{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TONXANCKU7EMYL7TNLAHT77HLQ","short_pith_number":"pith:TONXANCK","schema_version":"1.0","canonical_sha256":"9b9b70344aa7c8cc2ff36ac079ffe75c1dac917108f66432b5017ddf5f1bf57d","source":{"kind":"arxiv","id":"1508.01556","version":2},"attestation_state":"computed","paper":{"title":"Smooth Kuranishi atlases with isotropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dusa McDuff, Katrin Wehrheim","submitted_at":"2015-08-06T22:33:40Z","abstract_excerpt":"Kuranishi structures were introduced in the 1990s by Fukaya and Ono for the purpose of assigning a virtual cycle to moduli spaces of pseudoholomorphic curves that cannot be regularized by geometric methods. Their core idea was to build such a cycle by patching local finite dimensional reductions, given by smooth sections that are equivariant under a finite isotropy group.\n  Building on our notions of topological Kuranishi atlases and perturbation constructions in the case of trivial isotropy, we develop a theory of Kuranishi atlases and cobordisms that transparently resolves the challenges pos"},"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":"1508.01556","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-08-06T22:33:40Z","cross_cats_sorted":[],"title_canon_sha256":"acc4f6b5894bdeb7e684d7c34f6249c3a4422d66f25fd57b5d17ba09d2ecb2dc","abstract_canon_sha256":"045a67f27087aa22352478080d95a90c7499e7771c430193771603365fb7ece7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:00.288375Z","signature_b64":"r3HOnsCqLa6sYkNX/JYHhIWNWnC5OGEMSKrogXx/4WFIFoHt94lCUTr1G14It2QJeLugNsZjcz0mO//gnQnPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b9b70344aa7c8cc2ff36ac079ffe75c1dac917108f66432b5017ddf5f1bf57d","last_reissued_at":"2026-05-18T00:21:00.287830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:00.287830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smooth Kuranishi atlases with isotropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dusa McDuff, Katrin Wehrheim","submitted_at":"2015-08-06T22:33:40Z","abstract_excerpt":"Kuranishi structures were introduced in the 1990s by Fukaya and Ono for the purpose of assigning a virtual cycle to moduli spaces of pseudoholomorphic curves that cannot be regularized by geometric methods. Their core idea was to build such a cycle by patching local finite dimensional reductions, given by smooth sections that are equivariant under a finite isotropy group.\n  Building on our notions of topological Kuranishi atlases and perturbation constructions in the case of trivial isotropy, we develop a theory of Kuranishi atlases and cobordisms that transparently resolves the challenges pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01556","kind":"arxiv","version":2},"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":"1508.01556","created_at":"2026-05-18T00:21:00.287923+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.01556v2","created_at":"2026-05-18T00:21:00.287923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01556","created_at":"2026-05-18T00:21:00.287923+00:00"},{"alias_kind":"pith_short_12","alias_value":"TONXANCKU7EM","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TONXANCKU7EMYL7T","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TONXANCK","created_at":"2026-05-18T12:29:42.218222+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/TONXANCKU7EMYL7TNLAHT77HLQ","json":"https://pith.science/pith/TONXANCKU7EMYL7TNLAHT77HLQ.json","graph_json":"https://pith.science/api/pith-number/TONXANCKU7EMYL7TNLAHT77HLQ/graph.json","events_json":"https://pith.science/api/pith-number/TONXANCKU7EMYL7TNLAHT77HLQ/events.json","paper":"https://pith.science/paper/TONXANCK"},"agent_actions":{"view_html":"https://pith.science/pith/TONXANCKU7EMYL7TNLAHT77HLQ","download_json":"https://pith.science/pith/TONXANCKU7EMYL7TNLAHT77HLQ.json","view_paper":"https://pith.science/paper/TONXANCK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.01556&json=true","fetch_graph":"https://pith.science/api/pith-number/TONXANCKU7EMYL7TNLAHT77HLQ/graph.json","fetch_events":"https://pith.science/api/pith-number/TONXANCKU7EMYL7TNLAHT77HLQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TONXANCKU7EMYL7TNLAHT77HLQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TONXANCKU7EMYL7TNLAHT77HLQ/action/storage_attestation","attest_author":"https://pith.science/pith/TONXANCKU7EMYL7TNLAHT77HLQ/action/author_attestation","sign_citation":"https://pith.science/pith/TONXANCKU7EMYL7TNLAHT77HLQ/action/citation_signature","submit_replication":"https://pith.science/pith/TONXANCKU7EMYL7TNLAHT77HLQ/action/replication_record"}},"created_at":"2026-05-18T00:21:00.287923+00:00","updated_at":"2026-05-18T00:21:00.287923+00:00"}