{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OSYLFC563OX5R6RJ6KI2O2OC6B","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":"5e76514970bc7d1d7f48de0cf4375957094025da22d995b2e2887faf9a26e121","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-06-15T02:23:26Z","title_canon_sha256":"a7c5fdc650c03f219b39bfe9014cf6d7f944ba01b313d2302aee3e3f8bfd492b"},"schema_version":"1.0","source":{"id":"1506.04457","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04457","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04457v3","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04457","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"OSYLFC563OX5","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OSYLFC563OX5R6RJ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OSYLFC56","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:4b840537a1f96e65a4631e149e2c9fa1ae387efed36c3f2b253f0027ea71b49f","target":"graph","created_at":"2026-05-18T00:44:28Z","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":"In this paper, we investigate a nonlinear non-autonomous elliptic difference equation, which was constructed by Ramani, Carstea and Grammaticos by integrable deautonomization of a periodic reduction of the discrete Krichever-Novikov equation, or Q4. We show how to construct it as a birational mapping on a rational surface blown up at eight points in $\\mathbb P^1\\times \\mathbb P^1$, and find its affine Weyl symmetry, placing it in the geometric framework of the Painlev\\'e equations. The initial value space is ell-$A_0^{(1)}$ and its symmetry group is $W(F_4^{(1)})$. We show that the deautonomiz","authors_text":"James Atkinson, Nalini Joshi, Nobutaka Nakazono, Phil Howes","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-06-15T02:23:26Z","title":"Geometry of an elliptic-difference equation related to Q4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04457","kind":"arxiv","version":3},"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":"sha256:54e12f16d2b54f2fc6ff8e6053be94d808914bd8d0d7bdef51d5769e32e8495b","target":"record","created_at":"2026-05-18T00:44:28Z","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":"5e76514970bc7d1d7f48de0cf4375957094025da22d995b2e2887faf9a26e121","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-06-15T02:23:26Z","title_canon_sha256":"a7c5fdc650c03f219b39bfe9014cf6d7f944ba01b313d2302aee3e3f8bfd492b"},"schema_version":"1.0","source":{"id":"1506.04457","kind":"arxiv","version":3}},"canonical_sha256":"74b0b28bbedbafd8fa29f291a769c2f064e4c896be06191626a748899fa88e78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74b0b28bbedbafd8fa29f291a769c2f064e4c896be06191626a748899fa88e78","first_computed_at":"2026-05-18T00:44:28.309283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:28.309283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MsEdzm0eoRTD0ISxFJV7G5pZTpqDAMAQjdnsJ42pKLdja6irROtBdWMpPZKwhCzLEy/hz2jD+0K05NO1GCqNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:28.309860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04457","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54e12f16d2b54f2fc6ff8e6053be94d808914bd8d0d7bdef51d5769e32e8495b","sha256:4b840537a1f96e65a4631e149e2c9fa1ae387efed36c3f2b253f0027ea71b49f"],"state_sha256":"44a4580cfb52a74fccdf08b595cfafc05964530a6d05bf79a970e9f863803bf3"}