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We show the structures of all entire solutions to the non-linear partial differential-difference equation $$(p_{1} L(f)+p_{2}\\overline{f}+p_5 f)^{2}+(p_{3}L(f)+p_{4}\\overline{f"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2509.01862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-09-02T01:06:51Z","cross_cats_sorted":[],"title_canon_sha256":"b0878394cccc6e9ef83c92de485c839dde5bf5afee545339a722afeec37977c5","abstract_canon_sha256":"9a78caff387209217bbad5aa3367ddb6d76d6145e97b579a00280a6a4dde23b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:03:10.097939Z","signature_b64":"sFdL9coEmG63LhV43xUojs6pNlfMIqaiX6eyOadZDLePgGxTDw9MLlD8oMXvP/tFgjxcM1SYj1jSoYUAfqHXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"454f8f6e3c86602dbb239ce7cf15a6a3f3be3aaecc87077128c967f4fd5e5c13","last_reissued_at":"2026-07-05T12:03:10.097450Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:03:10.097450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Fermat-type partial differential-difference equations on $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jun Wang, Tingbin Cao, Zhuan Ye","submitted_at":"2025-09-02T01:06:51Z","abstract_excerpt":"Assume that $n$ is a positive integer, $p_{j}$ ($j=1,2, \\cdots, 6)$ are polynomials, $p$ is an irreducible polynomial, and $f$ is an entire function on $\\mathbb{C}^{n}.$ Let $ L(f)=\\sum_{j=1}^s q_{t_j}f_{z_{t_j}}$ and $\\overline{f}(z)=f(z_{1}+c_{1}, \\ldots, z_{n}+c_{n})$, where $q_{t_j}$ ($j=1,2, \\cdots, s\\le n$) are non-zero polynomials on $\\mathbb{C}^{n}$ and $c=(c_{1}, \\ldots, c_{n})\\in \\mathbb{C}^{n}\\setminus\\{0\\}$. We show the structures of all entire solutions to the non-linear partial differential-difference equation $$(p_{1} L(f)+p_{2}\\overline{f}+p_5 f)^{2}+(p_{3}L(f)+p_{4}\\overline{f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01862","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.01862/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2509.01862","created_at":"2026-07-05T12:03:10.097513+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.01862v1","created_at":"2026-07-05T12:03:10.097513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01862","created_at":"2026-07-05T12:03:10.097513+00:00"},{"alias_kind":"pith_short_12","alias_value":"IVHY63R4QZQC","created_at":"2026-07-05T12:03:10.097513+00:00"},{"alias_kind":"pith_short_16","alias_value":"IVHY63R4QZQC3OZD","created_at":"2026-07-05T12:03:10.097513+00:00"},{"alias_kind":"pith_short_8","alias_value":"IVHY63R4","created_at":"2026-07-05T12:03:10.097513+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IVHY63R4QZQC3OZDTTT46FNGUP","json":"https://pith.science/pith/IVHY63R4QZQC3OZDTTT46FNGUP.json","graph_json":"https://pith.science/api/pith-number/IVHY63R4QZQC3OZDTTT46FNGUP/graph.json","events_json":"https://pith.science/api/pith-number/IVHY63R4QZQC3OZDTTT46FNGUP/events.json","paper":"https://pith.science/paper/IVHY63R4"},"agent_actions":{"view_html":"https://pith.science/pith/IVHY63R4QZQC3OZDTTT46FNGUP","download_json":"https://pith.science/pith/IVHY63R4QZQC3OZDTTT46FNGUP.json","view_paper":"https://pith.science/paper/IVHY63R4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.01862&json=true","fetch_graph":"https://pith.science/api/pith-number/IVHY63R4QZQC3OZDTTT46FNGUP/graph.json","fetch_events":"https://pith.science/api/pith-number/IVHY63R4QZQC3OZDTTT46FNGUP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IVHY63R4QZQC3OZDTTT46FNGUP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IVHY63R4QZQC3OZDTTT46FNGUP/action/storage_attestation","attest_author":"https://pith.science/pith/IVHY63R4QZQC3OZDTTT46FNGUP/action/author_attestation","sign_citation":"https://pith.science/pith/IVHY63R4QZQC3OZDTTT46FNGUP/action/citation_signature","submit_replication":"https://pith.science/pith/IVHY63R4QZQC3OZDTTT46FNGUP/action/replication_record"}},"created_at":"2026-07-05T12:03:10.097513+00:00","updated_at":"2026-07-05T12:03:10.097513+00:00"}