{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DVVB3X5L2J35ZAVSKYGAA7BE5I","short_pith_number":"pith:DVVB3X5L","canonical_record":{"source":{"id":"1402.2409","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-02-11T09:35:59Z","cross_cats_sorted":[],"title_canon_sha256":"6847ecf492655b6f8ef494134728e8bac4be43cf714e76d8d2418f9dc5ebae9a","abstract_canon_sha256":"04a4be001861705a75c324a94ecd9ae0aa54e4033387ddfa6d4d77ea627b6417"},"schema_version":"1.0"},"canonical_sha256":"1d6a1ddfabd277dc82b2560c007c24ea094fb411196d13b00ec14f76e013e124","source":{"kind":"arxiv","id":"1402.2409","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2409","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2409v3","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2409","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"DVVB3X5L2J35","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DVVB3X5L2J35ZAVS","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DVVB3X5L","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DVVB3X5L2J35ZAVSKYGAA7BE5I","target":"record","payload":{"canonical_record":{"source":{"id":"1402.2409","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-02-11T09:35:59Z","cross_cats_sorted":[],"title_canon_sha256":"6847ecf492655b6f8ef494134728e8bac4be43cf714e76d8d2418f9dc5ebae9a","abstract_canon_sha256":"04a4be001861705a75c324a94ecd9ae0aa54e4033387ddfa6d4d77ea627b6417"},"schema_version":"1.0"},"canonical_sha256":"1d6a1ddfabd277dc82b2560c007c24ea094fb411196d13b00ec14f76e013e124","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:58.006898Z","signature_b64":"xu18BqSFxvTtJHmt8T0uc844yGX/pqxrxEZ8J5uU0EWmqgg1MOrI25wyF+vwJ5LOpwFnpG/8I60k3SGKbUiKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d6a1ddfabd277dc82b2560c007c24ea094fb411196d13b00ec14f76e013e124","last_reissued_at":"2026-05-18T02:45:58.006465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:58.006465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.2409","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ozX5sl2tGskTdifpMMBrSzhoIEthHbqxizr1ctmXqJ1OQ1vWEkaZqRHI4wPOQ7HBE988JLdoebpJyQy1CefMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:54:20.579036Z"},"content_sha256":"9084e228b18d88ae74c608210f42d7953cd3563a1f0200439de1c611dca39444","schema_version":"1.0","event_id":"sha256:9084e228b18d88ae74c608210f42d7953cd3563a1f0200439de1c611dca39444"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DVVB3X5L2J35ZAVSKYGAA7BE5I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Generalized Apagodu-Zeilberger Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Christoph Koutschan, Manuel Kauers, Shaoshi Chen","submitted_at":"2014-02-11T09:35:59Z","abstract_excerpt":"The Apagodu-Zeilberger algorithm can be used for computing annihilating operators for definite sums over hypergeometric terms, or for definite integrals over hyperexponential functions. In this paper, we propose a generalization of this algorithm which is applicable to arbitrary $\\partial$-finite functions. In analogy to the hypergeometric case, we introduce the notion of proper $\\partial$-finite functions. We show that the algorithm always succeeds for these functions, and we give a tight a priori bound for the order of the output operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2409","kind":"arxiv","version":3},"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":"2026-05-18T02:45:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ilcOC05AOqF/oaQD21IKw7P8hjRHga0bB4ncIvhJ9QR7dg5iUDnzhL4eRO3Femg1ujhFc6GayMvx8iAcZVtYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:54:20.579800Z"},"content_sha256":"3834cacb6bf78e1d6ed2d8d7297ba90bc5d348e40bd4109611bc841546f70077","schema_version":"1.0","event_id":"sha256:3834cacb6bf78e1d6ed2d8d7297ba90bc5d348e40bd4109611bc841546f70077"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DVVB3X5L2J35ZAVSKYGAA7BE5I/bundle.json","state_url":"https://pith.science/pith/DVVB3X5L2J35ZAVSKYGAA7BE5I