebra. As a main illustration, we consider the functionals over the cotangent bundle of the superloop space over a smooth manifold. We present a number of examples of the Courant-like brackets arising from this analysis.","authors_text":"Joel Ekstrand, Maxim Zabzine","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-03-18T18:22:49Z","title":"Courant-like brackets and loop spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3215","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":"sha256:79a22981792b5b05b26e834a87f3f99b0ca4960f675707b60b3167dd5c898074","target":"record","created_at":"2026-05-18T04:26:33Z","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":"4692ce94a72a3dc41cca807df168ccb55f7944d5d6483302b99caf016ab4c48a","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-03-18T18:22:49Z","title_canon_sha256":"784689a2eb4f997bc6097491107deadc3db71c42ba23e8480f6a1e68adedd4c7"},"schema_version":"1.0","source":{"id":"0903.3215","kind":"arxiv","version":3}},"canonical_sha256":"2bfc71fc65cae84bb07ff0f91af814298a630606b5e6d90d5d286e586bee2d20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bfc71fc65cae84bb07ff0f91af814298a630606b5e6d90d5d286e586bee2d20","first_computed_at":"2026-05-18T04:26:33.444641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:33.444641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t+lOSXKKqebp3nj//KpxSeeyi3SnOJ75pUa2IPr3R3idGQk0VCyodX1s+9IAhPcNx9pAnhXhYWhTAxgOm5RQDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:33.445300Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3215","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79a22981792b5b05b26e834a87f3f99b0ca4960f675707b60b3167dd5c898074","sha256:72237d7388ef320e880b71a301a78e9890013481f30f9d89ce6713fa05bc1ba5"],"state_sha256":"d8a2bac145cc6728531b99f4ae58f05a669014b2c9ebdee8b0514b7f61237898"}