{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JMRLNJWR6VUZ23LFYEFLXG65B4","short_pith_number":"pith:JMRLNJWR","schema_version":"1.0","canonical_sha256":"4b22b6a6d1f5699d6d65c10abb9bdd0f32ff2abd6dedf03cb7300274a255113b","source":{"kind":"arxiv","id":"1803.05096","version":1},"attestation_state":"computed","paper":{"title":"Markov spectra for modular billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Nickolas Andersen, William Duke","submitted_at":"2018-03-14T01:46:16Z","abstract_excerpt":"We introduce some analogues of the Markov spectrum defined in terms of modular billiards and consider the problem of characterizing that part of the spectrum below the lowest limit point."},"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":"1803.05096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-14T01:46:16Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f9bde17a77a578a3a89784ce747354ba772ef85a5edd888d1871c4fb597a8d4a","abstract_canon_sha256":"14084e8ec364dd83951c55209eb1ff10f3a6ca5b3f1d11c355ffb797c6e6bebf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:01.364487Z","signature_b64":"WGpTuN+vTrMPtUD3Uy0Ck7EZXThixR0Mg2YZthlMzq5Ts/g4NJzmpcXJY9Ah52MWsY/wG6tZiiPA8nNhsC5ZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b22b6a6d1f5699d6d65c10abb9bdd0f32ff2abd6dedf03cb7300274a255113b","last_reissued_at":"2026-05-18T00:21:01.363957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:01.363957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Markov spectra for modular billiards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Nickolas Andersen, William Duke","submitted_at":"2018-03-14T01:46:16Z","abstract_excerpt":"We introduce some analogues of the Markov spectrum defined in terms of modular billiards and consider the problem of characterizing that part of the spectrum below the lowest limit point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05096","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":"1803.05096","created_at":"2026-05-18T00:21:01.364040+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.05096v1","created_at":"2026-05-18T00:21:01.364040+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05096","created_at":"2026-05-18T00:21:01.364040+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMRLNJWR6VUZ","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMRLNJWR6VUZ23LF","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMRLNJWR","created_at":"2026-05-18T12:32:31.084164+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/JMRLNJWR6VUZ23LFYEFLXG65B4","json":"https://pith.science/pith/JMRLNJWR6VUZ23LFYEFLXG65B4.json","graph_json":"https://pith.science/api/pith-number/JMRLNJWR6VUZ23LFYEFLXG65B4/graph.json","events_json":"https://pith.science/api/pith-number/JMRLNJWR6VUZ23LFYEFLXG65B4/events.json","paper":"https://pith.science/paper/JMRLNJWR"},"agent_actions":{"view_html":"https://pith.science/pith/JMRLNJWR6VUZ23LFYEFLXG65B4","download_json":"https://pith.science/pith/JMRLNJWR6VUZ23LFYEFLXG65B4.json","view_paper":"https://pith.science/paper/JMRLNJWR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.05096&json=true","fetch_graph":"https://pith.science/api/pith-number/JMRLNJWR6VUZ23LFYEFLXG65B4/graph.json","fetch_events":"https://pith.science/api/pith-number/JMRLNJWR6VUZ23LFYEFLXG65B4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMRLNJWR6VUZ23LFYEFLXG65B4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMRLNJWR6VUZ23LFYEFLXG65B4/action/storage_attestation","attest_author":"https://pith.science/pith/JMRLNJWR6VUZ23LFYEFLXG65B4/action/author_attestation","sign_citation":"https://pith.science/pith/JMRLNJWR6VUZ23LFYEFLXG65B4/action/citation_signature","submit_replication":"https://pith.science/pith/JMRLNJWR6VUZ23LFYEFLXG65B4/action/replication_record"}},"created_at":"2026-05-18T00:21:01.364040+00:00","updated_at":"2026-05-18T00:21:01.364040+00:00"}