{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3UHUPPMFBTTKRYXDRCI6WJUQUB","short_pith_number":"pith:3UHUPPMF","canonical_record":{"source":{"id":"1503.04627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-16T12:44:48Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"a48ed92b55f675ef822fe352dc6b7ac85b1f22a5016363e37399cb860742a200","abstract_canon_sha256":"64fcdb8a4636ea102248a65784c4e1c05c5f4b2de50c1c612ff106a7a72c1208"},"schema_version":"1.0"},"canonical_sha256":"dd0f47bd850ce6a8e2e38891eb2690a06f9b839217253dc027ffc6d1f26d0b13","source":{"kind":"arxiv","id":"1503.04627","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04627","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04627v1","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04627","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"pith_short_12","alias_value":"3UHUPPMFBTTK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3UHUPPMFBTTKRYXD","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3UHUPPMF","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3UHUPPMFBTTKRYXDRCI6WJUQUB","target":"record","payload":{"canonical_record":{"source":{"id":"1503.04627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-16T12:44:48Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"a48ed92b55f675ef822fe352dc6b7ac85b1f22a5016363e37399cb860742a200","abstract_canon_sha256":"64fcdb8a4636ea102248a65784c4e1c05c5f4b2de50c1c612ff106a7a72c1208"},"schema_version":"1.0"},"canonical_sha256":"dd0f47bd850ce6a8e2e38891eb2690a06f9b839217253dc027ffc6d1f26d0b13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:24.477717Z","signature_b64":"s8JMjB7YDXxbW4pPYT9ewoSSHHNEOolDP+3L9lOSlnW8qc68cs4xhFJyQjhzga1/7CdKcM8EYAX/FSS7oLYhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd0f47bd850ce6a8e2e38891eb2690a06f9b839217253dc027ffc6d1f26d0b13","last_reissued_at":"2026-05-18T02:23:24.477179Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:24.477179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.04627","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":"2026-05-18T02:23:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rl02S+7BZrqvDvIUaAoMJNiHN4TrHhGdvJQemWkGlhR4MHmXjVv/UHX9HP4KW2+AY1eYT/r6O1kT3rSJK7XGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:55:40.462843Z"},"content_sha256":"7c6bfdc126178b0ff81f1dcfffa7e8ad7aec163acaadb574f66d33445f509e6f","schema_version":"1.0","event_id":"sha256:7c6bfdc126178b0ff81f1dcfffa7e8ad7aec163acaadb574f66d33445f509e6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3UHUPPMFBTTKRYXDRCI6WJUQUB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Foliations and webs inducing Galois coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DS","authors_text":"Andr\\'es Beltr\\'an, David Mar\\'in, Marcel Nicolau, Maycol Falla Luza","submitted_at":"2015-03-16T12:44:48Z","abstract_excerpt":"We introduce the notion of Galois holomorphic foliation on the complex projective space as that of foliations whose Gauss map is a Galois covering when restricted to an appropriate Zariski open subset. First, we establish general criteria assuring that a rational map between projective manifolds of the same dimension defines a Galois covering. Then, these criteria are used to give a geometric characterization of Galois foliations in terms of their inflection divisor and their singularities. We also characterize Galois foliations on $\\mathbb P^2$ admitting continuous symmetries, obtaining a com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04627","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":"2026-05-18T02:23:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KWd086h+nOCFZgZy3vk8ShAjNB1Tk0BghFODN79ulPnOoFKNiy+VRnF26geO33mRGVfEgBUVkrUNev2oagNfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:55:40.463502Z"},"content_sha256":"2bccde0a224d78dc0656d86855f147b96f8d38b01db7b6f1904f73f6ce956461","schema_version":"1.0","event_id":"sha256:2bccde0a224d78dc0656d86855f147b96f8d38b01db7b6f1904f73f6ce956461"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3UHUPPMFBTTKRYXDRCI6WJUQUB/bundle.json","state_url":"https://pith.science