{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:WHQDTCBAFNWFA3GK56AHVQRFO3","short_pith_number":"pith:WHQDTCBA","schema_version":"1.0","canonical_sha256":"b1e03988202b6c506ccaef807ac22576defbf74ad2f37aa9007dba3e46e46ef2","source":{"kind":"arxiv","id":"0905.3486","version":2},"attestation_state":"computed","paper":{"title":"Spectral multiplicities for infinite measure preserving transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DS","authors_text":"Alexandre I. Danilenko, Valery V. Ryzhikov","submitted_at":"2009-05-21T13:12:00Z","abstract_excerpt":"Each subset $E\\subset\\Bbb N$ is realized as the set of essential values of the multiplicity function for the Koopman operator of an ergodic conservative infinite measure preserving transformation."},"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":"0905.3486","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-05-21T13:12:00Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"5491b47b608cfa3fa190c76f3934124f4e4f450bfc74d8e078321edb2c240c1f","abstract_canon_sha256":"83c61c4dc137a778aedafe1059527524ac3232cc868dea86279655cee86a9614"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:44.125986Z","signature_b64":"zvP8wxJ9hKDfUMWJjCN+IDxpL1qkrPqan4M+LAukmlCO7a5wEWS5ep4AYdQUvjv7Hku/hDg/FbsOpepoItyECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1e03988202b6c506ccaef807ac22576defbf74ad2f37aa9007dba3e46e46ef2","last_reissued_at":"2026-05-18T04:41:44.125420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:44.125420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral multiplicities for infinite measure preserving transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DS","authors_text":"Alexandre I. Danilenko, Valery V. Ryzhikov","submitted_at":"2009-05-21T13:12:00Z","abstract_excerpt":"Each subset $E\\subset\\Bbb N$ is realized as the set of essential values of the multiplicity function for the Koopman operator of an ergodic conservative infinite measure preserving transformation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3486","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":"0905.3486","created_at":"2026-05-18T04:41:44.125508+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.3486v2","created_at":"2026-05-18T04:41:44.125508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3486","created_at":"2026-05-18T04:41:44.125508+00:00"},{"alias_kind":"pith_short_12","alias_value":"WHQDTCBAFNWF","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"WHQDTCBAFNWFA3GK","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"WHQDTCBA","created_at":"2026-05-18T12:26:02.257875+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/WHQDTCBAFNWFA3GK56AHVQRFO3","json":"https://pith.science/pith/WHQDTCBAFNWFA3GK56AHVQRFO3.json","graph_json":"https://pith.science/api/pith-number/WHQDTCBAFNWFA3GK56AHVQRFO3/graph.json","events_json":"https://pith.science/api/pith-number/WHQDTCBAFNWFA3GK56AHVQRFO3/events.json","paper":"https://pith.science/paper/WHQDTCBA"},"agent_actions":{"view_html":"https://pith.science/pith/WHQDTCBAFNWFA3GK56AHVQRFO3","download_json":"https://pith.science/pith/WHQDTCBAFNWFA3GK56AHVQRFO3.json","view_paper":"https://pith.science/paper/WHQDTCBA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.3486&json=true","fetch_graph":"https://pith.science/api/pith-number/WHQDTCBAFNWFA3GK56AHVQRFO3/graph.json","fetch_events":"https://pith.science/api/pith-number/WHQDTCBAFNWFA3GK56AHVQRFO3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WHQDTCBAFNWFA3GK56AHVQRFO3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WHQDTCBAFNWFA3GK56AHVQRFO3/action/storage_attestation","attest_author":"https://pith.science/pith/WHQDTCBAFNWFA3GK56AHVQRFO3/action/author_attestation","sign_citation":"https://pith.science/pith/WHQDTCBAFNWFA3GK56AHVQRFO3/action/citation_signature","submit_replication":"https://pith.science/pith/WHQDTCBAFNWFA3GK56AHVQRFO3/action/replication_record"}},"created_at":"2026-05-18T04:41:44.125508+00:00","updated_at":"2026-05-18T04:41:44.125508+00:00"}