{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:HSQENIV6HA7QR3FX3WEVYQD4HB","short_pith_number":"pith:HSQENIV6","schema_version":"1.0","canonical_sha256":"3ca046a2be383f08ecb7dd895c407c386137b05c44cdb5ab85d7d08f20581710","source":{"kind":"arxiv","id":"2012.10908","version":1},"attestation_state":"computed","paper":{"title":"Todd genus and $A_k$-genus of unitary $S^1$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jianbo Wang, Yuyu Wang, Zhiwang Yu","submitted_at":"2020-12-20T12:42:01Z","abstract_excerpt":"Assume that $M$ is a compact connected unitary 2n-dimensional manifold and admits a non-trivial circle action preserving the given complex structure. If the first Chern class of $M$ equals to $k_0x$ for a certain 2nd integral cohomology class $x$ with $|k_0|\\geq n + 2$, and its first integral cohomology group is zero, this short paper shows that the Todd genus and $A_k$-genus of $M$ vanish."},"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":"2012.10908","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-12-20T12:42:01Z","cross_cats_sorted":[],"title_canon_sha256":"9f82bd5684a255a096ea40077ba9b533dcef058da13805ec328853bbbeaa8b2d","abstract_canon_sha256":"4977d42801389b632c89c417a8d01454b93d56dc985db157034b66dff4746b20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:11:49.650958Z","signature_b64":"6OV0X3f42WZSznLUeSm3Z91K10XbPlwYXLEK6IIlbbOvfUr3DD3Ial/UKJT04PG1A/hAlkQqgvR0dnZAM3pIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ca046a2be383f08ecb7dd895c407c386137b05c44cdb5ab85d7d08f20581710","last_reissued_at":"2026-07-05T07:11:49.650537Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:11:49.650537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Todd genus and $A_k$-genus of unitary $S^1$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jianbo Wang, Yuyu Wang, Zhiwang Yu","submitted_at":"2020-12-20T12:42:01Z","abstract_excerpt":"Assume that $M$ is a compact connected unitary 2n-dimensional manifold and admits a non-trivial circle action preserving the given complex structure. If the first Chern class of $M$ equals to $k_0x$ for a certain 2nd integral cohomology class $x$ with $|k_0|\\geq n + 2$, and its first integral cohomology group is zero, this short paper shows that the Todd genus and $A_k$-genus of $M$ vanish."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10908","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.10908/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2012.10908","created_at":"2026-07-05T07:11:49.650597+00:00"},{"alias_kind":"arxiv_version","alias_value":"2012.10908v1","created_at":"2026-07-05T07:11:49.650597+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.10908","created_at":"2026-07-05T07:11:49.650597+00:00"},{"alias_kind":"pith_short_12","alias_value":"HSQENIV6HA7Q","created_at":"2026-07-05T07:11:49.650597+00:00"},{"alias_kind":"pith_short_16","alias_value":"HSQENIV6HA7QR3FX","created_at":"2026-07-05T07:11:49.650597+00:00"},{"alias_kind":"pith_short_8","alias_value":"HSQENIV6","created_at":"2026-07-05T07:11:49.650597+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/HSQENIV6HA7QR3FX3WEVYQD4HB","json":"https://pith.science/pith/HSQENIV6HA7QR3FX3WEVYQD4HB.json","graph_json":"https://pith.science/api/pith-number/HSQENIV6HA7QR3FX3WEVYQD4HB/graph.json","events_json":"https://pith.science/api/pith-number/HSQENIV6HA7QR3FX3WEVYQD4HB/events.json","paper":"https://pith.science/paper/HSQENIV6"},"agent_actions":{"view_html":"https://pith.science/pith/HSQENIV6HA7QR3FX3WEVYQD4HB","download_json":"https://pith.science/pith/HSQENIV6HA7QR3FX3WEVYQD4HB.json","view_paper":"https://pith.science/paper/HSQENIV6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2012.10908&json=true","fetch_graph":"https://pith.science/api/pith-number/HSQENIV6HA7QR3FX3WEVYQD4HB/graph.json","fetch_events":"https://pith.science/api/pith-number/HSQENIV6HA7QR3FX3WEVYQD4HB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HSQENIV6HA7QR3FX3WEVYQD4HB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HSQENIV6HA7QR3FX3WEVYQD4HB/action/storage_attestation","attest_author":"https://pith.science/pith/HSQENIV6HA7QR3FX3WEVYQD4HB/action/author_attestation","sign_citation":"https://pith.science/pith/HSQENIV6HA7QR3FX3WEVYQD4HB/action/citation_signature","submit_replication":"https://pith.science/pith/HSQENIV6HA7QR3FX3WEVYQD4HB/action/replication_record"}},"created_at":"2026-07-05T07:11:49.650597+00:00","updated_at":"2026-07-05T07:11:49.650597+00:00"}