/pith/3UHUPPMFBTTKRYXDRCI6WJUQUB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3UHUPPMFBTTKRYXDRCI6WJUQUB/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":"2026-05-27T11:55:40Z","links":{"resolver":"https://pith.science/pith/3UHUPPMFBTTKRYXDRCI6WJUQUB","bundle":"https://pith.science/pith/3UHUPPMFBTTKRYXDRCI6WJUQUB/bundle.json","state":"https://pith.science/pith/3UHUPPMFBTTKRYXDRCI6WJUQUB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3UHUPPMFBTTKRYXDRCI6WJUQUB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3UHUPPMFBTTKRYXDRCI6WJUQUB","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":"64fcdb8a4636ea102248a65784c4e1c05c5f4b2de50c1c612ff106a7a72c1208","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-16T12:44:48Z","title_canon_sha256":"a48ed92b55f675ef822fe352dc6b7ac85b1f22a5016363e37399cb860742a200"},"schema_version":"1.0","source":{"id":"1503.04627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04627","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04627v1","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04627","created_at":"2026-05-18T02:23:24Z"},{"alias_kind":"pith_short_12","alias_value":"3UHUPPMFBTTK","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3UHUPPMFBTTKRYXD","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3UHUPPMF","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:2bccde0a224d78dc0656d86855f147b96f8d38b01db7b6f1904f73f6ce956461","target":"graph","created_at":"2026-05-18T02:23:24Z","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 the notion of Galois holomorphic foliation on the complex projective space as that of foliations whose Gauss map is a Galois covering when restricted to an appropriate Zariski open subset. First, we establish general criteria assuring that a rational map between projective manifolds of the same dimension defines a Galois covering. Then, these criteria are used to give a geometric characterization of Galois foliations in terms of their inflection divisor and their singularities. We also characterize Galois foliations on $\\mathbb P^2$ admitting continuous symmetries, obtaining a com","authors_text":"Andr\\'es Beltr\\'an, David Mar\\'in, Marcel Nicolau, Maycol Falla Luza","cross_cats":["math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-16T12:44:48Z","title":"Foliations and webs inducing Galois coverings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04627","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":"sha256:7c6bfdc126178b0ff81f1dcfffa7e8ad7aec163acaadb574f66d33445f509e6f","target":"record","created_at":"2026-05-18T02:23:24Z","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":"64fcdb8a4636ea102248a65784c4e1c05c5f4b2de50c1c612ff106a7a72c1208","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-16T12:44:48Z","title_canon_sha256":"a48ed92b55f675ef822fe352dc6b7ac85b1f22a5016363e37399cb860742a200"},"schema_version":"1.0","source":{"id":"1503.04627","kind":"arxiv","version":1}},"canonical_sha256":"dd0f47bd850ce6a8e2e38891eb2690a06f9b839217253dc027ffc6d1f26d0b13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd0f47bd850ce6a8e2e38891eb2690a06f9b839217253dc027ffc6d1f26d0b13","first_computed_at":"2026-05-18T02:23:24.477179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:24.477179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s8JMjB7YDXxbW4pPYT9ewoSSHHNEOolDP+3L9lOSlnW8qc68cs4xhFJyQjhzga1/7CdKcM8EYAX/FSS7oLYhAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:24.477717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04627","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c6bfdc126178b0ff81f1dcfffa7e8ad7aec163acaadb574f66d33445f509e6f","sha256:2bccde0a224d78dc0656d86855f147b96f8d38b01db7b6f1904f73f6ce956461"],"state_sha256":"7ccbfaccf8f0dd9f95e79d5828629785c6e9d3f626bb69ca50bdd33c3b235ba2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gSrxvETjwxgNbG8NQHOMO3o3orUxPhPDYcqzZlQU90ynx1e03zTdiHAcqNCjuDJBL6gIbif5M9tdY4TzN9d7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:55:40.466877Z","bundle_sha256":"150236e4b5b59a6a1cb58fc295dd10c768669e203036f5ca6ac56f75bc562334"}}