{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5N7B42U4C5WT7ZVSIF4QOFNNUO","short_pith_number":"pith:5N7B42U4","schema_version":"1.0","canonical_sha256":"eb7e1e6a9c176d3fe6b241790715ada3bf553f822f7cbb36d455a83801ecb0f9","source":{"kind":"arxiv","id":"1705.00445","version":3},"attestation_state":"computed","paper":{"title":"Geometric description of discrete power function associated with the sixth Painlev\\'e equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Kenji Kajiwara, Nalini Joshi, Nobutaka Nakazono, Tetsu Masuda, Yang Shi","submitted_at":"2017-05-01T08:44:49Z","abstract_excerpt":"In this paper, we consider the discrete power function associated with the sixth Painlev\\'e equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with $\\widetilde{W}(3A_1^{(1)})$ symmetry. By constructing the action of $\\widetilde{W}(3A_1^{(1)})$ as a subgroup of $\\widetilde{W}(D_4^{(1)})$, i.e., the symmetry group of P$_{\\rm VI}$, we show how to relate $\\widetilde{W}(D_4^{(1)})$ to the symmetry group of the lattice. Moreover, by using translations in $\\widetilde{W}"},"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":"1705.00445","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-05-01T08:44:49Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"fd94e1509985fbe8e95621d57bb5220bbcf97a99fd2f312e9afed666bbc4ad5a","abstract_canon_sha256":"201fde8aeb63080488af90e04af6cc2bf8d6fcbc09002d5aeb53da0fd486e71b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:17.605173Z","signature_b64":"yu9S3XLlL1aNANucusQVZLEwh6JuXosklnHewy8BrSO4bvaDnChRVmzE9Holza+KwzZ4ueApGKuYv/4NKb6QDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb7e1e6a9c176d3fe6b241790715ada3bf553f822f7cbb36d455a83801ecb0f9","last_reissued_at":"2026-05-18T00:24:17.604705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:17.604705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric description of discrete power function associated with the sixth Painlev\\'e equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Kenji Kajiwara, Nalini Joshi, Nobutaka Nakazono, Tetsu Masuda, Yang Shi","submitted_at":"2017-05-01T08:44:49Z","abstract_excerpt":"In this paper, we consider the discrete power function associated with the sixth Painlev\\'e equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with $\\widetilde{W}(3A_1^{(1)})$ symmetry. By constructing the action of $\\widetilde{W}(3A_1^{(1)})$ as a subgroup of $\\widetilde{W}(D_4^{(1)})$, i.e., the symmetry group of P$_{\\rm VI}$, we show how to relate $\\widetilde{W}(D_4^{(1)})$ to the symmetry group of the lattice. Moreover, by using translations in $\\widetilde{W}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00445","kind":"arxiv","version":3},"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":"1705.00445","created_at":"2026-05-18T00:24:17.604778+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.00445v3","created_at":"2026-05-18T00:24:17.604778+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00445","created_at":"2026-05-18T00:24:17.604778+00:00"},{"alias_kind":"pith_short_12","alias_value":"5N7B42U4C5WT","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5N7B42U4C5WT7ZVS","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5N7B42U4","created_at":"2026-05-18T12:31:00.734936+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/5N7B42U4C5WT7ZVSIF4QOFNNUO","json":"https://pith.science/pith/5N7B42U4C5WT7ZVSIF4QOFNNUO.json","graph_json":"https://pith.science/api/pith-number/5N7B42U4C5WT7ZVSIF4QOFNNUO/graph.json","events_json":"https://pith.science/api/pith-number/5N7B42U4C5WT7ZVSIF4QOFNNUO/events.json","paper":"https://pith.science/paper/5N7B42U4"},"agent_actions":{"view_html":"https://pith.science/pith/5N7B42U4C5WT7ZVSIF4QOFNNUO","download_json":"https://pith.science/pith/5N7B42U4C5WT7ZVSIF4QOFNNUO.json","view_paper":"https://pith.science/paper/5N7B42U4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.00445&json=true","fetch_graph":"https://pith.science/api/pith-number/5N7B42U4C5WT7ZVSIF4QOFNNUO/graph.json","fetch_events":"https://pith.science/api/pith-number/5N7B42U4C5WT7ZVSIF4QOFNNUO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5N7B42U4C5WT7ZVSIF4QOFNNUO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5N7B42U4C5WT7ZVSIF4QOFNNUO/action/storage_attestation","attest_author":"https://pith.science/pith/5N7B42U4C5WT7ZVSIF4QOFNNUO/action/author_attestation","sign_citation":"https://pith.science/pith/5N7B42U4C5WT7ZVSIF4QOFNNUO/action/citation_signature","submit_replication":"https://pith.science/pith/5N7B42U4C5WT7ZVSIF4QOFNNUO/action/replication_record"}},"created_at":"2026-05-18T00:24:17.604778+00:00","updated_at":"2026-05-18T00:24:17.604778+00:00"}