{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VUHWDGWWPKD53UG5VJQHRK7J7D","short_pith_number":"pith:VUHWDGWW","schema_version":"1.0","canonical_sha256":"ad0f619ad67a87ddd0ddaa6078abe9f8ff219c56b119859a1208be551f51922a","source":{"kind":"arxiv","id":"1504.08064","version":1},"attestation_state":"computed","paper":{"title":"Periodic Cyclic Homology and Equivariant Gerbes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DG"],"primary_cat":"math.KT","authors_text":"Jean-Louis Tu, Ping Xu","submitted_at":"2015-04-30T02:59:29Z","abstract_excerpt":"This paper is our first step in establishing a de Rham model for equivariant twisted $K$-theory using machinery from noncommutative geometry. Let $G$ be a compact Lie group, $M$ a compact manifold on which $G$ acts smoothly. For any $\\alpha \\in H^3_G (M, {\\mathbb Z})$ we introduce a notion of localized equivariant twisted cohomology $H^\\bullet ({\\bar{\\Omega}}^\\bullet (M, G, L)_g, d^\\alpha_{G^g})$, indexed by $g\\in G$. We prove that there exists a natural family of chain maps, indexed by $g\\in G$, inducing a family of morphisms from the equivariant periodic cyclic homology $HP^G_\\bullet ( C^\\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":"1504.08064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2015-04-30T02:59:29Z","cross_cats_sorted":["math.AT","math.DG"],"title_canon_sha256":"d9f784ffb6bfe52244dd21c56426df531928327c73a8a8fe26b89560804bc564","abstract_canon_sha256":"a659d9e488a9a3376fd90c2a713e262cdd587a77590580b311f87b179c882da0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:23.413633Z","signature_b64":"rl4aA4P8G7crCG+rT1JGWcV1+wvfSPtrorTXLzkm8B99ybC82myg/wQWRJanGlAuPB1dAkupN+Ev0rsZr2kXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad0f619ad67a87ddd0ddaa6078abe9f8ff219c56b119859a1208be551f51922a","last_reissued_at":"2026-05-18T02:17:23.412813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:23.412813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periodic Cyclic Homology and Equivariant Gerbes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DG"],"primary_cat":"math.KT","authors_text":"Jean-Louis Tu, Ping Xu","submitted_at":"2015-04-30T02:59:29Z","abstract_excerpt":"This paper is our first step in establishing a de Rham model for equivariant twisted $K$-theory using machinery from noncommutative geometry. Let $G$ be a compact Lie group, $M$ a compact manifold on which $G$ acts smoothly. For any $\\alpha \\in H^3_G (M, {\\mathbb Z})$ we introduce a notion of localized equivariant twisted cohomology $H^\\bullet ({\\bar{\\Omega}}^\\bullet (M, G, L)_g, d^\\alpha_{G^g})$, indexed by $g\\in G$. We prove that there exists a natural family of chain maps, indexed by $g\\in G$, inducing a family of morphisms from the equivariant periodic cyclic homology $HP^G_\\bullet ( C^\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08064","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":"1504.08064","created_at":"2026-05-18T02:17:23.412960+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.08064v1","created_at":"2026-05-18T02:17:23.412960+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08064","created_at":"2026-05-18T02:17:23.412960+00:00"},{"alias_kind":"pith_short_12","alias_value":"VUHWDGWWPKD5","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VUHWDGWWPKD53UG5","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VUHWDGWW","created_at":"2026-05-18T12:29:47.479230+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/VUHWDGWWPKD53UG5VJQHRK7J7D","json":"https://pith.science/pith/VUHWDGWWPKD53UG5VJQHRK7J7D.json","graph_json":"https://pith.science/api/pith-number/VUHWDGWWPKD53UG5VJQHRK7J7D/graph.json","events_json":"https://pith.science/api/pith-number/VUHWDGWWPKD53UG5VJQHRK7J7D/events.json","paper":"https://pith.science/paper/VUHWDGWW"},"agent_actions":{"view_html":"https://pith.science/pith/VUHWDGWWPKD53UG5VJQHRK7J7D","download_json":"https://pith.science/pith/VUHWDGWWPKD53UG5VJQHRK7J7D.json","view_paper":"https://pith.science/paper/VUHWDGWW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.08064&json=true","fetch_graph":"https://pith.science/api/pith-number/VUHWDGWWPKD53UG5VJQHRK7J7D/graph.json","fetch_events":"https://pith.science/api/pith-number/VUHWDGWWPKD53UG5VJQHRK7J7D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VUHWDGWWPKD53UG5VJQHRK7J7D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VUHWDGWWPKD53UG5VJQHRK7J7D/action/storage_attestation","attest_author":"https://pith.science/pith/VUHWDGWWPKD53UG5VJQHRK7J7D/action/author_attestation","sign_citation":"https://pith.science/pith/VUHWDGWWPKD53UG5VJQHRK7J7D/action/citation_signature","submit_replication":"https://pith.science/pith/VUHWDGWWPKD53UG5VJQHRK7J7D/action/replication_record"}},"created_at":"2026-05-18T02:17:23.412960+00:00","updated_at":"2026-05-18T02:17:23.412960+00:00"}