{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RNUWSD7ILFGSIIE7VUQRQLWE55","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":"8d95ad8c610c95793f26b3f0959d53ae60a6fe179bb3baf3399eb07004441295","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-06-03T06:59:47Z","title_canon_sha256":"454be52c4f93491f6b235e97869355e3bf4f6e7b6339f8d9f5a7dd0d9c43ec61"},"schema_version":"1.0","source":{"id":"2606.05240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.05240","created_at":"2026-06-05T00:13:50Z"},{"alias_kind":"arxiv_version","alias_value":"2606.05240v1","created_at":"2026-06-05T00:13:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05240","created_at":"2026-06-05T00:13:50Z"},{"alias_kind":"pith_short_12","alias_value":"RNUWSD7ILFGS","created_at":"2026-06-05T00:13:50Z"},{"alias_kind":"pith_short_16","alias_value":"RNUWSD7ILFGSIIE7","created_at":"2026-06-05T00:13:50Z"},{"alias_kind":"pith_short_8","alias_value":"RNUWSD7I","created_at":"2026-06-05T00:13:50Z"}],"graph_snapshots":[{"event_id":"sha256:34caae0777d8d510ce211513a929ec3afdeeaf31f0e49d36966224183acdec9b","target":"graph","created_at":"2026-06-05T00:13:50Z","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/2606.05240/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The primary objective of this paper is to determine the explicit existence form and structure of finite-order entire solutions in $\\mathbb{C}^n$ of the following system of Fermat-type partial differential-difference equations: \\[\\begin{cases} \\left(\\frac{\\partial f_1\\left(z\\right)}{\\partial z_1}\\right)^{n_1} + (f_2 \\left(z+c\\right)-f_1(z) )^{m_1}= 1,\n  \\medskip \\left(\\frac{\\partial f_2\\left(z\\right)}{\\partial z_1}\\right)^{n_2} + (f_1 \\left(z+c \\right)-f_2(z) )^{m_2}= 1, \\end{cases}\\] \nfor different choices of the positive integers $n_1$, $n_2$, $m_1$, and $m_2$, where $c=(c_1,c_2,\\ldots,c_n)$.","authors_text":"Abhijit Banerjee, Jhilik Banerjee, Sujoy Majumder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-06-03T06:59:47Z","title":"A Complete Characterization of Finite-Order Entire Solutions to Fermat-Type Partial Differential-Difference Systems in $\\mathbb{C}^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05240","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":"sha256:0287fadc4bf17c92d32e604b133ec15a16127c50f99d4a7d5a2698ad44807ece","target":"record","created_at":"2026-06-05T00:13:50Z","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":"8d95ad8c610c95793f26b3f0959d53ae60a6fe179bb3baf3399eb07004441295","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-06-03T06:59:47Z","title_canon_sha256":"454be52c4f93491f6b235e97869355e3bf4f6e7b6339f8d9f5a7dd0d9c43ec61"},"schema_version":"1.0","source":{"id":"2606.05240","kind":"arxiv","version":1}},"canonical_sha256":"8b69690fe8594d24209fad21182ec4ef63ac4badd39554129bedcca11c3574ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b69690fe8594d24209fad21182ec4ef63ac4badd39554129bedcca11c3574ef","first_computed_at":"2026-06-05T00:13:50.105896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T00:13:50.105896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4S3CRyhRnTx96GQUuZiEJEIIsneoPC3MqEYGABIAH+KjHxeESJkC76iZPsyWXDsQlu6HOJBKflN6RbMpDIoOCg==","signature_status":"signed_v1","signed_at":"2026-06-05T00:13:50.106552Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.05240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0287fadc4bf17c92d32e604b133ec15a16127c50f99d4a7d5a2698ad44807ece","sha256:34caae0777d8d510ce211513a929ec3afdeeaf31f0e49d36966224183acdec9b"],"state_sha256":"4b610d783ababe8061c3641361de2a220eef2f145aa45ba9a36e447901036b8f"}