{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:NJ3QDMKNJLZUWPJATD7UDWXBTN","short_pith_number":"pith:NJ3QDMKN","canonical_record":{"source":{"id":"2410.24064","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-10-31T16:00:01Z","cross_cats_sorted":["math.AT","math.GT"],"title_canon_sha256":"409c7981b5c946aa5430d00b513d17755dec2d8c17dc6b478d2f355ecac897c2","abstract_canon_sha256":"d1f05b3226811330722d303bad6e7cc86ecbde09d71c4ea0b6e1127028faba61"},"schema_version":"1.0"},"canonical_sha256":"6a7701b14d4af34b3d2098ff41dae19b4d9fd39b05cd294440ef103dc9092193","source":{"kind":"arxiv","id":"2410.24064","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.24064","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"2410.24064v3","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.24064","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"NJ3QDMKNJLZU","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"pith_short_16","alias_value":"NJ3QDMKNJLZUWPJA","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"pith_short_8","alias_value":"NJ3QDMKN","created_at":"2026-07-05T11:20:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:NJ3QDMKNJLZUWPJATD7UDWXBTN","target":"record","payload":{"canonical_record":{"source":{"id":"2410.24064","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-10-31T16:00:01Z","cross_cats_sorted":["math.AT","math.GT"],"title_canon_sha256":"409c7981b5c946aa5430d00b513d17755dec2d8c17dc6b478d2f355ecac897c2","abstract_canon_sha256":"d1f05b3226811330722d303bad6e7cc86ecbde09d71c4ea0b6e1127028faba61"},"schema_version":"1.0"},"canonical_sha256":"6a7701b14d4af34b3d2098ff41dae19b4d9fd39b05cd294440ef103dc9092193","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:20:47.727719Z","signature_b64":"TWGdfnanbxEGQByELlERspnJBffRrdHrZIL9F7/YlGrQ8WI4Qj7WEIdFyvfZHTe3tKd250G+I7eRJgwcoQ1ZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a7701b14d4af34b3d2098ff41dae19b4d9fd39b05cd294440ef103dc9092193","last_reissued_at":"2026-07-05T11:20:47.727210Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:20:47.727210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.24064","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VJt+Ng8L6/QtFeNTFfbf1QfJ9oqV4DynON558lXNUitHMXWuL/wyr844TURTLfqgXE9uU6lKIoBWv3zexotiAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:09:02.605372Z"},"content_sha256":"ddd58bd1a3965f94c6aa4f768c36c554b04ded3f83eebe894a12e762cedba18c","schema_version":"1.0","event_id":"sha256:ddd58bd1a3965f94c6aa4f768c36c554b04ded3f83eebe894a12e762cedba18c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:NJ3QDMKNJLZUWPJATD7UDWXBTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular vector fields in non-commutative geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GT"],"primary_cat":"math.QA","authors_text":"Toyo Taniguchi","submitted_at":"2024-10-31T16:00:01Z","abstract_excerpt":"We construct a non-commutative analogue of the modular vector field on a Poisson manifold for a given pair of a double bracket and a connection on a space of 1-forms. The key ingredient, the triple divergence map, is directly constructed from a connection on a linear category to deal with multiple base points. As an application, we give an algebraic description of the framed, groupoid version of Turaev's loop operation $\\mu$ similar to the one obtained by Alekseev-Kawazumi-Kuno-Naef and the author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.24064","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.24064/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:20:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FiimjlceAOJc1ujwyK4Ej+kTgLsBCtcQqA/3YQlt5iRK9k8XOTszY4SO57cOBxHoCApbl9cMFm1ELvTXfKwoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:09:02.606251Z"},"content_sha256":"a990a7523fcf6cf58f79943026235cbc23ffa337ac8deb4d0763dc0a4179f83f","schema_version":"1.0","event_id":"sha256:a990a7523fcf6cf58f79943026235cbc23ffa337ac8deb4d0763dc0a4179f83f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJ3QDMKNJLZUWPJATD7UDWXBTN/bundle.json","state_url":"https://pith.science/pith/NJ3QDMKNJLZUWPJATD7UDWXBTