{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:YHNTIH3IOIMNXWJBDLSKTWVDVI","short_pith_number":"pith:YHNTIH3I","schema_version":"1.0","canonical_sha256":"c1db341f687218dbd9211ae4a9daa3aa295667aa46484d4b62a44bf92db5d094","source":{"kind":"arxiv","id":"1912.02148","version":2},"attestation_state":"computed","paper":{"title":"Integration of singular foliations via paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alfonso Garmendia, Joel Villatoro","submitted_at":"2019-12-04T17:54:38Z","abstract_excerpt":"We give a new construction of the holonomy and fundamental groupoids of a singular foliation. In contrast with the existing construction of Androulidakis and Skandalis, our method proceeds by taking a quotient of an infinite dimensional space of paths. This strategy is a direct extension of the classical construction for regular foliations and mirrors the integration of Lie algebroids via paths (per Crainic and Fernandes). In this way, we obtain a characterization of the holonomy and fundamental groupoids of a singular foliation that more clearly reflects the homotopic character of these invar"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1912.02148","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-12-04T17:54:38Z","cross_cats_sorted":[],"title_canon_sha256":"c2e5f368e2b6d80446b286950fc18e27d50fa5f1c066184cf8aa927defcde6ee","abstract_canon_sha256":"a119e5e0c1073b2cc4e07edb04dd74ee4cdc771592b835dd73424dfbad5da91a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:48:50.121216Z","signature_b64":"0x+D2nEPDw7YnHRsqfojInNLs+CDfyUokMC3J6TYdTHJpliBWYK0CbhkEuaSQnzr7rZYDuixgifLkIEHyWSZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1db341f687218dbd9211ae4a9daa3aa295667aa46484d4b62a44bf92db5d094","last_reissued_at":"2026-07-05T02:48:50.120736Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:48:50.120736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integration of singular foliations via paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alfonso Garmendia, Joel Villatoro","submitted_at":"2019-12-04T17:54:38Z","abstract_excerpt":"We give a new construction of the holonomy and fundamental groupoids of a singular foliation. In contrast with the existing construction of Androulidakis and Skandalis, our method proceeds by taking a quotient of an infinite dimensional space of paths. This strategy is a direct extension of the classical construction for regular foliations and mirrors the integration of Lie algebroids via paths (per Crainic and Fernandes). In this way, we obtain a characterization of the holonomy and fundamental groupoids of a singular foliation that more clearly reflects the homotopic character of these invar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.02148","kind":"arxiv","version":2},"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/1912.02148/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1912.02148","created_at":"2026-07-05T02:48:50.120793+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.02148v2","created_at":"2026-07-05T02:48:50.120793+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.02148","created_at":"2026-07-05T02:48:50.120793+00:00"},{"alias_kind":"pith_short_12","alias_value":"YHNTIH3IOIMN","created_at":"2026-07-05T02:48:50.120793+00:00"},{"alias_kind":"pith_short_16","alias_value":"YHNTIH3IOIMNXWJB","created_at":"2026-07-05T02:48:50.120793+00:00"},{"alias_kind":"pith_short_8","alias_value":"YHNTIH3I","created_at":"2026-07-05T02:48:50.120793+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YHNTIH3IOIMNXWJBDLSKTWVDVI","json":"https://pith.science/pith/YHNTIH3IOIMNXWJBDLSKTWVDVI.json","graph_json":"https://pith.science/api/pith-number/YHNTIH3IOIMNXWJBDLSKTWVDVI/graph.json","events_json":"https://pith.science/api/pith-number/YHNTIH3IOIMNXWJBDLSKTWVDVI/events.json","paper":"https://pith.science/paper/YHNTIH3I"},"agent_actions":{"view_html":"https://pith.science/pith/YHNTIH3IOIMNXWJBDLSKTWVDVI","download_json":"https://pith.science/pith/YHNTIH3IOIMNXWJBDLSKTWVDVI.json","view_paper":"https://pith.science/paper/YHNTIH3I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.02148&json=true","fetch_graph":"https://pith.science/api/pith-number/YHNTIH3IOIMNXWJBDLSKTWVDVI/graph.json","fetch_events":"https://pith.science/api/pith-number/YHNTIH3IOIMNXWJBDLSKTWVDVI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YHNTIH3IOIMNXWJBDLSKTWVDVI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YHNTIH3IOIMNXWJBDLSKTWVDVI/action/storage_attestation","attest_author":"https://pith.science/pith/YHNTIH3IOIMNXWJBDLSKTWVDVI/action/author_attestation","sign_citation":"https://pith.science/pith/YHNTIH3IOIMNXWJBDLSKTWVDVI/action/citation_signature","submit_replication":"https://pith.science/pith/YHNTIH3IOIMNXWJBDLSKTWVDVI/action/replication_record"}},"created_at":"2026-07-05T02:48:50.120793+00:00","updated_at":"2026-07-05T02:48:50.120793+00:00"}