{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6OBT3F5CBQ2JDPQ5EXTCYYS5MC","short_pith_number":"pith:6OBT3F5C","schema_version":"1.0","canonical_sha256":"f3833d97a20c3491be1d25e62c625d608233f62463b707350dfbb6570fec438b","source":{"kind":"arxiv","id":"2607.01889","version":1},"attestation_state":"computed","paper":{"title":"Reduced characteristic number criteria for equivariant bordism of $T^k$- and $(\\mathbb{Z}_2)^k$-manifolds with isolated fixed points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Leqi Yang, Runze Chen, Zhi L\\\"u","submitted_at":"2026-07-02T08:39:30Z","abstract_excerpt":"Classical equivariant bordism theories require computing the full collection of equivariant characteristic numbers to detect whether an equivariant manifold bounds equivariantly or not. This paper establishes simplified equivariant bordism characterizations for two families of equivariant manifolds with isolated fixed points: unitary $T^k$-manifolds and closed smooth $(\\mathbb{Z}_2)^k$-manifolds. For any unitary $T^k$-manifold $M$ with isolated fixed points, we establish an equivariant unitary bordism criterion built entirely from a single polynomial of equivariant Chern classes. We further in"},"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":"2607.01889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-07-02T08:39:30Z","cross_cats_sorted":[],"title_canon_sha256":"fe3353bf3801fd4daec6f1c5ede8e2a1eb71b85b9ae98f014e7c92f356a79b82","abstract_canon_sha256":"c1db11968c80a2d0aa2153f005b88f9ae8eab068c527d1806a2924c5cf264ee5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:32.670382Z","signature_b64":"ph0jyeWQZXQZSo0ysNnHR238hrsxBhJ+AZKUeRIwxeAWTyGun0E21SEWFnsdFOoLfOIVFEGq+P0SouXuqAySCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3833d97a20c3491be1d25e62c625d608233f62463b707350dfbb6570fec438b","last_reissued_at":"2026-07-03T01:17:32.669967Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:32.669967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reduced characteristic number criteria for equivariant bordism of $T^k$- and $(\\mathbb{Z}_2)^k$-manifolds with isolated fixed points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Leqi Yang, Runze Chen, Zhi L\\\"u","submitted_at":"2026-07-02T08:39:30Z","abstract_excerpt":"Classical equivariant bordism theories require computing the full collection of equivariant characteristic numbers to detect whether an equivariant manifold bounds equivariantly or not. This paper establishes simplified equivariant bordism characterizations for two families of equivariant manifolds with isolated fixed points: unitary $T^k$-manifolds and closed smooth $(\\mathbb{Z}_2)^k$-manifolds. For any unitary $T^k$-manifold $M$ with isolated fixed points, we establish an equivariant unitary bordism criterion built entirely from a single polynomial of equivariant Chern classes. We further in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01889","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/2607.01889/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":"2607.01889","created_at":"2026-07-03T01:17:32.670031+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.01889v1","created_at":"2026-07-03T01:17:32.670031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01889","created_at":"2026-07-03T01:17:32.670031+00:00"},{"alias_kind":"pith_short_12","alias_value":"6OBT3F5CBQ2J","created_at":"2026-07-03T01:17:32.670031+00:00"},{"alias_kind":"pith_short_16","alias_value":"6OBT3F5CBQ2JDPQ5","created_at":"2026-07-03T01:17:32.670031+00:00"},{"alias_kind":"pith_short_8","alias_value":"6OBT3F5C","created_at":"2026-07-03T01:17:32.670031+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/6OBT3F5CBQ2JDPQ5EXTCYYS5MC","json":"https://pith.science/pith/6OBT3F5CBQ2JDPQ5EXTCYYS5MC.json","graph_json":"https://pith.science/api/pith-number/6OBT3F5CBQ2JDPQ5EXTCYYS5MC/graph.json","events_json":"https://pith.science/api/pith-number/6OBT3F5CBQ2JDPQ5EXTCYYS5MC/events.json","paper":"https://pith.science/paper/6OBT3F5C"},"agent_actions":{"view_html":"https://pith.science/pith/6OBT3F5CBQ2JDPQ5EXTCYYS5MC","download_json":"https://pith.science/pith/6OBT3F5CBQ2JDPQ5EXTCYYS5MC.json","view_paper":"https://pith.science/paper/6OBT3F5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.01889&json=true","fetch_graph":"https://pith.science/api/pith-number/6OBT3F5CBQ2JDPQ5EXTCYYS5MC/graph.json","fetch_events":"https://pith.science/api/pith-number/6OBT3F5CBQ2JDPQ5EXTCYYS5MC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6OBT3F5CBQ2JDPQ5EXTCYYS5MC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6OBT3F5CBQ2JDPQ5EXTCYYS5MC/action/storage_attestation","attest_author":"https://pith.science/pith/6OBT3F5CBQ2JDPQ5EXTCYYS5MC/action/author_attestation","sign_citation":"https://pith.science/pith/6OBT3F5CBQ2JDPQ5EXTCYYS5MC/action/citation_signature","submit_replication":"https://pith.science/pith/6OBT3F5CBQ2JDPQ5EXTCYYS5MC/action/replication_record"}},"created_at":"2026-07-03T01:17:32.670031+00:00","updated_at":"2026-07-03T01:17:32.670031+00:00"}