{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WPCOISSW2RXCRCH3WV73ATYZVO","short_pith_number":"pith:WPCOISSW","schema_version":"1.0","canonical_sha256":"b3c4e44a56d46e2888fbb57fb04f19ab9c911a70cf9dc76e3efc4ac8e8b23fb4","source":{"kind":"arxiv","id":"1902.09920","version":1},"attestation_state":"computed","paper":{"title":"Constructing discrete Painlev\\'e equations: from E$_8^{(1)}$ to A$_1^{(1)}$ and back","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alfred Ramani, Basil Grammaticos, Ralph Willox, Tamizharasi Tamizhmani","submitted_at":"2019-02-26T13:27:48Z","abstract_excerpt":"The `restoration method' is a novel method we recently introduced for systematically deriving discrete Painlev\\'e equations. In this method we start from a given Painlev\\'e equation, typically with E$_8^{(1)}$ symmetry, obtain its autonomous limit and construct all possible QRT-canonical forms of mappings that are equivalent to it by homographic transformations. Discrete Painlev\\'e equations are then obtained by deautonomising the various mappings thus obtained. We apply the restoration method to two challenging examples, one of which does not lead to a QRT mapping at the autonomous limit but "},"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":"1902.09920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-02-26T13:27:48Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"99394cda8e43b9eaac7e0092c73a121968a4f3e2a16c32fde298be4f8066112c","abstract_canon_sha256":"5bfbb6f2896aebbf93a38868d891296945d15d6265466814065798a976ddf5ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:35.037935Z","signature_b64":"R2jJn6hiaU61V0WuCWssHU/ARHUWAimYVEnEMW8uaS8tERoC76G4WumWq0I2nWEmnXg2rguBasa7Rb7GVLyyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3c4e44a56d46e2888fbb57fb04f19ab9c911a70cf9dc76e3efc4ac8e8b23fb4","last_reissued_at":"2026-05-17T23:52:35.037445Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:35.037445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructing discrete Painlev\\'e equations: from E$_8^{(1)}$ to A$_1^{(1)}$ and back","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alfred Ramani, Basil Grammaticos, Ralph Willox, Tamizharasi Tamizhmani","submitted_at":"2019-02-26T13:27:48Z","abstract_excerpt":"The `restoration method' is a novel method we recently introduced for systematically deriving discrete Painlev\\'e equations. In this method we start from a given Painlev\\'e equation, typically with E$_8^{(1)}$ symmetry, obtain its autonomous limit and construct all possible QRT-canonical forms of mappings that are equivalent to it by homographic transformations. Discrete Painlev\\'e equations are then obtained by deautonomising the various mappings thus obtained. We apply the restoration method to two challenging examples, one of which does not lead to a QRT mapping at the autonomous limit but "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09920","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":"1902.09920","created_at":"2026-05-17T23:52:35.037528+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.09920v1","created_at":"2026-05-17T23:52:35.037528+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09920","created_at":"2026-05-17T23:52:35.037528+00:00"},{"alias_kind":"pith_short_12","alias_value":"WPCOISSW2RXC","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"WPCOISSW2RXCRCH3","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"WPCOISSW","created_at":"2026-05-18T12:33:30.264802+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/WPCOISSW2RXCRCH3WV73ATYZVO","json":"https://pith.science/pith/WPCOISSW2RXCRCH3WV73ATYZVO.json","graph_json":"https://pith.science/api/pith-number/WPCOISSW2RXCRCH3WV73ATYZVO/graph.json","events_json":"https://pith.science/api/pith-number/WPCOISSW2RXCRCH3WV73ATYZVO/events.json","paper":"https://pith.science/paper/WPCOISSW"},"agent_actions":{"view_html":"https://pith.science/pith/WPCOISSW2RXCRCH3WV73ATYZVO","download_json":"https://pith.science/pith/WPCOISSW2RXCRCH3WV73ATYZVO.json","view_paper":"https://pith.science/paper/WPCOISSW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.09920&json=true","fetch_graph":"https://pith.science/api/pith-number/WPCOISSW2RXCRCH3WV73ATYZVO/graph.json","fetch_events":"https://pith.science/api/pith-number/WPCOISSW2RXCRCH3WV73ATYZVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WPCOISSW2RXCRCH3WV73ATYZVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WPCOISSW2RXCRCH3WV73ATYZVO/action/storage_attestation","attest_author":"https://pith.science/pith/WPCOISSW2RXCRCH3WV73ATYZVO/action/author_attestation","sign_citation":"https://pith.science/pith/WPCOISSW2RXCRCH3WV73ATYZVO/action/citation_signature","submit_replication":"https://pith.science/pith/WPCOISSW2RXCRCH3WV73ATYZVO/action/replication_record"}},"created_at":"2026-05-17T23:52:35.037528+00:00","updated_at":"2026-05-17T23:52:35.037528+00:00"}