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DVVB3X5L2J35ZAVSKYGAA7BE5I/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":"2026-06-11T16:54:20Z","links":{"resolver":"https://pith.science/pith/DVVB3X5L2J35ZAVSKYGAA7BE5I","bundle":"https://pith.science/pith/DVVB3X5L2J35ZAVSKYGAA7BE5I/bundle.json","state":"https://pith.science/pith/DVVB3X5L2J35ZAVSKYGAA7BE5I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DVVB3X5L2J35ZAVSKYGAA7BE5I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DVVB3X5L2J35ZAVSKYGAA7BE5I","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":"04a4be001861705a75c324a94ecd9ae0aa54e4033387ddfa6d4d77ea627b6417","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-02-11T09:35:59Z","title_canon_sha256":"6847ecf492655b6f8ef494134728e8bac4be43cf714e76d8d2418f9dc5ebae9a"},"schema_version":"1.0","source":{"id":"1402.2409","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2409","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2409v3","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2409","created_at":"2026-05-18T02:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"DVVB3X5L2J35","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DVVB3X5L2J35ZAVS","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DVVB3X5L","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:3834cacb6bf78e1d6ed2d8d7297ba90bc5d348e40bd4109611bc841546f70077","target":"graph","created_at":"2026-05-18T02:45:58Z","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":"The Apagodu-Zeilberger algorithm can be used for computing annihilating operators for definite sums over hypergeometric terms, or for definite integrals over hyperexponential functions. In this paper, we propose a generalization of this algorithm which is applicable to arbitrary $\\partial$-finite functions. In analogy to the hypergeometric case, we introduce the notion of proper $\\partial$-finite functions. We show that the algorithm always succeeds for these functions, and we give a tight a priori bound for the order of the output operator.","authors_text":"Christoph Koutschan, Manuel Kauers, Shaoshi Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-02-11T09:35:59Z","title":"A Generalized Apagodu-Zeilberger Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2409","kind":"arxiv","version":3},"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":"sha256:9084e228b18d88ae74c608210f42d7953cd3563a1f0200439de1c611dca39444","target":"record","created_at":"2026-05-18T02:45:58Z","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":"04a4be001861705a75c324a94ecd9ae0aa54e4033387ddfa6d4d77ea627b6417","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-02-11T09:35:59Z","title_canon_sha256":"6847ecf492655b6f8ef494134728e8bac4be43cf714e76d8d2418f9dc5ebae9a"},"schema_version":"1.0","source":{"id":"1402.2409","kind":"arxiv","version":3}},"canonical_sha256":"1d6a1ddfabd277dc82b2560c007c24ea094fb411196d13b00ec14f76e013e124","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d6a1ddfabd277dc82b2560c007c24ea094fb411196d13b00ec14f76e013e124","first_computed_at":"2026-05-18T02:45:58.006465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:58.006465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xu18BqSFxvTtJHmt8T0uc844yGX/pqxrxEZ8J5uU0EWmqgg1MOrI25wyF+vwJ5LOpwFnpG/8I60k3SGKbUiKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:58.006898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2409","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9084e228b18d88ae74c608210f42d7953cd3563a1f0200439de1c611dca39444","sha256:3834cacb6bf78e1d6ed2d8d7297ba90bc5d348e40bd4109611bc841546f70077"],"state_sha256":"5e831ce5d72b32ca9372106972858d52cbbc94889d5f3786c2e673e3b953b51f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZLvkvnTjZ9sZzvvGajVfIfAkaICbjTpk0VHO6G6CFsOLCV0KMwt5ETUnoAoGNlLuTxeG8B2299uS9MRpDGYBCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:54:20.584000Z","bundle_sha256":"a658be00f34033af3fa4c7190af2a9f4ac1abb7516e39c1befefa0d1e72cb8f7"}}