{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CESBYDDHDDHXJ6PY2OAK3RWNIX","short_pith_number":"pith:CESBYDDH","schema_version":"1.0","canonical_sha256":"11241c0c6718cf74f9f8d380adc6cd45cb689e20c34294db200b514898a46c83","source":{"kind":"arxiv","id":"1409.6909","version":4},"attestation_state":"computed","paper":{"title":"Rigorous approximation of diffusion coefficients for expanding maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Isaia Nisoli, Stefano Galatolo, Wael Bahsoun, Xiaolong Niu","submitted_at":"2014-09-24T11:48:14Z","abstract_excerpt":"We use Ulam's method to provide rigorous approximation of diffusion coefficients for uniformly expanding maps. An algorithm is provided and its implementation is illustrated using Lanford's map."},"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":"1409.6909","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-24T11:48:14Z","cross_cats_sorted":[],"title_canon_sha256":"20b11bd4ad04c06af2ed2d6e020304756b4fc4affe950a194d7264d7c8132b00","abstract_canon_sha256":"3f9e3306565218daea9dc377533fdbc31c038eec4dde63f9ea0e163499ea7233"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:20.810999Z","signature_b64":"pk9mqz0aBRn/8ClcONEyx0OLlC7t18xIgvsk0ZkxJWgCzv/Yb/O8u5L8mayPAmT35cuIttjVeGP2Fs1CGJ0GAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11241c0c6718cf74f9f8d380adc6cd45cb689e20c34294db200b514898a46c83","last_reissued_at":"2026-05-18T01:17:20.810371Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:20.810371Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigorous approximation of diffusion coefficients for expanding maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Isaia Nisoli, Stefano Galatolo, Wael Bahsoun, Xiaolong Niu","submitted_at":"2014-09-24T11:48:14Z","abstract_excerpt":"We use Ulam's method to provide rigorous approximation of diffusion coefficients for uniformly expanding maps. An algorithm is provided and its implementation is illustrated using Lanford's map."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6909","kind":"arxiv","version":4},"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":"1409.6909","created_at":"2026-05-18T01:17:20.810479+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.6909v4","created_at":"2026-05-18T01:17:20.810479+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6909","created_at":"2026-05-18T01:17:20.810479+00:00"},{"alias_kind":"pith_short_12","alias_value":"CESBYDDHDDHX","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CESBYDDHDDHXJ6PY","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CESBYDDH","created_at":"2026-05-18T12:28:22.404517+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/CESBYDDHDDHXJ6PY2OAK3RWNIX","json":"https://pith.science/pith/CESBYDDHDDHXJ6PY2OAK3RWNIX.json","graph_json":"https://pith.science/api/pith-number/CESBYDDHDDHXJ6PY2OAK3RWNIX/graph.json","events_json":"https://pith.science/api/pith-number/CESBYDDHDDHXJ6PY2OAK3RWNIX/events.json","paper":"https://pith.science/paper/CESBYDDH"},"agent_actions":{"view_html":"https://pith.science/pith/CESBYDDHDDHXJ6PY2OAK3RWNIX","download_json":"https://pith.science/pith/CESBYDDHDDHXJ6PY2OAK3RWNIX.json","view_paper":"https://pith.science/paper/CESBYDDH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.6909&json=true","fetch_graph":"https://pith.science/api/pith-number/CESBYDDHDDHXJ6PY2OAK3RWNIX/graph.json","fetch_events":"https://pith.science/api/pith-number/CESBYDDHDDHXJ6PY2OAK3RWNIX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CESBYDDHDDHXJ6PY2OAK3RWNIX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CESBYDDHDDHXJ6PY2OAK3RWNIX/action/storage_attestation","attest_author":"https://pith.science/pith/CESBYDDHDDHXJ6PY2OAK3RWNIX/action/author_attestation","sign_citation":"https://pith.science/pith/CESBYDDHDDHXJ6PY2OAK3RWNIX/action/citation_signature","submit_replication":"https://pith.science/pith/CESBYDDHDDHXJ6PY2OAK3RWNIX/action/replication_record"}},"created_at":"2026-05-18T01:17:20.810479+00:00","updated_at":"2026-05-18T01:17:20.810479+00:00"}