{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:T6W333KJZL5GB6YPZBAMNDQ4EM","short_pith_number":"pith:T6W333KJ","schema_version":"1.0","canonical_sha256":"9fadbded49cafa60fb0fc840c68e1c232c02dacce0ed2e18c0e70579e5c58bbb","source":{"kind":"arxiv","id":"1109.5394","version":3},"attestation_state":"computed","paper":{"title":"Dualization invariance and a new complex elliptic genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Stefan Schreieder","submitted_at":"2011-09-25T20:27:04Z","abstract_excerpt":"We define a new elliptic genus psi on the complex bordism ring. With coefficients in Z[1/2], we prove that it induces an isomorphism of the complex bordism ring modulo the ideal which is generated by all differences P(E)-P(E*) of projective bundles and their duals onto a polynomial ring on 4 generators in degrees 2, 4, 6 and 8. As an alternative geometric description of psi, we prove that it is the universal genus which is multiplicative in projective bundles over Calabi-Yau 3-folds. With the help of the q-expansion of modular forms we will see that for a complex manifold M, the value psi(M) i"},"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":"1109.5394","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-09-25T20:27:04Z","cross_cats_sorted":[],"title_canon_sha256":"fafb2c68c059da78f25cffabab68ccd018632baf5e70183651b68032b99de263","abstract_canon_sha256":"0523d505ae240eb15c5ed70703e7744b60032dd937be426134f2fb6582b7e8c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:02.530109Z","signature_b64":"SXlVH2yGYOeulDxV+Xg0hY7VzSII9IoRT7xbDhREDHeozDBhJI5aXx9GJ34Ukds1296EUB7gGL/ZGBWFwip+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fadbded49cafa60fb0fc840c68e1c232c02dacce0ed2e18c0e70579e5c58bbb","last_reissued_at":"2026-05-18T00:02:02.529629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:02.529629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dualization invariance and a new complex elliptic genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Stefan Schreieder","submitted_at":"2011-09-25T20:27:04Z","abstract_excerpt":"We define a new elliptic genus psi on the complex bordism ring. With coefficients in Z[1/2], we prove that it induces an isomorphism of the complex bordism ring modulo the ideal which is generated by all differences P(E)-P(E*) of projective bundles and their duals onto a polynomial ring on 4 generators in degrees 2, 4, 6 and 8. As an alternative geometric description of psi, we prove that it is the universal genus which is multiplicative in projective bundles over Calabi-Yau 3-folds. With the help of the q-expansion of modular forms we will see that for a complex manifold M, the value psi(M) i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5394","kind":"arxiv","version":3},"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":"1109.5394","created_at":"2026-05-18T00:02:02.529696+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5394v3","created_at":"2026-05-18T00:02:02.529696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5394","created_at":"2026-05-18T00:02:02.529696+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6W333KJZL5G","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6W333KJZL5GB6YP","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6W333KJ","created_at":"2026-05-18T12:26:41.206345+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/T6W333KJZL5GB6YPZBAMNDQ4EM","json":"https://pith.science/pith/T6W333KJZL5GB6YPZBAMNDQ4EM.json","graph_json":"https://pith.science/api/pith-number/T6W333KJZL5GB6YPZBAMNDQ4EM/graph.json","events_json":"https://pith.science/api/pith-number/T6W333KJZL5GB6YPZBAMNDQ4EM/events.json","paper":"https://pith.science/paper/T6W333KJ"},"agent_actions":{"view_html":"https://pith.science/pith/T6W333KJZL5GB6YPZBAMNDQ4EM","download_json":"https://pith.science/pith/T6W333KJZL5GB6YPZBAMNDQ4EM.json","view_paper":"https://pith.science/paper/T6W333KJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5394&json=true","fetch_graph":"https://pith.science/api/pith-number/T6W333KJZL5GB6YPZBAMNDQ4EM/graph.json","fetch_events":"https://pith.science/api/pith-number/T6W333KJZL5GB6YPZBAMNDQ4EM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6W333KJZL5GB6YPZBAMNDQ4EM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6W333KJZL5GB6YPZBAMNDQ4EM/action/storage_attestation","attest_author":"https://pith.science/pith/T6W333KJZL5GB6YPZBAMNDQ4EM/action/author_attestation","sign_citation":"https://pith.science/pith/T6W333KJZL5GB6YPZBAMNDQ4EM/action/citation_signature","submit_replication":"https://pith.science/pith/T6W333KJZL5GB6YPZBAMNDQ4EM/action/replication_record"}},"created_at":"2026-05-18T00:02:02.529696+00:00","updated_at":"2026-05-18T00:02:02.529696+00:00"}