{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NE3BNTO24NEQJPQ6KRVOYYLXZY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f8d1521ca411d2794123f4955e8a3610c9eab04430fe46884647a25e4bf09d49","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-17T13:30:13Z","title_canon_sha256":"3ce8acdb08240c4d1c1d61b4cc45a92834dda448b2a49063f5f46e74c6013f06"},"schema_version":"1.0","source":{"id":"1509.05248","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05248","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05248v1","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05248","created_at":"2026-05-18T00:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"NE3BNTO24NEQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NE3BNTO24NEQJPQ6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NE3BNTO2","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:05961d3bf6bc346bb1b1fe2183297ef45cc1bb592198615268a07557fe3a9659","target":"graph","created_at":"2026-05-18T00:25:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The q-difference Painleve II equation admits special solutions written in terms of determinant whose entries are the general solution of the q-Airy equation. An ultradiscrete limit of the special solutions is studied by the procedure of ultradiscretization with parity varialbes. Then we obtain new Airy-type solutions of the ultradiscrete Painleve II equation with parity variables, and the solutions have richer structure than the known solutions.","authors_text":"Hikaru Igarashi, Kouichi Takemura, Shin Isojima","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-17T13:30:13Z","title":"New Airy-type solutions of the ultradiscrete Painleve II equation with parity variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05248","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d7e098298d502977fc14f6671007f13539f7e4276b763a809c7d81eab047b323","target":"record","created_at":"2026-05-18T00:25:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f8d1521ca411d2794123f4955e8a3610c9eab04430fe46884647a25e4bf09d49","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-17T13:30:13Z","title_canon_sha256":"3ce8acdb08240c4d1c1d61b4cc45a92834dda448b2a49063f5f46e74c6013f06"},"schema_version":"1.0","source":{"id":"1509.05248","kind":"arxiv","version":1}},"canonical_sha256":"693616cddae34904be1e546aec6177ce3909bbdba76853a4f7d925b84e94bd86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"693616cddae34904be1e546aec6177ce3909bbdba76853a4f7d925b84e94bd86","first_computed_at":"2026-05-18T00:25:08.159927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:08.159927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JAKGvdr9tzajW+McoG/Q6ZIjQmlIzFZwyqyR6fZJDTHw8JqwLxAPsIDBwdbSJTGpjvmu/UQNV/lUur/nt1wXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:08.160584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05248","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7e098298d502977fc14f6671007f13539f7e4276b763a809c7d81eab047b323","sha256:05961d3bf6bc346bb1b1fe2183297ef45cc1bb592198615268a07557fe3a9659"],"state_sha256":"c4dab6e5508ad12a09e0989226bfacec05d0b7eb06aa85400dc46c1ce1e968a7"}