{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:L6LTA7D7VFOVYC52YKLP5276B2","short_pith_number":"pith:L6LTA7D7","schema_version":"1.0","canonical_sha256":"5f97307c7fa95d5c0bbac296feebfe0e9b86b29ba047276da45a7fc0f8166e41","source":{"kind":"arxiv","id":"1104.1325","version":1},"attestation_state":"computed","paper":{"title":"Transversal Homotopy Monoids of Complex Projective Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Conor Smyth","submitted_at":"2011-04-07T13:20:56Z","abstract_excerpt":"We will give a geometric description of the nth transversal homotopy monoid of k-dimensional complex projective space, where we stratify by lower dimensional complex projective spaces in the usual way. Transversal homotopy monoids are defined as classes of based transversal maps into Whitney stratified spaces up to equivalence through such maps. We will show the nth transversal homotopy monoid of k-dimensional complex projective space is isomorphic to isotopy classes of certain filtrations of the n-sphere. The required filtrations are by nested closed subspaces $X_0 \\subset ... \\subset X_k=S^n"},"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":"1104.1325","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-04-07T13:20:56Z","cross_cats_sorted":[],"title_canon_sha256":"4665909cf382568a49a6de88e3065ff6265c51f9c67f5f6b071e094841e51713","abstract_canon_sha256":"b6d701f4c92587f66a5108d61fce724563cfd8e6b3606d63612ab442b2d74050"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:52.443760Z","signature_b64":"dWWBQY6x8Wid8mNJ/ucAuf5u5HsSP9PfHJXlVS/LTr/KkIyJqkdvWzBNJzE5fsOcjdh2wqfqrR0apTfEyLijDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f97307c7fa95d5c0bbac296feebfe0e9b86b29ba047276da45a7fc0f8166e41","last_reissued_at":"2026-05-18T04:24:52.443307Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:52.443307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transversal Homotopy Monoids of Complex Projective Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Conor Smyth","submitted_at":"2011-04-07T13:20:56Z","abstract_excerpt":"We will give a geometric description of the nth transversal homotopy monoid of k-dimensional complex projective space, where we stratify by lower dimensional complex projective spaces in the usual way. Transversal homotopy monoids are defined as classes of based transversal maps into Whitney stratified spaces up to equivalence through such maps. We will show the nth transversal homotopy monoid of k-dimensional complex projective space is isomorphic to isotopy classes of certain filtrations of the n-sphere. The required filtrations are by nested closed subspaces $X_0 \\subset ... \\subset X_k=S^n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1325","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1104.1325","created_at":"2026-05-18T04:24:52.443383+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.1325v1","created_at":"2026-05-18T04:24:52.443383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1325","created_at":"2026-05-18T04:24:52.443383+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6LTA7D7VFOV","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6LTA7D7VFOVYC52","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6LTA7D7","created_at":"2026-05-18T12:26:34.985390+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/L6LTA7D7VFOVYC52YKLP5276B2","json":"https://pith.science/pith/L6LTA7D7VFOVYC52YKLP5276B2.json","graph_json":"https://pith.science/api/pith-number/L6LTA7D7VFOVYC52YKLP5276B2/graph.json","events_json":"https://pith.science/api/pith-number/L6LTA7D7VFOVYC52YKLP5276B2/events.json","paper":"https://pith.science/paper/L6LTA7D7"},"agent_actions":{"view_html":"https://pith.science/pith/L6LTA7D7VFOVYC52YKLP5276B2","download_json":"https://pith.science/pith/L6LTA7D7VFOVYC52YKLP5276B2.json","view_paper":"https://pith.science/paper/L6LTA7D7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.1325&json=true","fetch_graph":"https://pith.science/api/pith-number/L6LTA7D7VFOVYC52YKLP5276B2/graph.json","fetch_events":"https://pith.science/api/pith-number/L6LTA7D7VFOVYC52YKLP5276B2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6LTA7D7VFOVYC52YKLP5276B2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6LTA7D7VFOVYC52YKLP5276B2/action/storage_attestation","attest_author":"https://pith.science/pith/L6LTA7D7VFOVYC52YKLP5276B2/action/author_attestation","sign_citation":"https://pith.science/pith/L6LTA7D7VFOVYC52YKLP5276B2/action/citation_signature","submit_replication":"https://pith.science/pith/L6LTA7D7VFOVYC52YKLP5276B2/action/replication_record"}},"created_at":"2026-05-18T04:24:52.443383+00:00","updated_at":"2026-05-18T04:24:52.443383+00:00"}