{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:M3A4DVPW6RA6TTLJBTPAPCDRDY","short_pith_number":"pith:M3A4DVPW","schema_version":"1.0","canonical_sha256":"66c1c1d5f6f441e9cd690cde0788711e380a5bb68279aefabae4ec79527aefee","source":{"kind":"arxiv","id":"funct-an/9301003","version":1},"attestation_state":"computed","paper":{"title":"A Factorization Theorem for Smooth Crossed Products","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"funct-an","authors_text":"Larry B. Schweitzer","submitted_at":"1993-01-29T01:55:37Z","abstract_excerpt":"We show that if E is a Frechet G\\rtimes S(M)-module, for which the canonical map from the projective completion G\\rtimes S(M) {\\widehat \\otimes} E to E is surjective, then every element of E can be written as a finite sum of elements of the form ae where e\\in E and a is an element of the smooth crossed product G\\rtimes S(M). We require that the Schwartz functions S(M) vanish rapidly with repsect to a continuous, proper map \\s : M ---> [0, \\infty)."},"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":"funct-an/9301003","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"funct-an","submitted_at":"1993-01-29T01:55:37Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"2f7ce5235e21b5bbfc13f242e0ac2aa3138976eca92c6ebd4ed425befc1aa96f","abstract_canon_sha256":"2b2f86a90d8ebd3c14fc12a6137ad34aa41da878036a45d4c95d147c8a477426"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:54.253264Z","signature_b64":"YP9Avv9pgNgAFGFybhsJpiriKdgFqMr5mDo5sdxUC1tptoJSLxs63GBQKbSShXtPhFE8T1nANKx/NbWOF5ntCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66c1c1d5f6f441e9cd690cde0788711e380a5bb68279aefabae4ec79527aefee","last_reissued_at":"2026-05-18T01:20:54.252496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:54.252496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Factorization Theorem for Smooth Crossed Products","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"funct-an","authors_text":"Larry B. Schweitzer","submitted_at":"1993-01-29T01:55:37Z","abstract_excerpt":"We show that if E is a Frechet G\\rtimes S(M)-module, for which the canonical map from the projective completion G\\rtimes S(M) {\\widehat \\otimes} E to E is surjective, then every element of E can be written as a finite sum of elements of the form ae where e\\in E and a is an element of the smooth crossed product G\\rtimes S(M). We require that the Schwartz functions S(M) vanish rapidly with repsect to a continuous, proper map \\s : M ---> [0, \\infty)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"funct-an/9301003","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":"funct-an/9301003","created_at":"2026-05-18T01:20:54.252612+00:00"},{"alias_kind":"arxiv_version","alias_value":"funct-an/9301003v1","created_at":"2026-05-18T01:20:54.252612+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.funct-an/9301003","created_at":"2026-05-18T01:20:54.252612+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3A4DVPW6RA6","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3A4DVPW6RA6TTLJ","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3A4DVPW","created_at":"2026-05-18T12:25:47.102015+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/M3A4DVPW6RA6TTLJBTPAPCDRDY","json":"https://pith.science/pith/M3A4DVPW6RA6TTLJBTPAPCDRDY.json","graph_json":"https://pith.science/api/pith-number/M3A4DVPW6RA6TTLJBTPAPCDRDY/graph.json","events_json":"https://pith.science/api/pith-number/M3A4DVPW6RA6TTLJBTPAPCDRDY/events.json","paper":"https://pith.science/paper/M3A4DVPW"},"agent_actions":{"view_html":"https://pith.science/pith/M3A4DVPW6RA6TTLJBTPAPCDRDY","download_json":"https://pith.science/pith/M3A4DVPW6RA6TTLJBTPAPCDRDY.json","view_paper":"https://pith.science/paper/M3A4DVPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=funct-an/9301003&json=true","fetch_graph":"https://pith.science/api/pith-number/M3A4DVPW6RA6TTLJBTPAPCDRDY/graph.json","fetch_events":"https://pith.science/api/pith-number/M3A4DVPW6RA6TTLJBTPAPCDRDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3A4DVPW6RA6TTLJBTPAPCDRDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3A4DVPW6RA6TTLJBTPAPCDRDY/action/storage_attestation","attest_author":"https://pith.science/pith/M3A4DVPW6RA6TTLJBTPAPCDRDY/action/author_attestation","sign_citation":"https://pith.science/pith/M3A4DVPW6RA6TTLJBTPAPCDRDY/action/citation_signature","submit_replication":"https://pith.science/pith/M3A4DVPW6RA6TTLJBTPAPCDRDY/action/replication_record"}},"created_at":"2026-05-18T01:20:54.252612+00:00","updated_at":"2026-05-18T01:20:54.252612+00:00"}