{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SK5SXL4V3WCTEEWIFVLEJH2TSL","short_pith_number":"pith:SK5SXL4V","schema_version":"1.0","canonical_sha256":"92bb2baf95dd853212c82d56449f5392db40329026e6b459ab0cf56c86c0101c","source":{"kind":"arxiv","id":"1412.8448","version":2},"attestation_state":"computed","paper":{"title":"Skew flat fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AT","authors_text":"Michael Harrison","submitted_at":"2014-12-29T20:27:40Z","abstract_excerpt":"A fibration of ${\\mathbb R}^n$ by oriented copies of ${\\mathbb R}^p$ is called skew if no two fibers intersect nor contain parallel directions. Conditions on $p$ and $n$ for the existence of such a fibration were given by Ovsienko and Tabachnikov. A classification of smooth fibrations of ${\\mathbb R}^3$ by skew oriented lines was given by Salvai, in analogue with the classification of oriented great circle fibrations of $S^3$ by Gluck and Warner. We show that Salvai's classification has a topological variation which generalizes to characterize all continuous fibrations of ${\\mathbb R}^n$ by sk"},"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":"1412.8448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-12-29T20:27:40Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"de4f28e75dd23fcbc644974103d2e46959d3692993cd71eb1284dc28b54ce688","abstract_canon_sha256":"4283ac79f03815865aaf5a7e177f7272b37a4293edd5fdf7a8e6be12332732ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:08.271450Z","signature_b64":"g4SM8KXFz9CYL4O/5rzwI+WmgojCIeSrj4Ch/FFNe+/la8yHGO3R+XK4AJ9oJUbMuHSPqaXtLmYhYBlBXGS1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92bb2baf95dd853212c82d56449f5392db40329026e6b459ab0cf56c86c0101c","last_reissued_at":"2026-05-18T01:32:08.270808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:08.270808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skew flat fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AT","authors_text":"Michael Harrison","submitted_at":"2014-12-29T20:27:40Z","abstract_excerpt":"A fibration of ${\\mathbb R}^n$ by oriented copies of ${\\mathbb R}^p$ is called skew if no two fibers intersect nor contain parallel directions. Conditions on $p$ and $n$ for the existence of such a fibration were given by Ovsienko and Tabachnikov. A classification of smooth fibrations of ${\\mathbb R}^3$ by skew oriented lines was given by Salvai, in analogue with the classification of oriented great circle fibrations of $S^3$ by Gluck and Warner. We show that Salvai's classification has a topological variation which generalizes to characterize all continuous fibrations of ${\\mathbb R}^n$ by sk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8448","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":""},"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":"1412.8448","created_at":"2026-05-18T01:32:08.270899+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.8448v2","created_at":"2026-05-18T01:32:08.270899+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8448","created_at":"2026-05-18T01:32:08.270899+00:00"},{"alias_kind":"pith_short_12","alias_value":"SK5SXL4V3WCT","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SK5SXL4V3WCTEEWI","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SK5SXL4V","created_at":"2026-05-18T12:28:49.207871+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/SK5SXL4V3WCTEEWIFVLEJH2TSL","json":"https://pith.science/pith/SK5SXL4V3WCTEEWIFVLEJH2TSL.json","graph_json":"https://pith.science/api/pith-number/SK5SXL4V3WCTEEWIFVLEJH2TSL/graph.json","events_json":"https://pith.science/api/pith-number/SK5SXL4V3WCTEEWIFVLEJH2TSL/events.json","paper":"https://pith.science/paper/SK5SXL4V"},"agent_actions":{"view_html":"https://pith.science/pith/SK5SXL4V3WCTEEWIFVLEJH2TSL","download_json":"https://pith.science/pith/SK5SXL4V3WCTEEWIFVLEJH2TSL.json","view_paper":"https://pith.science/paper/SK5SXL4V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.8448&json=true","fetch_graph":"https://pith.science/api/pith-number/SK5SXL4V3WCTEEWIFVLEJH2TSL/graph.json","fetch_events":"https://pith.science/api/pith-number/SK5SXL4V3WCTEEWIFVLEJH2TSL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SK5SXL4V3WCTEEWIFVLEJH2TSL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SK5SXL4V3WCTEEWIFVLEJH2TSL/action/storage_attestation","attest_author":"https://pith.science/pith/SK5SXL4V3WCTEEWIFVLEJH2TSL/action/author_attestation","sign_citation":"https://pith.science/pith/SK5SXL4V3WCTEEWIFVLEJH2TSL/action/citation_signature","submit_replication":"https://pith.science/pith/SK5SXL4V3WCTEEWIFVLEJH2TSL/action/replication_record"}},"created_at":"2026-05-18T01:32:08.270899+00:00","updated_at":"2026-05-18T01:32:08.270899+00:00"}