{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:P5LQ2YC6LH4NXFX6CBQKJNE6JQ","short_pith_number":"pith:P5LQ2YC6","schema_version":"1.0","canonical_sha256":"7f570d605e59f8db96fe1060a4b49e4c0ad1df317e99d8641723dfe104626445","source":{"kind":"arxiv","id":"1305.1672","version":1},"attestation_state":"computed","paper":{"title":"Kervaire invariants and selfcoincidences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Duane Randall, Ulrich Koschorke","submitted_at":"2013-05-07T22:43:48Z","abstract_excerpt":"Minimum numbers decide e.g. whether a given map f: S^m --> S^n/G from a sphere into a spherical space form can be deformed to a map f' such that f(x) not equal f'(x) for all x in S^m. In this paper we compare minimum numbers to (geometrically defined) Nielsen numbers (which are more computable). In the stable dimension range these numbers coincide. But already in the first nonstable range (when m=2n-2) the Kervaire invariant appears as a decisive additional obstruction which detects interesting geometric coincidence phenomena. Similar results (involving e.g. Hopf invariants, taken mod 4) are o"},"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":"1305.1672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-05-07T22:43:48Z","cross_cats_sorted":[],"title_canon_sha256":"bd87f4bf55652977d8cef7f79306bdca0fbc9c1ffe2e9ba28581187c66970ad9","abstract_canon_sha256":"b3094f22ebf278b6eaca9a0e565676077b1145a84dbd729dfe90cefcbf59c408"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:00.175736Z","signature_b64":"iKerU1ocM/ViINDMz/pslT7ghFWNtzlsFW088u39YWGVb065fuqfRjFQ05S4xfC0VHsyhz8gbN7RFPhsLRLyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f570d605e59f8db96fe1060a4b49e4c0ad1df317e99d8641723dfe104626445","last_reissued_at":"2026-05-18T03:21:00.174909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:00.174909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kervaire invariants and selfcoincidences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Duane Randall, Ulrich Koschorke","submitted_at":"2013-05-07T22:43:48Z","abstract_excerpt":"Minimum numbers decide e.g. whether a given map f: S^m --> S^n/G from a sphere into a spherical space form can be deformed to a map f' such that f(x) not equal f'(x) for all x in S^m. In this paper we compare minimum numbers to (geometrically defined) Nielsen numbers (which are more computable). In the stable dimension range these numbers coincide. But already in the first nonstable range (when m=2n-2) the Kervaire invariant appears as a decisive additional obstruction which detects interesting geometric coincidence phenomena. Similar results (involving e.g. Hopf invariants, taken mod 4) are o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1672","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":"1305.1672","created_at":"2026-05-18T03:21:00.175054+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.1672v1","created_at":"2026-05-18T03:21:00.175054+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1672","created_at":"2026-05-18T03:21:00.175054+00:00"},{"alias_kind":"pith_short_12","alias_value":"P5LQ2YC6LH4N","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"P5LQ2YC6LH4NXFX6","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"P5LQ2YC6","created_at":"2026-05-18T12:27:54.935989+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/P5LQ2YC6LH4NXFX6CBQKJNE6JQ","json":"https://pith.science/pith/P5LQ2YC6LH4NXFX6CBQKJNE6JQ.json","graph_json":"https://pith.science/api/pith-number/P5LQ2YC6LH4NXFX6CBQKJNE6JQ/graph.json","events_json":"https://pith.science/api/pith-number/P5LQ2YC6LH4NXFX6CBQKJNE6JQ/events.json","paper":"https://pith.science/paper/P5LQ2YC6"},"agent_actions":{"view_html":"https://pith.science/pith/P5LQ2YC6LH4NXFX6CBQKJNE6JQ","download_json":"https://pith.science/pith/P5LQ2YC6LH4NXFX6CBQKJNE6JQ.json","view_paper":"https://pith.science/paper/P5LQ2YC6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.1672&json=true","fetch_graph":"https://pith.science/api/pith-number/P5LQ2YC6LH4NXFX6CBQKJNE6JQ/graph.json","fetch_events":"https://pith.science/api/pith-number/P5LQ2YC6LH4NXFX6CBQKJNE6JQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P5LQ2YC6LH4NXFX6CBQKJNE6JQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P5LQ2YC6LH4NXFX6CBQKJNE6JQ/action/storage_attestation","attest_author":"https://pith.science/pith/P5LQ2YC6LH4NXFX6CBQKJNE6JQ/action/author_attestation","sign_citation":"https://pith.science/pith/P5LQ2YC6LH4NXFX6CBQKJNE6JQ/action/citation_signature","submit_replication":"https://pith.science/pith/P5LQ2YC6LH4NXFX6CBQKJNE6JQ/action/replication_record"}},"created_at":"2026-05-18T03:21:00.175054+00:00","updated_at":"2026-05-18T03:21:00.175054+00:00"}