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJ3QDMKNJLZUWPJATD7UDWXBTN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T12:09:02Z","links":{"resolver":"https://pith.science/pith/NJ3QDMKNJLZUWPJATD7UDWXBTN","bundle":"https://pith.science/pith/NJ3QDMKNJLZUWPJATD7UDWXBTN/bundle.json","state":"https://pith.science/pith/NJ3QDMKNJLZUWPJATD7UDWXBTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJ3QDMKNJLZUWPJATD7UDWXBTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NJ3QDMKNJLZUWPJATD7UDWXBTN","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":"d1f05b3226811330722d303bad6e7cc86ecbde09d71c4ea0b6e1127028faba61","cross_cats_sorted":["math.AT","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-10-31T16:00:01Z","title_canon_sha256":"409c7981b5c946aa5430d00b513d17755dec2d8c17dc6b478d2f355ecac897c2"},"schema_version":"1.0","source":{"id":"2410.24064","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.24064","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"arxiv_version","alias_value":"2410.24064v3","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.24064","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"pith_short_12","alias_value":"NJ3QDMKNJLZU","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"pith_short_16","alias_value":"NJ3QDMKNJLZUWPJA","created_at":"2026-07-05T11:20:47Z"},{"alias_kind":"pith_short_8","alias_value":"NJ3QDMKN","created_at":"2026-07-05T11:20:47Z"}],"graph_snapshots":[{"event_id":"sha256:a990a7523fcf6cf58f79943026235cbc23ffa337ac8deb4d0763dc0a4179f83f","target":"graph","created_at":"2026-07-05T11:20:47Z","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/2410.24064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a non-commutative analogue of the modular vector field on a Poisson manifold for a given pair of a double bracket and a connection on a space of 1-forms. The key ingredient, the triple divergence map, is directly constructed from a connection on a linear category to deal with multiple base points. As an application, we give an algebraic description of the framed, groupoid version of Turaev's loop operation $\\mu$ similar to the one obtained by Alekseev-Kawazumi-Kuno-Naef and the author.","authors_text":"Toyo Taniguchi","cross_cats":["math.AT","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-10-31T16:00:01Z","title":"Modular vector fields in non-commutative geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.24064","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:ddd58bd1a3965f94c6aa4f768c36c554b04ded3f83eebe894a12e762cedba18c","target":"record","created_at":"2026-07-05T11:20:47Z","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":"d1f05b3226811330722d303bad6e7cc86ecbde09d71c4ea0b6e1127028faba61","cross_cats_sorted":["math.AT","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-10-31T16:00:01Z","title_canon_sha256":"409c7981b5c946aa5430d00b513d17755dec2d8c17dc6b478d2f355ecac897c2"},"schema_version":"1.0","source":{"id":"2410.24064","kind":"arxiv","version":3}},"canonical_sha256":"6a7701b14d4af34b3d2098ff41dae19b4d9fd39b05cd294440ef103dc9092193","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a7701b14d4af34b3d2098ff41dae19b4d9fd39b05cd294440ef103dc9092193","first_computed_at":"2026-07-05T11:20:47.727210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:47.727210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TWGdfnanbxEGQByELlERspnJBffRrdHrZIL9F7/YlGrQ8WI4Qj7WEIdFyvfZHTe3tKd250G+I7eRJgwcoQ1ZDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:47.727719Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.24064","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddd58bd1a3965f94c6aa4f768c36c554b04ded3f83eebe894a12e762cedba18c","sha256:a990a7523fcf6cf58f79943026235cbc23ffa337ac8deb4d0763dc0a4179f83f"],"state_sha256":"0ad9cb0b8712afaa7121303f633708f7f3252e5abe2dab6fa8ac2fe5baa4168c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hL9tUeF+8wXq/l4z5PtZEeQ83D7hx4+EsdniW1GTBVau7FPjKlejECTLci4MfSgCcdbmdU5DhA2RPJbo4CJPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T12:09:02.614337Z","bundle_sha256":"07c2fb3cd003d15f24e1bd88501682789c793fc406b357cb16d459cf0859be14"}}