{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ANS7XK7CZDZRGW4FPNFBSCBKY7","short_pith_number":"pith:ANS7XK7C","schema_version":"1.0","canonical_sha256":"0365fbabe2c8f3135b857b4a19082ac7dc52824e7c6e9b0ac191c4e3552ae0a1","source":{"kind":"arxiv","id":"1007.2402","version":4},"attestation_state":"computed","paper":{"title":"Functional equations for orbifold wreath products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AT","authors_text":"Carla Farsi, Christopher Seaton","submitted_at":"2010-07-14T19:44:51Z","abstract_excerpt":"We present generating functions for extensions of multiplicative invariants of wreath symmetric products of orbifolds presented as the quotient by the locally free action of a compact, connected Lie group in terms of orbifold sector decompositions. Particularly interesting instances of these product formulas occur for the Euler and Euler--Satake characteristics, which we compute for a class of weighted projective spaces. This generalizes results known for global quotients by finite groups to all closed, effective orbifolds. We also describe a combinatorial approach to extensions of multiplicat"},"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":"1007.2402","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-07-14T19:44:51Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4c376490ca0321b65fa9bf85a7bcf55b82bd0988937550dfb62c2adbcb46d1a4","abstract_canon_sha256":"fb81a5bcb70f1466e23ddbb2f3709c6b7d8ed502779ef446ce9e8cc70412188c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:44.681905Z","signature_b64":"pkQ7KTUgJ14lnIX1+GYErl+lqg3ljtoZrwuln11U+JqVx+H/idmZZH/OGYU0vO8qnxhzRelIyP+VIw3A6fhOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0365fbabe2c8f3135b857b4a19082ac7dc52824e7c6e9b0ac191c4e3552ae0a1","last_reissued_at":"2026-05-17T23:53:44.681475Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:44.681475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional equations for orbifold wreath products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AT","authors_text":"Carla Farsi, Christopher Seaton","submitted_at":"2010-07-14T19:44:51Z","abstract_excerpt":"We present generating functions for extensions of multiplicative invariants of wreath symmetric products of orbifolds presented as the quotient by the locally free action of a compact, connected Lie group in terms of orbifold sector decompositions. Particularly interesting instances of these product formulas occur for the Euler and Euler--Satake characteristics, which we compute for a class of weighted projective spaces. This generalizes results known for global quotients by finite groups to all closed, effective orbifolds. We also describe a combinatorial approach to extensions of multiplicat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2402","kind":"arxiv","version":4},"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":"1007.2402","created_at":"2026-05-17T23:53:44.681539+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.2402v4","created_at":"2026-05-17T23:53:44.681539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2402","created_at":"2026-05-17T23:53:44.681539+00:00"},{"alias_kind":"pith_short_12","alias_value":"ANS7XK7CZDZR","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"ANS7XK7CZDZRGW4F","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"ANS7XK7C","created_at":"2026-05-18T12:26:05.355336+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/ANS7XK7CZDZRGW4FPNFBSCBKY7","json":"https://pith.science/pith/ANS7XK7CZDZRGW4FPNFBSCBKY7.json","graph_json":"https://pith.science/api/pith-number/ANS7XK7CZDZRGW4FPNFBSCBKY7/graph.json","events_json":"https://pith.science/api/pith-number/ANS7XK7CZDZRGW4FPNFBSCBKY7/events.json","paper":"https://pith.science/paper/ANS7XK7C"},"agent_actions":{"view_html":"https://pith.science/pith/ANS7XK7CZDZRGW4FPNFBSCBKY7","download_json":"https://pith.science/pith/ANS7XK7CZDZRGW4FPNFBSCBKY7.json","view_paper":"https://pith.science/paper/ANS7XK7C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.2402&json=true","fetch_graph":"https://pith.science/api/pith-number/ANS7XK7CZDZRGW4FPNFBSCBKY7/graph.json","fetch_events":"https://pith.science/api/pith-number/ANS7XK7CZDZRGW4FPNFBSCBKY7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ANS7XK7CZDZRGW4FPNFBSCBKY7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ANS7XK7CZDZRGW4FPNFBSCBKY7/action/storage_attestation","attest_author":"https://pith.science/pith/ANS7XK7CZDZRGW4FPNFBSCBKY7/action/author_attestation","sign_citation":"https://pith.science/pith/ANS7XK7CZDZRGW4FPNFBSCBKY7/action/citation_signature","submit_replication":"https://pith.science/pith/ANS7XK7CZDZRGW4FPNFBSCBKY7/action/replication_record"}},"created_at":"2026-05-17T23:53:44.681539+00:00","updated_at":"2026-05-17T23:53:44.681539+00:00"}