{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RY76ZQDHNMEIYLCPZTQ2WGEVLZ","short_pith_number":"pith:RY76ZQDH","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"},"canonical_sha256":"8e3fecc0676b088c2c4fcce1ab18955e6cf6abb2617d6178e1dbea5a8bdd0d64","source":{"kind":"arxiv","id":"1301.5046","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5046","created_at":"2026-05-18T03:35:40Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5046v2","created_at":"2026-05-18T03:35:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5046","created_at":"2026-05-18T03:35:40Z"},{"alias_kind":"pith_short_12","alias_value":"RY76ZQDHNMEI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RY76ZQDHNMEIYLCP","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RY76ZQDH","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RY76ZQDHNMEIYLCPZTQ2WGEVLZ","target":"record","payload":{"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"},"canonical_sha256":"8e3fecc0676b088c2c4fcce1ab18955e6cf6abb2617d6178e1dbea5a8bdd0d64","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"},"source_kind":"arxiv","source_id":"1301.5046","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:35:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"adUV5g6o0H6tYZwF58jcqNZCAPb5+w4Ys5A/2rpEUCubNRPtpLS4+B9B2M1mk4YJzdTcpc3LtZb/+3i5zSksDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:20:03.438172Z"},"content_sha256":"fad778a10f99bed8054a1f58ad8e2dc9fc6269eba7f8764dec5b9d7a15968580","schema_version":"1.0","event_id":"sha256:fad778a10f99bed8054a1f58ad8e2dc9fc6269eba7f8764dec5b9d7a15968580"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RY76ZQDHNMEIYLCPZTQ2WGEVLZ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:35:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RXUjrAQrIfZUV2MY1bIvccGOSUob1H9Mmk3DCZ3gifXTAo1zQweIMosOxqFKmPML7K+Sb26oknSRhDf+6sNqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:20:03.438536Z"},"content_sha256":"fc1067e575ea6bd38aa8e6100319794fb94e108ec1fb7f1a8560c5508b940baf","schema_version":"1.0","event_id":"sha256:fc1067e575ea6bd38aa8e6100319794fb94e108ec1fb7f1a8560c5508b940baf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/bundle.json","state_url":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T04:20:03Z","links":{"resolver":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ","bundle":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/bundle.json","state":"https://pith.science/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RY76ZQDHNMEIYLCPZTQ2WGEVLZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RY76ZQDHNMEIYLCPZTQ2WGEVLZ","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":"fccb2013e751acada5a3d27f4603823eebb2981b651119c8ac616703ebd8c310","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-22T00:37:06Z","title_canon_sha256":"d4d0cd6f3ff4dc21d805f70df6a9645c59fffb099980ded1029d802664f9a736"},"schema_version":"1.0","source":{"id":"1301.5046","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5046","created_at":"2026-05-18T03:35:40Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5046v2","created_at":"2026-05-18T03:35:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5046","created_at":"2026-05-18T03:35:40Z"},{"alias_kind":"pith_short_12","alias_value":"RY76ZQDHNMEI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RY76ZQDHNMEIYLCP","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RY76ZQDH","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:fc1067e575ea6bd38aa8e6100319794fb94e108ec1fb7f1a8560c5508b940baf","target":"graph","created_at":"2026-05-18T03:35:40Z","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":"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.","authors_text":"Guofeng Fu, Ruyong Feng, Shaoshi Chen, Ziming Li","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-22T00:37:06Z","title":"On the Structure of Compatible Rational Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5046","kind":"arxiv","version":2},"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:fad778a10f99bed8054a1f58ad8e2dc9fc6269eba7f8764dec5b9d7a15968580","target":"record","created_at":"2026-05-18T03:35:40Z","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":"fccb2013e751acada5a3d27f4603823eebb2981b651119c8ac616703ebd8c310","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-22T00:37:06Z","title_canon_sha256":"d4d0cd6f3ff4dc21d805f70df6a9645c59fffb099980ded1029d802664f9a736"},"schema_version":"1.0","source":{"id":"1301.5046","kind":"arxiv","version":2}},"canonical_sha256":"8e3fecc0676b088c2c4fcce1ab18955e6cf6abb2617d6178e1dbea5a8bdd0d64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e3fecc0676b088c2c4fcce1ab18955e6cf6abb2617d6178e1dbea5a8bdd0d64","first_computed_at":"2026-05-18T03:35:40.488324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:40.488324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D2WvF/NxX2x5S1yqf/ItYyoxhvlzfKtQR3QisqC1DEoavqwvkYyovF9iJxXa4Utt3+V1ghaFBLvPDGsu0CPyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:40.489118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5046","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fad778a10f99bed8054a1f58ad8e2dc9fc6269eba7f8764dec5b9d7a15968580","sha256:fc1067e575ea6bd38aa8e6100319794fb94e108ec1fb7f1a8560c5508b940baf"],"state_sha256":"eddfde015210d619baba4d50a5d063ca82e39bd62573677b28de66eacb7cf110"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HzPWenw+FOl+tmnkoC0jFMLhtjAEF6M7oYQDAyWdY/HU6+wAlHGo1HzADYqWLF/Zl/Lvy0xq8Wu33wXi5cmaCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:20:03.440413Z","bundle_sha256":"157b5e5d1ac9ac89f7539797e0c033d180d887682bf906ee2675c567f21840e0"}}