{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TKVETI3CEM2AVDFHSKEOHB3Q4P","short_pith_number":"pith:TKVETI3C","canonical_record":{"source":{"id":"1309.4568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-18T07:55:37Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7bce794c1ff8c0a61c70aec30c8888066998d8ce5d609217d0dac6e40d194c8b","abstract_canon_sha256":"c20ccbc72d5b916e4d6c457dac118399b7001ff73c82a07044fae376c524fe95"},"schema_version":"1.0"},"canonical_sha256":"9aaa49a36223340a8ca79288e38770e3ee07523a3b426c3bf1ae14eec0ec5037","source":{"kind":"arxiv","id":"1309.4568","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4568","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4568v1","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4568","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"TKVETI3CEM2A","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TKVETI3CEM2AVDFH","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TKVETI3C","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TKVETI3CEM2AVDFHSKEOHB3Q4P","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4568","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-18T07:55:37Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7bce794c1ff8c0a61c70aec30c8888066998d8ce5d609217d0dac6e40d194c8b","abstract_canon_sha256":"c20ccbc72d5b916e4d6c457dac118399b7001ff73c82a07044fae376c524fe95"},"schema_version":"1.0"},"canonical_sha256":"9aaa49a36223340a8ca79288e38770e3ee07523a3b426c3bf1ae14eec0ec5037","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.992888Z","signature_b64":"7Y1sZl0f4peceWlc9+A00dLrbjsFBdwBT7yVOeg0COhRNI6Vex8oNcIEaCWJkqWL7hi8YqSTGWpbm20uS9iJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aaa49a36223340a8ca79288e38770e3ee07523a3b426c3bf1ae14eec0ec5037","last_reissued_at":"2026-05-18T03:12:58.992150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.992150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4568","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":"2026-05-18T03:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IsuyVJflPYcn9pwXvafx0SBUpiZ0OwOjKd+wfHRtbmwUlhS47J8cIcC/JitQa4/G+kk+V9InhqiMNlaXvKegBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:30:05.252931Z"},"content_sha256":"226019518f8263d042b0ac0f0fb0e630f347996931aeba8618f2e0c097970dcd","schema_version":"1.0","event_id":"sha256:226019518f8263d042b0ac0f0fb0e630f347996931aeba8618f2e0c097970dcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TKVETI3CEM2AVDFHSKEOHB3Q4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypergeometric Functions I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Ian G. Macdonald","submitted_at":"2013-09-18T07:55:37Z","abstract_excerpt":"This is the typewritten version of a handwritten manuscript which was completed by Ian G. Macdonald in 1987 or 1988. The manuscript is a very informal working paper, never intended for formal publication. Nevertheless, copies of the manuscript have circulated widely, giving rise to quite a few citations in the subsequent 25 years. Therefore it seems justified to make the manuscript available for the whole mathematical community. The author kindly gave his permission that a typewritten version be posted on arXiv."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4568","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":"2026-05-18T03:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALfp+dAstfr7ju9B5mZN3sDPDTMi7Bit8a/yPtNW4i9f5cEvs+g8lLohFG2k9aAc4KqvO28WEFZU67Q9XunWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T03:30:05.253602Z"},"content_sha256":"5e6cdec6099a92b3032cf4de34db54499c6d15b9d6f770edf0e5e042f59aecfa","schema_version":"1.0","event_id":"sha256:5e6cdec6099a92b3032cf4de34db54499c6d15b9d6f770edf0e5e042f59aecfa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKVETI3CEM2AVDFHSKEOHB3Q4P/bundle.json","state_url":"https://pith.science/pith/TKVETI3CEM2AVDFHSKEOHB3Q4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKVETI3CEM2AVDFHSKEOHB3Q4P/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":"2026-05-22T03:30:05Z","links":{"resolver":"https://pith.science/pith/TKVETI3CEM2AVDFHSKEOHB3Q4P","bundle":"https://pith.science/pith/TKVETI3CEM2AVDFHSKEOHB3Q4P/bundle.json","state":"https://pith.science/pith/TKVETI3CEM2AVDFHSKEOHB3Q4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKVETI3CEM2AVDFHSKEOHB3Q4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TKVETI3CEM2AVDFHSKEOHB3Q4P","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":"c20ccbc72d5b916e4d6c457dac118399b7001ff73c82a07044fae376c524fe95","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-18T07:55:37Z","title_canon_sha256":"7bce794c1ff8c0a61c70aec30c8888066998d8ce5d609217d0dac6e40d194c8b"},"schema_version":"1.0","source":{"id":"1309.4568","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4568","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4568v1","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4568","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"TKVETI3CEM2A","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TKVETI3CEM2AVDFH","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TKVETI3C","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:5e6cdec6099a92b3032cf4de34db54499c6d15b9d6f770edf0e5e042f59aecfa","target":"graph","created_at":"2026-05-18T03:12:58Z","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":"This is the typewritten version of a handwritten manuscript which was completed by Ian G. Macdonald in 1987 or 1988. The manuscript is a very informal working paper, never intended for formal publication. Nevertheless, copies of the manuscript have circulated widely, giving rise to quite a few citations in the subsequent 25 years. Therefore it seems justified to make the manuscript available for the whole mathematical community. The author kindly gave his permission that a typewritten version be posted on arXiv.","authors_text":"Ian G. Macdonald","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-18T07:55:37Z","title":"Hypergeometric Functions I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4568","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":"sha256:226019518f8263d042b0ac0f0fb0e630f347996931aeba8618f2e0c097970dcd","target":"record","created_at":"2026-05-18T03:12:58Z","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":"c20ccbc72d5b916e4d6c457dac118399b7001ff73c82a07044fae376c524fe95","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-18T07:55:37Z","title_canon_sha256":"7bce794c1ff8c0a61c70aec30c8888066998d8ce5d609217d0dac6e40d194c8b"},"schema_version":"1.0","source":{"id":"1309.4568","kind":"arxiv","version":1}},"canonical_sha256":"9aaa49a36223340a8ca79288e38770e3ee07523a3b426c3bf1ae14eec0ec5037","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9aaa49a36223340a8ca79288e38770e3ee07523a3b426c3bf1ae14eec0ec5037","first_computed_at":"2026-05-18T03:12:58.992150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:58.992150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Y1sZl0f4peceWlc9+A00dLrbjsFBdwBT7yVOeg0COhRNI6Vex8oNcIEaCWJkqWL7hi8YqSTGWpbm20uS9iJBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:58.992888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4568","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:226019518f8263d042b0ac0f0fb0e630f347996931aeba8618f2e0c097970dcd","sha256:5e6cdec6099a92b3032cf4de34db54499c6d15b9d6f770edf0e5e042f59aecfa"],"state_sha256":"11182beb9b4d1dee6f3163b58544d45102ca8f8641f560e11bc2c9f59243f466"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4J9FSPWzesQ8og78s34BaemisqqlEwhw6tdh4kY/T5sLXhG0dp+hKF/1deZwOK/nc7fwRtce8cHu9hn4pxOrDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T03:30:05.259158Z","bundle_sha256":"6320010d7a9e23bdae8ca024573d971e56179fd1c2e1c726965757ac6648195e"}}