{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XEO6Z6EEQRUU7B5SNIFX623ZYT","short_pith_number":"pith:XEO6Z6EE","schema_version":"1.0","canonical_sha256":"b91decf88484694f87b26a0b7f6b79c4d10c47ac5f009657d19753c1c489f967","source":{"kind":"arxiv","id":"1209.0666","version":2},"attestation_state":"computed","paper":{"title":"On the universal tiling conjecture in dimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dorin Ervin Dutkay, Palle E. T. Jorgensen","submitted_at":"2012-09-04T15:02:39Z","abstract_excerpt":"We show that the spectral-tile implication in the Fuglede conjecture in dimension 1 is equivalent to a Universal Tiling Conjecture and also to similar forms of the same implication for some simpler sets, such as unions of intervals with rational or integer endpoints."},"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":"1209.0666","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-04T15:02:39Z","cross_cats_sorted":[],"title_canon_sha256":"a9e7e94d2f974f8cf5af1002301295b4a127968ec0ec17198ae53f0db0d3a807","abstract_canon_sha256":"02f33e05222a008eade510c7f6a5031cf6cd29135851fa8fe5b6ad8028855396"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:38.295265Z","signature_b64":"LN55fM2ENR3W3kXv3kYJDj4hNIaso1OhdvJLPqRIfoWdCjH4NLVRh9zxv24LDEF9mo+m2vCG/n9Rskc5EpnYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b91decf88484694f87b26a0b7f6b79c4d10c47ac5f009657d19753c1c489f967","last_reissued_at":"2026-05-18T03:35:38.294301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:38.294301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the universal tiling conjecture in dimension one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dorin Ervin Dutkay, Palle E. T. Jorgensen","submitted_at":"2012-09-04T15:02:39Z","abstract_excerpt":"We show that the spectral-tile implication in the Fuglede conjecture in dimension 1 is equivalent to a Universal Tiling Conjecture and also to similar forms of the same implication for some simpler sets, such as unions of intervals with rational or integer endpoints."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0666","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":"1209.0666","created_at":"2026-05-18T03:35:38.294478+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.0666v2","created_at":"2026-05-18T03:35:38.294478+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0666","created_at":"2026-05-18T03:35:38.294478+00:00"},{"alias_kind":"pith_short_12","alias_value":"XEO6Z6EEQRUU","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XEO6Z6EEQRUU7B5S","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XEO6Z6EE","created_at":"2026-05-18T12:27:27.928770+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/XEO6Z6EEQRUU7B5SNIFX623ZYT","json":"https://pith.science/pith/XEO6Z6EEQRUU7B5SNIFX623ZYT.json","graph_json":"https://pith.science/api/pith-number/XEO6Z6EEQRUU7B5SNIFX623ZYT/graph.json","events_json":"https://pith.science/api/pith-number/XEO6Z6EEQRUU7B5SNIFX623ZYT/events.json","paper":"https://pith.science/paper/XEO6Z6EE"},"agent_actions":{"view_html":"https://pith.science/pith/XEO6Z6EEQRUU7B5SNIFX623ZYT","download_json":"https://pith.science/pith/XEO6Z6EEQRUU7B5SNIFX623ZYT.json","view_paper":"https://pith.science/paper/XEO6Z6EE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.0666&json=true","fetch_graph":"https://pith.science/api/pith-number/XEO6Z6EEQRUU7B5SNIFX623ZYT/graph.json","fetch_events":"https://pith.science/api/pith-number/XEO6Z6EEQRUU7B5SNIFX623ZYT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XEO6Z6EEQRUU7B5SNIFX623ZYT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XEO6Z6EEQRUU7B5SNIFX623ZYT/action/storage_attestation","attest_author":"https://pith.science/pith/XEO6Z6EEQRUU7B5SNIFX623ZYT/action/author_attestation","sign_citation":"https://pith.science/pith/XEO6Z6EEQRUU7B5SNIFX623ZYT/action/citation_signature","submit_replication":"https://pith.science/pith/XEO6Z6EEQRUU7B5SNIFX623ZYT/action/replication_record"}},"created_at":"2026-05-18T03:35:38.294478+00:00","updated_at":"2026-05-18T03:35:38.294478+00:00"}