{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:M3HD4Z2ISYVEI22MIAPE7Y77NJ","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":"879753cc93e7b398b6ff7d20b4101090ebe5c55ec88a9d829a4568b5c6f19737","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-03-25T14:52:13Z","title_canon_sha256":"bad9927fe0b09351ac6e5c604b012e8ce7e6c87297b609741bce41de55c0c869"},"schema_version":"1.0","source":{"id":"1603.07930","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07930","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07930v1","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07930","created_at":"2026-05-18T01:18:15Z"},{"alias_kind":"pith_short_12","alias_value":"M3HD4Z2ISYVE","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M3HD4Z2ISYVEI22M","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M3HD4Z2I","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:a718ac58040faf4012bc99c5613e74fb9ffbade3905cb4a4f87f651e07e18350","target":"graph","created_at":"2026-05-18T01:18:15Z","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":"We discuss the non autonomous nonlinear partial difference equations belonging to Boll classification of quad graph equations consistent around the cube. We show how starting from the compatible equations on a cell we can construct the lattice equations, its B\\\"acklund transformations and Lax pairs. By carrying out the algebraic entropy calculations we show that the $H^4$ trapezoidal and the $H^6$ families are linearizable and in a few examples we show how we can effectively linearize them.","authors_text":"Christian Scimiterna, Decio Levi, Giorgio Gubbiotti","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-03-25T14:52:13Z","title":"Algebraic entropy, symmetries and linearization of quad equations consistent on the cube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07930","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:a895521225cc9b8b42ad186091ec01104af277203cbdf597fcb44825dc39bb33","target":"record","created_at":"2026-05-18T01:18:15Z","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":"879753cc93e7b398b6ff7d20b4101090ebe5c55ec88a9d829a4568b5c6f19737","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-03-25T14:52:13Z","title_canon_sha256":"bad9927fe0b09351ac6e5c604b012e8ce7e6c87297b609741bce41de55c0c869"},"schema_version":"1.0","source":{"id":"1603.07930","kind":"arxiv","version":1}},"canonical_sha256":"66ce3e6748962a446b4c401e4fe3ff6a6bd08e27a1598ea0a0de6ef906c1e354","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66ce3e6748962a446b4c401e4fe3ff6a6bd08e27a1598ea0a0de6ef906c1e354","first_computed_at":"2026-05-18T01:18:15.836230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:15.836230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9I/0kU1vYJddP7+EJ0ogQuC9AusJ+alzfE7sTXtO2K3BCYXtlVKPnbz5r3JMtWpOa4ZM3jCir/OwgZO+TtgSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:15.836950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07930","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a895521225cc9b8b42ad186091ec01104af277203cbdf597fcb44825dc39bb33","sha256:a718ac58040faf4012bc99c5613e74fb9ffbade3905cb4a4f87f651e07e18350"],"state_sha256":"e254cbbfe93d81f4ae4381da46d791638213fd2ebe3c6a587c33c6bbea76a1d3"}