{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RX4SYEDRVY7HBOPXICAEMMOXGC","short_pith_number":"pith:RX4SYEDR","schema_version":"1.0","canonical_sha256":"8df92c1071ae3e70b9f740804631d730bbe37fb6dc19a59a5e07f4e2ec94a7ae","source":{"kind":"arxiv","id":"1404.4541","version":1},"attestation_state":"computed","paper":{"title":"Fermat and the number of fixed points of periodic flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.SG"],"primary_cat":"math.AT","authors_text":"\\'Alvaro Pelayo, Leonor Godinho, Silvia Sabatini","submitted_at":"2014-04-17T14:37:10Z","abstract_excerpt":"We obtain a general lower bound for the number of fixed points of a circle action on a compact almost complex manifold $M$ of dimension $2n$ with nonempty fixed point set, provided the Chern number $c_1c_{n-1}[M]$ vanishes. The proof combines techniques originating in equivariant K-theory with celebrated number theory results on polygonal numbers, introduced by Pierre de Fermat. This lower bound confirms in many cases a conjecture of Kosniowski from 1979, and is better than existing bounds for some symplectic actions. Moreover, if the fixed point set is discrete, we prove divisibility properti"},"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":"1404.4541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-04-17T14:37:10Z","cross_cats_sorted":["math.GT","math.SG"],"title_canon_sha256":"1f84b1ee1f42b266e597e344c97d93ed63fcaa0b2cf99f0614f5c94175aa2053","abstract_canon_sha256":"f25b6b0e0cd58b939379cbdd39c7cc273dba7cb3313e21d9324c820234e777c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:04.055650Z","signature_b64":"dceiAHsqPLZ3Na56sHd07PnxJssO/GWwaZ/fj9CYjGniAHcvCDGC7mJnoxT+iHGX+uMVpIZo4VQ/g6k3TVIxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8df92c1071ae3e70b9f740804631d730bbe37fb6dc19a59a5e07f4e2ec94a7ae","last_reissued_at":"2026-05-18T02:54:04.055149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:04.055149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fermat and the number of fixed points of periodic flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.SG"],"primary_cat":"math.AT","authors_text":"\\'Alvaro Pelayo, Leonor Godinho, Silvia Sabatini","submitted_at":"2014-04-17T14:37:10Z","abstract_excerpt":"We obtain a general lower bound for the number of fixed points of a circle action on a compact almost complex manifold $M$ of dimension $2n$ with nonempty fixed point set, provided the Chern number $c_1c_{n-1}[M]$ vanishes. The proof combines techniques originating in equivariant K-theory with celebrated number theory results on polygonal numbers, introduced by Pierre de Fermat. This lower bound confirms in many cases a conjecture of Kosniowski from 1979, and is better than existing bounds for some symplectic actions. Moreover, if the fixed point set is discrete, we prove divisibility properti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4541","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":"1404.4541","created_at":"2026-05-18T02:54:04.055222+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4541v1","created_at":"2026-05-18T02:54:04.055222+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4541","created_at":"2026-05-18T02:54:04.055222+00:00"},{"alias_kind":"pith_short_12","alias_value":"RX4SYEDRVY7H","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RX4SYEDRVY7HBOPX","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RX4SYEDR","created_at":"2026-05-18T12:28:46.137349+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/RX4SYEDRVY7HBOPXICAEMMOXGC","json":"https://pith.science/pith/RX4SYEDRVY7HBOPXICAEMMOXGC.json","graph_json":"https://pith.science/api/pith-number/RX4SYEDRVY7HBOPXICAEMMOXGC/graph.json","events_json":"https://pith.science/api/pith-number/RX4SYEDRVY7HBOPXICAEMMOXGC/events.json","paper":"https://pith.science/paper/RX4SYEDR"},"agent_actions":{"view_html":"https://pith.science/pith/RX4SYEDRVY7HBOPXICAEMMOXGC","download_json":"https://pith.science/pith/RX4SYEDRVY7HBOPXICAEMMOXGC.json","view_paper":"https://pith.science/paper/RX4SYEDR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4541&json=true","fetch_graph":"https://pith.science/api/pith-number/RX4SYEDRVY7HBOPXICAEMMOXGC/graph.json","fetch_events":"https://pith.science/api/pith-number/RX4SYEDRVY7HBOPXICAEMMOXGC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RX4SYEDRVY7HBOPXICAEMMOXGC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RX4SYEDRVY7HBOPXICAEMMOXGC/action/storage_attestation","attest_author":"https://pith.science/pith/RX4SYEDRVY7HBOPXICAEMMOXGC/action/author_attestation","sign_citation":"https://pith.science/pith/RX4SYEDRVY7HBOPXICAEMMOXGC/action/citation_signature","submit_replication":"https://pith.science/pith/RX4SYEDRVY7HBOPXICAEMMOXGC/action/replication_record"}},"created_at":"2026-05-18T02:54:04.055222+00:00","updated_at":"2026-05-18T02:54:04.055222+00:00"}