{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:3ASRWUE2ARA3CPHZQPK2XWASBY","short_pith_number":"pith:3ASRWUE2","schema_version":"1.0","canonical_sha256":"d8251b509a0441b13cf983d5abd8120e308c84001d5963b85e0fe85b706c211c","source":{"kind":"arxiv","id":"0710.3508","version":1},"attestation_state":"computed","paper":{"title":"Wavelet sets without groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gestur Olafsson, Mihaela Dobrescu","submitted_at":"2007-10-18T13:41:13Z","abstract_excerpt":"Most of the examples of wavelet sets are for dilation sets which are groups. We find a necessary and sufficient condition under which subspace wavelet sets exist for dilation sets of the form $A B$, which are not necessarily groups. We explain the construction by a few examples."},"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":"0710.3508","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2007-10-18T13:41:13Z","cross_cats_sorted":[],"title_canon_sha256":"e150728f5df8871073469e956105c812d2bbae95ededdf520f3f2218cd346577","abstract_canon_sha256":"52f5dacf24b31ce3dc5ecf06472749e17b278aa3567d9d8888e02d5b694638c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:05:01.245549Z","signature_b64":"xb2qda3yOwqf0Z/V6zmKTpT0cc1qVTw8Q+19mfAieCMDlwDE0gzDyrpo1KpAZrhGPSIWywarqXpfIbD/emyyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8251b509a0441b13cf983d5abd8120e308c84001d5963b85e0fe85b706c211c","last_reissued_at":"2026-07-04T15:05:01.245139Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:05:01.245139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wavelet sets without groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gestur Olafsson, Mihaela Dobrescu","submitted_at":"2007-10-18T13:41:13Z","abstract_excerpt":"Most of the examples of wavelet sets are for dilation sets which are groups. We find a necessary and sufficient condition under which subspace wavelet sets exist for dilation sets of the form $A B$, which are not necessarily groups. We explain the construction by a few examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3508","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0710.3508/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"0710.3508","created_at":"2026-07-04T15:05:01.245202+00:00"},{"alias_kind":"arxiv_version","alias_value":"0710.3508v1","created_at":"2026-07-04T15:05:01.245202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3508","created_at":"2026-07-04T15:05:01.245202+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ASRWUE2ARA3","created_at":"2026-07-04T15:05:01.245202+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ASRWUE2ARA3CPHZ","created_at":"2026-07-04T15:05:01.245202+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ASRWUE2","created_at":"2026-07-04T15:05:01.245202+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/3ASRWUE2ARA3CPHZQPK2XWASBY","json":"https://pith.science/pith/3ASRWUE2ARA3CPHZQPK2XWASBY.json","graph_json":"https://pith.science/api/pith-number/3ASRWUE2ARA3CPHZQPK2XWASBY/graph.json","events_json":"https://pith.science/api/pith-number/3ASRWUE2ARA3CPHZQPK2XWASBY/events.json","paper":"https://pith.science/paper/3ASRWUE2"},"agent_actions":{"view_html":"https://pith.science/pith/3ASRWUE2ARA3CPHZQPK2XWASBY","download_json":"https://pith.science/pith/3ASRWUE2ARA3CPHZQPK2XWASBY.json","view_paper":"https://pith.science/paper/3ASRWUE2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0710.3508&json=true","fetch_graph":"https://pith.science/api/pith-number/3ASRWUE2ARA3CPHZQPK2XWASBY/graph.json","fetch_events":"https://pith.science/api/pith-number/3ASRWUE2ARA3CPHZQPK2XWASBY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ASRWUE2ARA3CPHZQPK2XWASBY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ASRWUE2ARA3CPHZQPK2XWASBY/action/storage_attestation","attest_author":"https://pith.science/pith/3ASRWUE2ARA3CPHZQPK2XWASBY/action/author_attestation","sign_citation":"https://pith.science/pith/3ASRWUE2ARA3CPHZQPK2XWASBY/action/citation_signature","submit_replication":"https://pith.science/pith/3ASRWUE2ARA3CPHZQPK2XWASBY/action/replication_record"}},"created_at":"2026-07-04T15:05:01.245202+00:00","updated_at":"2026-07-04T15:05:01.245202+00:00"}