{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PWVJ4TIHRF5UF6NXHJUIGCDSRS","short_pith_number":"pith:PWVJ4TIH","schema_version":"1.0","canonical_sha256":"7daa9e4d07897b42f9b73a688308728c995f61bd755038151772e61bfc2cbbd7","source":{"kind":"arxiv","id":"2406.00404","version":1},"attestation_state":"computed","paper":{"title":"The universal property of bordism of commuting involutions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Markus Hausmann, Stefan Schwede","submitted_at":"2024-06-01T11:14:54Z","abstract_excerpt":"We propose a formalism to capture the structure of the equivariant bordism rings of smooth manifolds with commuting involutions. We introduce the concept of an oriented el$_2^{RO}$-algebra, an algebraic structure featuring representation graded rings for all elementary abelian 2-groups, connected by restriction homomorphisms, a pre-Euler class, and an inverse Thom class; this data is subject to one exactness property. Besides equivariant bordism, oriented global ring spectra also give rise to oriented el$_2^{RO}$-algebras, so examples abound. Inverting the inverse Thom classes yields a global "},"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":"2406.00404","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-06-01T11:14:54Z","cross_cats_sorted":[],"title_canon_sha256":"082d1e4a954de3d127fd68c20b57cb267f23e184fd435a1c2426bf9fb4138485","abstract_canon_sha256":"d05e4f473fc4c0de5f1de5a41d7bdec01c594a57461d770f54fb2e55d679a506"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:01.482443Z","signature_b64":"fBJn7QYVterJ/J6xX9m/8y3i4Bg+7/BIy1yQmfnxtU6HOdRXQ0rygXTJK2C+K2IEpiw5SEpeq3n6Q83a07eGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7daa9e4d07897b42f9b73a688308728c995f61bd755038151772e61bfc2cbbd7","last_reissued_at":"2026-07-05T08:26:01.481811Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:01.481811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The universal property of bordism of commuting involutions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Markus Hausmann, Stefan Schwede","submitted_at":"2024-06-01T11:14:54Z","abstract_excerpt":"We propose a formalism to capture the structure of the equivariant bordism rings of smooth manifolds with commuting involutions. We introduce the concept of an oriented el$_2^{RO}$-algebra, an algebraic structure featuring representation graded rings for all elementary abelian 2-groups, connected by restriction homomorphisms, a pre-Euler class, and an inverse Thom class; this data is subject to one exactness property. Besides equivariant bordism, oriented global ring spectra also give rise to oriented el$_2^{RO}$-algebras, so examples abound. Inverting the inverse Thom classes yields a global "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.00404","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/2406.00404/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":"2406.00404","created_at":"2026-07-05T08:26:01.481879+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.00404v1","created_at":"2026-07-05T08:26:01.481879+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.00404","created_at":"2026-07-05T08:26:01.481879+00:00"},{"alias_kind":"pith_short_12","alias_value":"PWVJ4TIHRF5U","created_at":"2026-07-05T08:26:01.481879+00:00"},{"alias_kind":"pith_short_16","alias_value":"PWVJ4TIHRF5UF6NX","created_at":"2026-07-05T08:26:01.481879+00:00"},{"alias_kind":"pith_short_8","alias_value":"PWVJ4TIH","created_at":"2026-07-05T08:26:01.481879+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/PWVJ4TIHRF5UF6NXHJUIGCDSRS","json":"https://pith.science/pith/PWVJ4TIHRF5UF6NXHJUIGCDSRS.json","graph_json":"https://pith.science/api/pith-number/PWVJ4TIHRF5UF6NXHJUIGCDSRS/graph.json","events_json":"https://pith.science/api/pith-number/PWVJ4TIHRF5UF6NXHJUIGCDSRS/events.json","paper":"https://pith.science/paper/PWVJ4TIH"},"agent_actions":{"view_html":"https://pith.science/pith/PWVJ4TIHRF5UF6NXHJUIGCDSRS","download_json":"https://pith.science/pith/PWVJ4TIHRF5UF6NXHJUIGCDSRS.json","view_paper":"https://pith.science/paper/PWVJ4TIH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.00404&json=true","fetch_graph":"https://pith.science/api/pith-number/PWVJ4TIHRF5UF6NXHJUIGCDSRS/graph.json","fetch_events":"https://pith.science/api/pith-number/PWVJ4TIHRF5UF6NXHJUIGCDSRS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PWVJ4TIHRF5UF6NXHJUIGCDSRS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PWVJ4TIHRF5UF6NXHJUIGCDSRS/action/storage_attestation","attest_author":"https://pith.science/pith/PWVJ4TIHRF5UF6NXHJUIGCDSRS/action/author_attestation","sign_citation":"https://pith.science/pith/PWVJ4TIHRF5UF6NXHJUIGCDSRS/action/citation_signature","submit_replication":"https://pith.science/pith/PWVJ4TIHRF5UF6NXHJUIGCDSRS/action/replication_record"}},"created_at":"2026-07-05T08:26:01.481879+00:00","updated_at":"2026-07-05T08:26:01.481879+00:00"}