{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SXRHSNQXCJBIUNNGHVAMXGIMJL","short_pith_number":"pith:SXRHSNQX","canonical_record":{"source":{"id":"1204.3400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-16T08:32:45Z","cross_cats_sorted":[],"title_canon_sha256":"dbde6d1005f10c1cf94504400c5cbfee42c5a9d8f04842cf5db18dd87ad13f9d","abstract_canon_sha256":"faebcd1bf52b4b4dfb510f953baa6f295dd4954c92ef19073fa98a9d5ae1d10d"},"schema_version":"1.0"},"canonical_sha256":"95e279361712428a35a63d40cb990c4aff2974135938fa3dc3ac2078c1614903","source":{"kind":"arxiv","id":"1204.3400","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3400","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3400v1","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3400","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"SXRHSNQXCJBI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SXRHSNQXCJBIUNNG","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SXRHSNQX","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SXRHSNQXCJBIUNNGHVAMXGIMJL","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-16T08:32:45Z","cross_cats_sorted":[],"title_canon_sha256":"dbde6d1005f10c1cf94504400c5cbfee42c5a9d8f04842cf5db18dd87ad13f9d","abstract_canon_sha256":"faebcd1bf52b4b4dfb510f953baa6f295dd4954c92ef19073fa98a9d5ae1d10d"},"schema_version":"1.0"},"canonical_sha256":"95e279361712428a35a63d40cb990c4aff2974135938fa3dc3ac2078c1614903","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:51.632571Z","signature_b64":"CbK87sZwUaL96tH+48REP3aMFa3LQbu6NVZBrBSyDv1Pnwh7YlbZ0HJu1Easks0p2CweIU/9nBnF0dFVbma5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95e279361712428a35a63d40cb990c4aff2974135938fa3dc3ac2078c1614903","last_reissued_at":"2026-05-18T03:57:51.632002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:51.632002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3400","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ibS2j7+9Y6XthYDfAigTETpHwrCBqykhfdubVKeA66ase5Y/DIqKcV5unqvXYUMzhQ5IRnq/ZO5Qrm8X7JnzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:43:44.425061Z"},"content_sha256":"c7fbbc39c26acffa637ea788980af537a048621eaafe88b6331d180a83c51756","schema_version":"1.0","event_id":"sha256:c7fbbc39c26acffa637ea788980af537a048621eaafe88b6331d180a83c51756"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SXRHSNQXCJBIUNNGHVAMXGIMJL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Apparent singular points of factors of reducible generalized hypergeometric equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Akihito Ebisu","submitted_at":"2012-04-16T08:32:45Z","abstract_excerpt":"We consider a reducible generalized hypergeometric equation, whose sub-equation possesses apparent singular points. We determine the polynomial whose roots are these points. We show that this polynomial is a generalized hypergeometric polynomial.\n  Key Words and Phrases. the generalized hypergeometric equation, reducible, apparent singular point, minor of Wronskian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3400","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":""},"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":"2026-05-18T03:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LGqarX2mu7fkyRsqJU6ztnyL6jtU9rSpGkTzFOAHsLtgBYRiP5KVplFOr6xW6XmvmZV+WEs1OmmOMrq7qcE5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:43:44.425717Z"},"content_sha256":"6da61bf77845d41be5610d330e8d4cdec12c986bd5b4d4333f2dd84eeed38adc","schema_version":"1.0","event_id":"sha256:6da61bf77845d41be5610d330e8d4cdec12c986bd5b4d4333f2dd84eeed38adc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SXRHSNQXCJBIUNNGHVAMXGIMJL/bundle.json","state_url":"https://pith.science/pith/SXRHSNQXCJBIUNNGHVAMXGIMJL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SXRHSNQXCJBIUNNGHVAMXGIMJL/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":"2026-06-11T03:43:44Z","links":{"resolver":"https://pith.science/pith/SXRHSNQXCJBIUNNGHVAMXGIMJL","bundle":"https://pith.science/pith/SXRHSNQXCJBIUNNGHVAMXGIMJL/bundle.json","state":"https://pith.science/pith/SXRHSNQXCJBIUNNGHVAMXGIMJL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SXRHSNQXCJBIUNNGHVAMXGIMJL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SXRHSNQXCJBIUNNGHVAMXGIMJL","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":"faebcd1bf52b4b4dfb510f953baa6f295dd4954c92ef19073fa98a9d5ae1d10d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-16T08:32:45Z","title_canon_sha256":"dbde6d1005f10c1cf94504400c5cbfee42c5a9d8f04842cf5db18dd87ad13f9d"},"schema_version":"1.0","source":{"id":"1204.3400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3400","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3400v1","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3400","created_at":"2026-05-18T03:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"SXRHSNQXCJBI","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SXRHSNQXCJBIUNNG","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SXRHSNQX","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:6da61bf77845d41be5610d330e8d4cdec12c986bd5b4d4333f2dd84eeed38adc","target":"graph","created_at":"2026-05-18T03:57:51Z","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":"We consider a reducible generalized hypergeometric equation, whose sub-equation possesses apparent singular points. We determine the polynomial whose roots are these points. We show that this polynomial is a generalized hypergeometric polynomial.\n  Key Words and Phrases. the generalized hypergeometric equation, reducible, apparent singular point, minor of Wronskian.","authors_text":"Akihito Ebisu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-16T08:32:45Z","title":"Apparent singular points of factors of reducible generalized hypergeometric equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3400","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:c7fbbc39c26acffa637ea788980af537a048621eaafe88b6331d180a83c51756","target":"record","created_at":"2026-05-18T03:57:51Z","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":"faebcd1bf52b4b4dfb510f953baa6f295dd4954c92ef19073fa98a9d5ae1d10d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-16T08:32:45Z","title_canon_sha256":"dbde6d1005f10c1cf94504400c5cbfee42c5a9d8f04842cf5db18dd87ad13f9d"},"schema_version":"1.0","source":{"id":"1204.3400","kind":"arxiv","version":1}},"canonical_sha256":"95e279361712428a35a63d40cb990c4aff2974135938fa3dc3ac2078c1614903","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95e279361712428a35a63d40cb990c4aff2974135938fa3dc3ac2078c1614903","first_computed_at":"2026-05-18T03:57:51.632002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:51.632002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CbK87sZwUaL96tH+48REP3aMFa3LQbu6NVZBrBSyDv1Pnwh7YlbZ0HJu1Easks0p2CweIU/9nBnF0dFVbma5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:51.632571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7fbbc39c26acffa637ea788980af537a048621eaafe88b6331d180a83c51756","sha256:6da61bf77845d41be5610d330e8d4cdec12c986bd5b4d4333f2dd84eeed38adc"],"state_sha256":"404f1186291b4e438fced82b5152cf566ebc440484d0215883d45ef2663e0345"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nvznv7OxuX9qUClVi4/8q9ishVqcokp/V1/e4zdtOX8aqQwISlvbtmqghnZj7fyqkp/ZnhDWE1fEmJil58alAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:43:44.429482Z","bundle_sha256":"dbfe50e6cd5e2a1f667fbcecc62d97897d67f8942972e441fe4949d696ca61cd"}}