{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MZCXIIAPPJOZ5TQHD2CN6XFZSZ","short_pith_number":"pith:MZCXIIAP","canonical_record":{"source":{"id":"1803.00896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T15:32:41Z","cross_cats_sorted":[],"title_canon_sha256":"d818f9965a63c05454f8569c7632a064e1af39c50ada52dd4ee6cc94bc3dc61c","abstract_canon_sha256":"856771b637542c4b817673566d4c468a460123ae67ae1b6d1fed3c3ffeb4026d"},"schema_version":"1.0"},"canonical_sha256":"664574200f7a5d9ece071e84df5cb9967de5db5efd05132837e5d2791504ffcc","source":{"kind":"arxiv","id":"1803.00896","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00896","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00896v1","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00896","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"pith_short_12","alias_value":"MZCXIIAPPJOZ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MZCXIIAPPJOZ5TQH","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MZCXIIAP","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MZCXIIAPPJOZ5TQHD2CN6XFZSZ","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T15:32:41Z","cross_cats_sorted":[],"title_canon_sha256":"d818f9965a63c05454f8569c7632a064e1af39c50ada52dd4ee6cc94bc3dc61c","abstract_canon_sha256":"856771b637542c4b817673566d4c468a460123ae67ae1b6d1fed3c3ffeb4026d"},"schema_version":"1.0"},"canonical_sha256":"664574200f7a5d9ece071e84df5cb9967de5db5efd05132837e5d2791504ffcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:53.372730Z","signature_b64":"7IVCAYXyFVqbyKJKIAhjWstBqHWGs+zB5g0pBK4PU8OuL1mso4gl61DlOJ7+ouj9uqF5ZVmyp/ue07kRJY3+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"664574200f7a5d9ece071e84df5cb9967de5db5efd05132837e5d2791504ffcc","last_reissued_at":"2026-05-17T23:52:53.372100Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:53.372100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00896","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":"2026-05-17T23:52:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWm+f+7hxtmqfcXESTviZA+ED7BCQc2cIORXrTWsJ/cdQEfFaei7BKK3GnOw3NbJIABW/LhdLtvNkFMgihzpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:11:08.302241Z"},"content_sha256":"f3a2424f76f30cd0bdfd3b68682fbe3c6a8542a76b994a1874c776d1e217de2b","schema_version":"1.0","event_id":"sha256:f3a2424f76f30cd0bdfd3b68682fbe3c6a8542a76b994a1874c776d1e217de2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MZCXIIAPPJOZ5TQHD2CN6XFZSZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hausdorff Morita Equivalence of singular foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alfonso Garmendia, Marco Zambon","submitted_at":"2018-03-02T15:32:41Z","abstract_excerpt":"We introduce a notion of equivalence for singular foliations - understood as suitable families of vector fields - that preserves their transverse geometry. Associated to every singular foliation there is a holonomy groupoid, by the work of Androulidakis-Skandalis. We show that our notion of equivalence is compatible with this assignment, and as a consequence we obtain several invariants. Further, we show that it unifies some of the notions of transverse equivalence for regular foliations that appeared in the 1980's."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00896","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":""},"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":"2026-05-17T23:52:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zn7cUowUAPvP+ZD+HcF+/FYlECbRjztC6RjvM9+3hGwasMCcWoUjBT9Sj1jN6GRJ3NirMkPV6ywx80YB4RELDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:11:08.302599Z"},"content_sha256":"376877ef8373d95c59c17ed5dc2dbd35bc7d49ee8a61c594af205e6ccfb3c352","schema_version":"1.0","event_id":"sha256:376877ef8373d95c59c17ed5dc2dbd35bc7d49ee8a61c594af205e6ccfb3c352"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZCXIIAPPJOZ5TQHD2CN6XFZSZ/bundle.json","state_url":"https://pith.science/pith/MZCXIIAPPJOZ5TQHD2CN6XFZSZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZCXIIAPPJOZ5TQHD2CN6XFZSZ/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":"2026-05-30T22:11:08Z","links":{"resolver":"https://pith.science/pith/MZCXIIAPPJOZ5TQHD2CN6XFZSZ","bundle":"https://pith.science/pith/MZCXIIAPPJOZ5TQHD2CN6XFZSZ/bundle.json","state":"https://pith.science/pith/MZCXIIAPPJOZ5TQHD2CN6XFZSZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZCXIIAPPJOZ5TQHD2CN6XFZSZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MZCXIIAPPJOZ5TQHD2CN6XFZSZ","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":"856771b637542c4b817673566d4c468a460123ae67ae1b6d1fed3c3ffeb4026d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T15:32:41Z","title_canon_sha256":"d818f9965a63c05454f8569c7632a064e1af39c50ada52dd4ee6cc94bc3dc61c"},"schema_version":"1.0","source":{"id":"1803.00896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00896","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00896v1","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00896","created_at":"2026-05-17T23:52:53Z"},{"alias_kind":"pith_short_12","alias_value":"MZCXIIAPPJOZ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MZCXIIAPPJOZ5TQH","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MZCXIIAP","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:376877ef8373d95c59c17ed5dc2dbd35bc7d49ee8a61c594af205e6ccfb3c352","target":"graph","created_at":"2026-05-17T23:52:53Z","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 introduce a notion of equivalence for singular foliations - understood as suitable families of vector fields - that preserves their transverse geometry. Associated to every singular foliation there is a holonomy groupoid, by the work of Androulidakis-Skandalis. We show that our notion of equivalence is compatible with this assignment, and as a consequence we obtain several invariants. Further, we show that it unifies some of the notions of transverse equivalence for regular foliations that appeared in the 1980's.","authors_text":"Alfonso Garmendia, Marco Zambon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T15:32:41Z","title":"Hausdorff Morita Equivalence of singular foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00896","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:f3a2424f76f30cd0bdfd3b68682fbe3c6a8542a76b994a1874c776d1e217de2b","target":"record","created_at":"2026-05-17T23:52:53Z","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":"856771b637542c4b817673566d4c468a460123ae67ae1b6d1fed3c3ffeb4026d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T15:32:41Z","title_canon_sha256":"d818f9965a63c05454f8569c7632a064e1af39c50ada52dd4ee6cc94bc3dc61c"},"schema_version":"1.0","source":{"id":"1803.00896","kind":"arxiv","version":1}},"canonical_sha256":"664574200f7a5d9ece071e84df5cb9967de5db5efd05132837e5d2791504ffcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"664574200f7a5d9ece071e84df5cb9967de5db5efd05132837e5d2791504ffcc","first_computed_at":"2026-05-17T23:52:53.372100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:53.372100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7IVCAYXyFVqbyKJKIAhjWstBqHWGs+zB5g0pBK4PU8OuL1mso4gl61DlOJ7+ouj9uqF5ZVmyp/ue07kRJY3+Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:53.372730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3a2424f76f30cd0bdfd3b68682fbe3c6a8542a76b994a1874c776d1e217de2b","sha256:376877ef8373d95c59c17ed5dc2dbd35bc7d49ee8a61c594af205e6ccfb3c352"],"state_sha256":"e8479c609a3d397f2daf7ed59ed68e4c6c08a53078a10f1b73551ad1077dd657"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2wraluYMYMCM3Tci11EsIyRssmE7aYaM6Ixcukl31Kbe9BT6EvntHOdpUtH7ejhOwPQcwz/O0BdbPK/UH+NUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:11:08.304795Z","bundle_sha256":"20fb10eeb5e5460b54d99d1f6e1b2a5bec32d563e31b4681e38a45181b61b486"}}