{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:L72OGBNPFGRJYHTWW6V4NSXRDZ","short_pith_number":"pith:L72OGBNP","canonical_record":{"source":{"id":"2411.18757","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-11-27T21:22:31Z","cross_cats_sorted":[],"title_canon_sha256":"07f1c0fe27607e1df058eb1867f4da48e7bafee40391a325b4d4e3d6d760d16f","abstract_canon_sha256":"d4dd9d9bafe77dc1f40cf06e50116a7dfae4502849ed3a63b2c3cf832cabf85a"},"schema_version":"1.0"},"canonical_sha256":"5ff4e305af29a29c1e76b7abc6caf11e4fa4aeeff56f43104232d6c92e316740","source":{"kind":"arxiv","id":"2411.18757","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18757","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18757v1","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18757","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"L72OGBNPFGRJ","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"pith_short_16","alias_value":"L72OGBNPFGRJYHTW","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"pith_short_8","alias_value":"L72OGBNP","created_at":"2026-07-05T09:41:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:L72OGBNPFGRJYHTWW6V4NSXRDZ","target":"record","payload":{"canonical_record":{"source":{"id":"2411.18757","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-11-27T21:22:31Z","cross_cats_sorted":[],"title_canon_sha256":"07f1c0fe27607e1df058eb1867f4da48e7bafee40391a325b4d4e3d6d760d16f","abstract_canon_sha256":"d4dd9d9bafe77dc1f40cf06e50116a7dfae4502849ed3a63b2c3cf832cabf85a"},"schema_version":"1.0"},"canonical_sha256":"5ff4e305af29a29c1e76b7abc6caf11e4fa4aeeff56f43104232d6c92e316740","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:41:51.020694Z","signature_b64":"3SAk8JOk0LL+2l3RFAs4islt7qXhNkvxD7b5DEFLqG9UiyG1Rd6PTxAbDWmSkB/SH6VNPLSFwtMoPw6ImieaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ff4e305af29a29c1e76b7abc6caf11e4fa4aeeff56f43104232d6c92e316740","last_reissued_at":"2026-07-05T09:41:51.020199Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:41:51.020199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.18757","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1MT+AesmcgzhU3e1GwUQ9UH6jSNBO+kSFaEbk5L1Wx1uUignDh9PZxm+upvVodAoWOqhS+BIGvKISW+/VFbRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:09:26.586563Z"},"content_sha256":"df07f8ec57a92011a72c9eb9a4ded422a07385c91e156d24d4e033cf2ede7c65","schema_version":"1.0","event_id":"sha256:df07f8ec57a92011a72c9eb9a4ded422a07385c91e156d24d4e033cf2ede7c65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:L72OGBNPFGRJYHTWW6V4NSXRDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cocycles in Lie Groups, Cochains and Regularity Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ros\\'ario D. Laureano","submitted_at":"2024-11-27T21:22:31Z","abstract_excerpt":"After the fundamental work of Livschitz in [1; 2], various research directions emerged, among which the following stand out: (i) the study of cocycles with values in groups and semigroups beyond R, as well as the investigation of corresponding regularity results; (ii) the analysis of how a certain degree of regularity of the cocycle can confer corresponding regularity to the solution of the cohomological equation; and (iii) the study of higher-dimensional cohomology naturally associated with the action of groups other than Z or R. The aim of this article is to present, as self-contained as pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18757","kind":"arxiv","version":1},"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/2411.18757/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":"2026-07-05T09:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hyAvlmLZAXpsoYkyvXGOQd6sez8C6vCU5JTqubZmsiExh3Booevd0bJs92FSVkfS9mYlnjzpq9fwPiqc2GkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T07:09:26.587176Z"},"content_sha256":"1485c9eba8db880d00e3e1c04443046e4b296860f6fa169f3315a11ae678ea8b","schema_version":"1.0","event_id":"sha256:1485c9eba8db880d00e3e1c04443046e4b296860f6fa169f3315a11ae678ea8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L72OGBNPFGRJYHTWW6V4NSXRDZ/bundle.json","state_url":"https://pith.science