{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CDYMRNJ6HAJAKSTVBWT7KBH2QK","short_pith_number":"pith:CDYMRNJ6","schema_version":"1.0","canonical_sha256":"10f0c8b53e3812054a750da7f504fa828a494dbb27a93b489e7a48a7bb57b892","source":{"kind":"arxiv","id":"1301.4033","version":2},"attestation_state":"computed","paper":{"title":"Rigorous pointwise approximations for invariant densities of nonuniformly expanding maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christopher Bose, Wael Bahsoun, Yuejiao Duan","submitted_at":"2013-01-17T10:14:50Z","abstract_excerpt":"We use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a rate $C^*\\cdot\\frac{\\ln m}{m}$, where $C^*$ is a computable fixed constant and $m^{-1}$ is the mesh size of the discretization."},"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":"1301.4033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-01-17T10:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"394a6d9685aa24ddaca688ce19ebf7a50f6eab60a00f3e83464fd537e947132f","abstract_canon_sha256":"e5a723c889b429a8615f0d6bffebeee101a058759d21621c3b745b5536fb1fc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:06.213113Z","signature_b64":"wMdpSe8C3okcwyuLIEuJZcOiyDxYHbszDIZhAOMgzaFsuyUr2UkCVsRbae/+sVwUwmbOfUayyjKvHuI0thAEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10f0c8b53e3812054a750da7f504fa828a494dbb27a93b489e7a48a7bb57b892","last_reissued_at":"2026-05-18T03:18:06.212444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:06.212444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigorous pointwise approximations for invariant densities of nonuniformly expanding maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christopher Bose, Wael Bahsoun, Yuejiao Duan","submitted_at":"2013-01-17T10:14:50Z","abstract_excerpt":"We use an Ulam-type discretization scheme to provide pointwise approximations for invariant densities of interval maps with a neutral fixed point. We prove that the approximate invariant density converges pointwise to the true density at a rate $C^*\\cdot\\frac{\\ln m}{m}$, where $C^*$ is a computable fixed constant and $m^{-1}$ is the mesh size of the discretization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4033","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":"1301.4033","created_at":"2026-05-18T03:18:06.212537+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.4033v2","created_at":"2026-05-18T03:18:06.212537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4033","created_at":"2026-05-18T03:18:06.212537+00:00"},{"alias_kind":"pith_short_12","alias_value":"CDYMRNJ6HAJA","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CDYMRNJ6HAJAKSTV","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CDYMRNJ6","created_at":"2026-05-18T12:27:40.988391+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/CDYMRNJ6HAJAKSTVBWT7KBH2QK","json":"https://pith.science/pith/CDYMRNJ6HAJAKSTVBWT7KBH2QK.json","graph_json":"https://pith.science/api/pith-number/CDYMRNJ6HAJAKSTVBWT7KBH2QK/graph.json","events_json":"https://pith.science/api/pith-number/CDYMRNJ6HAJAKSTVBWT7KBH2QK/events.json","paper":"https://pith.science/paper/CDYMRNJ6"},"agent_actions":{"view_html":"https://pith.science/pith/CDYMRNJ6HAJAKSTVBWT7KBH2QK","download_json":"https://pith.science/pith/CDYMRNJ6HAJAKSTVBWT7KBH2QK.json","view_paper":"https://pith.science/paper/CDYMRNJ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.4033&json=true","fetch_graph":"https://pith.science/api/pith-number/CDYMRNJ6HAJAKSTVBWT7KBH2QK/graph.json","fetch_events":"https://pith.science/api/pith-number/CDYMRNJ6HAJAKSTVBWT7KBH2QK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CDYMRNJ6HAJAKSTVBWT7KBH2QK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CDYMRNJ6HAJAKSTVBWT7KBH2QK/action/storage_attestation","attest_author":"https://pith.science/pith/CDYMRNJ6HAJAKSTVBWT7KBH2QK/action/author_attestation","sign_citation":"https://pith.science/pith/CDYMRNJ6HAJAKSTVBWT7KBH2QK/action/citation_signature","submit_replication":"https://pith.science/pith/CDYMRNJ6HAJAKSTVBWT7KBH2QK/action/replication_record"}},"created_at":"2026-05-18T03:18:06.212537+00:00","updated_at":"2026-05-18T03:18:06.212537+00:00"}