{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CVMMULYO6AXZS55V5PCIGBCOYH","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":"725a5b3b5715409980961ed68b96798957b1ff6c1c5c53a6bdee3041bdbd5442","cross_cats_sorted":["math.DS","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-06-02T21:34:15Z","title_canon_sha256":"f3126c5640d6210a466688c9f83dd50825b7750a8b1310282202b56d7e38bbe9"},"schema_version":"1.0","source":{"id":"2506.02275","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02275","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02275v1","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02275","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"CVMMULYO6AXZ","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"CVMMULYO6AXZS55V","created_at":"2026-07-05T11:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"CVMMULYO","created_at":"2026-07-05T11:17:46Z"}],"graph_snapshots":[{"event_id":"sha256:3e0470a392a926dea8bbf5a151b675878de919daf576d0d5a59969d4024a59b1","target":"graph","created_at":"2026-07-05T11:17:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.02275/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we extend the novel approach to discrete Painlev\\'e equations initiated in our previous work [2]. A classification scheme for discrete Painlev\\'e equations proposed by Sakai interprets them as birational isomorphisms between generalized Halphen surfaces (surfaces obtained from $\\mathbb P^1\\times\\mathbb P^1$ by blowing up at eight points). Sakai's classification is thus based on the classification of generalized Halphen surfaces. In our scheme, the family of generalized Halphen surfaces is replaced by a pencil of quadrics in $\\mathbb P^3$. A discrete Painlev\\'e equation is viewed ","authors_text":"Jaume Alonso, Yuri B. Suris","cross_cats":["math.DS","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-06-02T21:34:15Z","title":"Discrete Painlev\\'e equations from pencils of quadrics in $\\mathbb P^3$ with branching generators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02275","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":"sha256:8cd84994a84f65b764b3c9019833ff4760be38684fb7ac8f2434767efdaa8134","target":"record","created_at":"2026-07-05T11:17:46Z","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":"725a5b3b5715409980961ed68b96798957b1ff6c1c5c53a6bdee3041bdbd5442","cross_cats_sorted":["math.DS","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-06-02T21:34:15Z","title_canon_sha256":"f3126c5640d6210a466688c9f83dd50825b7750a8b1310282202b56d7e38bbe9"},"schema_version":"1.0","source":{"id":"2506.02275","kind":"arxiv","version":1}},"canonical_sha256":"1558ca2f0ef02f9977b5ebc483044ec1c943d672362c047afc3b45e18ab9985d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1558ca2f0ef02f9977b5ebc483044ec1c943d672362c047afc3b45e18ab9985d","first_computed_at":"2026-07-05T11:17:46.785988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:46.785988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UABjhOiNIMr4KtCQ5QUU9Y9wxPP5HPoAm4PdfOhl7AU2K3JfyDFICi7ms8iabWnuiuFGn7t1eCovJyGYX10zBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:46.786594Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02275","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cd84994a84f65b764b3c9019833ff4760be38684fb7ac8f2434767efdaa8134","sha256:3e0470a392a926dea8bbf5a151b675878de919daf576d0d5a59969d4024a59b1"],"state_sha256":"1090e1b67347b13878d41876ab13c110477ea5bdf216ff853f59b5e098ed6c94"}