/pith/L72OGBNPFGRJYHTWW6V4NSXRDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L72OGBNPFGRJYHTWW6V4NSXRDZ/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":"2026-08-13T07:09:26Z","links":{"resolver":"https://pith.science/pith/L72OGBNPFGRJYHTWW6V4NSXRDZ","bundle":"https://pith.science/pith/L72OGBNPFGRJYHTWW6V4NSXRDZ/bundle.json","state":"https://pith.science/pith/L72OGBNPFGRJYHTWW6V4NSXRDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L72OGBNPFGRJYHTWW6V4NSXRDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:L72OGBNPFGRJYHTWW6V4NSXRDZ","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":"d4dd9d9bafe77dc1f40cf06e50116a7dfae4502849ed3a63b2c3cf832cabf85a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-11-27T21:22:31Z","title_canon_sha256":"07f1c0fe27607e1df058eb1867f4da48e7bafee40391a325b4d4e3d6d760d16f"},"schema_version":"1.0","source":{"id":"2411.18757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18757","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18757v1","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18757","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"L72OGBNPFGRJ","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"pith_short_16","alias_value":"L72OGBNPFGRJYHTW","created_at":"2026-07-05T09:41:51Z"},{"alias_kind":"pith_short_8","alias_value":"L72OGBNP","created_at":"2026-07-05T09:41:51Z"}],"graph_snapshots":[{"event_id":"sha256:1485c9eba8db880d00e3e1c04443046e4b296860f6fa169f3315a11ae678ea8b","target":"graph","created_at":"2026-07-05T09:41:51Z","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/2411.18757/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"After the fundamental work of Livschitz in [1; 2], various research directions emerged, among which the following stand out: (i) the study of cocycles with values in groups and semigroups beyond R, as well as the investigation of corresponding regularity results; (ii) the analysis of how a certain degree of regularity of the cocycle can confer corresponding regularity to the solution of the cohomological equation; and (iii) the study of higher-dimensional cohomology naturally associated with the action of groups other than Z or R. The aim of this article is to present, as self-contained as pos","authors_text":"Ros\\'ario D. Laureano","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-11-27T21:22:31Z","title":"Cocycles in Lie Groups, Cochains and Regularity Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18757","kind":"arxiv","version":1},"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:df07f8ec57a92011a72c9eb9a4ded422a07385c91e156d24d4e033cf2ede7c65","target":"record","created_at":"2026-07-05T09:41:51Z","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":"d4dd9d9bafe77dc1f40cf06e50116a7dfae4502849ed3a63b2c3cf832cabf85a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2024-11-27T21:22:31Z","title_canon_sha256":"07f1c0fe27607e1df058eb1867f4da48e7bafee40391a325b4d4e3d6d760d16f"},"schema_version":"1.0","source":{"id":"2411.18757","kind":"arxiv","version":1}},"canonical_sha256":"5ff4e305af29a29c1e76b7abc6caf11e4fa4aeeff56f43104232d6c92e316740","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ff4e305af29a29c1e76b7abc6caf11e4fa4aeeff56f43104232d6c92e316740","first_computed_at":"2026-07-05T09:41:51.020199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:51.020199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3SAk8JOk0LL+2l3RFAs4islt7qXhNkvxD7b5DEFLqG9UiyG1Rd6PTxAbDWmSkB/SH6VNPLSFwtMoPw6ImieaAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:51.020694Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df07f8ec57a92011a72c9eb9a4ded422a07385c91e156d24d4e033cf2ede7c65","sha256:1485c9eba8db880d00e3e1c04443046e4b296860f6fa169f3315a11ae678ea8b"],"state_sha256":"d6697e0936c2531ba7e906104d04518d9184e7d814199f38544e4bf4736decc1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JoPObxxO3+pGlrkhwRhOd4Dn7xe0tthq/0VG2OZUn6Gs00BwyYVz/1U/L5zeBTl23dlnaQOM1q2NPdVeUTYzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T07:09:26.592775Z","bundle_sha256":"6d534d8d253d7eb14266f28a506b69fcd2e6be06bc52285e7f6cd613a3bfa1c6"}}