{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RY76ZQDHNMEIYLCPZTQ2WGEVLZ","short_pith_number":"pith:RY76ZQDH","schema_version":"1.0","canonical_sha256":"8e3fecc0676b088c2c4fcce1ab18955e6cf6abb2617d6178e1dbea5a8bdd0d64","source":{"kind":"arxiv","id":"1301.5046","version":2},"attestation_state":"computed","paper":{"title":"On the Structure of Compatible Rational Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.SC","authors_text":"Guofeng Fu, Ruyong Feng, Shaoshi Chen, Ziming Li","submitted_at":"2013-01-22T00:37:06Z","abstract_excerpt":"A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the structure of compatible rational functions. The theorem enables us to decompose a solution of such a system as a product of a rational function, several symbolic powers, a hyperexponential function, a hypergeometric term, and a q-hypergeometric term. We outline an algorithm for computing this product, and present an application."},"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":"1301.5046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-22T00:37:06Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d4d0cd6f3ff4dc21d805f70df6a9645c59fffb099980ded1029d802664f9a736","abstract_canon_sha256":"fccb2013e751acada5a3d27f4603823eebb2981b651119c8ac616703ebd8c310"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:40.489118Z","signature_b64":"D2WvF/NxX2x5S1yqf/ItYyoxhvlzfKtQR3QisqC1DEoavqwvkYyovF9iJxXa4Utt3+V1ghaFBLvPDGsu0CPyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e3fecc0676b088c2c4fcce1ab18955e6cf6abb2617d6178e1dbea5a8bdd0d64","last_reissued_at":"2026-05-18T03:35:40.488324Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:40.488324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Structure of Compatible Rational Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.SC","authors_text":"Guofeng Fu, Ruyong Feng, Shaoshi Chen, Ziming Li","submitted_at":"2013-01-22T00:37:06Z","abstract_excerpt":"A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the structure of compatible rational functions. The theorem enables us to decompose a solution of such a system as a product of a rational function, several symbolic powers, a hyperexponential function, a hypergeometric term, and a q-hypergeometric term. We outline an algorithm for computing this product, and present an application."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5046","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1301.5046","created_at":"2026-05-18T03:35:40.488453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.5046v2","created_at":"2026-05-18T03:35:40.488453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5046","created_at":"2026-05-18T03:35:40.488453+00:00"},{"alias_kind":"pith_short_12","alias_value":"RY76ZQDHNMEI","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"RY76ZQDHNMEIYLCP","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"RY76ZQDH","created_at":"2026-05-18T12:27:59.945178+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/RY76ZQDHNMEIYLCPZTQ2WGEVLZ","json":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ.json","graph_json":"https://pith.science/api/pith-number/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/graph.json","events_json":"https://pith.science/api/pith-number/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/events.json","paper":"https://pith.science/paper/RY76ZQDH"},"agent_actions":{"view_html":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ","download_json":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ.json","view_paper":"https://pith.science/paper/RY76ZQDH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.5046&json=true","fetch_graph":"https://pith.science/api/pith-number/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/graph.json","fetch_events":"https://pith.science/api/pith-number/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/action/storage_attestation","attest_author":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/action/author_attestation","sign_citation":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/action/citation_signature","submit_replication":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/action/replication_record"}},"created_at":"2026-05-18T03:35:40.488453+00:00","updated_at":"2026-05-18T03:35:40.488453+00:00"}