{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3DDTCK4WFNMQNF6X67DYXFSX5U","short_pith_number":"pith:3DDTCK4W","canonical_record":{"source":{"id":"1304.5830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-22T04:10:08Z","cross_cats_sorted":[],"title_canon_sha256":"685308af1b6b77f94363160336ae6b376928b8c02e43aa0b7e10f8d68ebb4878","abstract_canon_sha256":"53e582bfb2124ceb0eeeff068eaa6bfca7f0f73340ac5201ed527e46efb7b680"},"schema_version":"1.0"},"canonical_sha256":"d8c7312b962b590697d7f7c78b9657ed2aee0022178707e506de94f0fcd650ea","source":{"kind":"arxiv","id":"1304.5830","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5830","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5830v1","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5830","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"3DDTCK4WFNMQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3DDTCK4WFNMQNF6X","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3DDTCK4W","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3DDTCK4WFNMQNF6X67DYXFSX5U","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-22T04:10:08Z","cross_cats_sorted":[],"title_canon_sha256":"685308af1b6b77f94363160336ae6b376928b8c02e43aa0b7e10f8d68ebb4878","abstract_canon_sha256":"53e582bfb2124ceb0eeeff068eaa6bfca7f0f73340ac5201ed527e46efb7b680"},"schema_version":"1.0"},"canonical_sha256":"d8c7312b962b590697d7f7c78b9657ed2aee0022178707e506de94f0fcd650ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:23.986141Z","signature_b64":"HcOJ3zWhROd+537z17JtW7FrZBSc+5BP03qaeZVf/jOquyKOSac429IZhFJQnf4lQuYzaGWbjnPI4JTJlJDKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8c7312b962b590697d7f7c78b9657ed2aee0022178707e506de94f0fcd650ea","last_reissued_at":"2026-05-18T03:27:23.985361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:23.985361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5830","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":"2026-05-18T03:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lW1Y2ucqJaexbNp79U5jHrigjYYMFWDt8QjuLeasmTjwDaI5bm4lUQ8v5OM4waFk7aYqquQruICvygAzeYnBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:42:11.749103Z"},"content_sha256":"041ffe1db809618674a97a6fd71d4147570d146814c654c2e95c833623e86c7f","schema_version":"1.0","event_id":"sha256:041ffe1db809618674a97a6fd71d4147570d146814c654c2e95c833623e86c7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3DDTCK4WFNMQNF6X67DYXFSX5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contiguous relations and summation and transformation formulas for basic hypergeometric series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Feng Gao, Victor J. W. Guo","submitted_at":"2013-04-22T04:10:08Z","abstract_excerpt":"By using contiguous relations for basic hypergeometric series, we give simple proofs of Bailey's $_4\\phi_3$ summation, Carlitz's $_5\\phi_4$ summation, Sears' $_3\\phi_2$ to $_5\\phi_4$ transformation, Sears' ${}_4\\phi_3$ transformations, Chen's bibasic summation, Gasper's split poised $_{10}\\phi_9$ transformation, Chu's bibasic symmetric transformation. Along the same line, finite forms of Sylvester's identity, Jacobi's triple product identity, and Kang's identity are also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5830","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":"2026-05-18T03:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OCuDk1NEJMCiqNfMOZYyucl45Gh5hS02f5VbfPWmBXKVXPZ4URcv8m0vi+nEd6GPD9EtxarhOOIzzdVYGeDKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:42:11.749787Z"},"content_sha256":"ff74c120804c4571e302b766b4de65a2c6ac94123155c2ac7fe75d34e548881e","schema_version":"1.0","event_id":"sha256:ff74c120804c4571e302b766b4de65a2c6ac94123155c2ac7fe75d34e548881e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DDTCK4WFNMQNF6X67DYXFSX5U/bundle.json","state_url":"https://pith.science/pith/3DDTCK4WFNMQNF6X67DYXFSX5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DDTCK4WFNMQNF6X67DYXFSX5U/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":"2026-05-26T01:42:11Z","links":{"resolver":"https://pith.science/pith/3DDTCK4WFNMQNF6X67DYXFSX5U","bundle":"https://pith.science/pith/3DDTCK4WFNMQNF6X67DYXFSX5U/bundle.json","state":"https://pith.science/pith/3DDTCK4WFNMQNF6X67DYXFSX5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DDTCK4WFNMQNF6X67DYXFSX5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3DDTCK4WFNMQNF6X67DYXFSX5U","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":"53e582bfb2124ceb0eeeff068eaa6bfca7f0f73340ac5201ed527e46efb7b680","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-22T04:10:08Z","title_canon_sha256":"685308af1b6b77f94363160336ae6b376928b8c02e43aa0b7e10f8d68ebb4878"},"schema_version":"1.0","source":{"id":"1304.5830","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5830","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5830v1","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5830","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"3DDTCK4WFNMQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3DDTCK4WFNMQNF6X","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3DDTCK4W","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:ff74c120804c4571e302b766b4de65a2c6ac94123155c2ac7fe75d34e548881e","target":"graph","created_at":"2026-05-18T03:27:23Z","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":"By using contiguous relations for basic hypergeometric series, we give simple proofs of Bailey's $_4\\phi_3$ summation, Carlitz's $_5\\phi_4$ summation, Sears' $_3\\phi_2$ to $_5\\phi_4$ transformation, Sears' ${}_4\\phi_3$ transformations, Chen's bibasic summation, Gasper's split poised $_{10}\\phi_9$ transformation, Chu's bibasic symmetric transformation. Along the same line, finite forms of Sylvester's identity, Jacobi's triple product identity, and Kang's identity are also obtained.","authors_text":"Feng Gao, Victor J. W. Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-22T04:10:08Z","title":"Contiguous relations and summation and transformation formulas for basic hypergeometric series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5830","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":"sha256:041ffe1db809618674a97a6fd71d4147570d146814c654c2e95c833623e86c7f","target":"record","created_at":"2026-05-18T03:27:23Z","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":"53e582bfb2124ceb0eeeff068eaa6bfca7f0f73340ac5201ed527e46efb7b680","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-22T04:10:08Z","title_canon_sha256":"685308af1b6b77f94363160336ae6b376928b8c02e43aa0b7e10f8d68ebb4878"},"schema_version":"1.0","source":{"id":"1304.5830","kind":"arxiv","version":1}},"canonical_sha256":"d8c7312b962b590697d7f7c78b9657ed2aee0022178707e506de94f0fcd650ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8c7312b962b590697d7f7c78b9657ed2aee0022178707e506de94f0fcd650ea","first_computed_at":"2026-05-18T03:27:23.985361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:23.985361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HcOJ3zWhROd+537z17JtW7FrZBSc+5BP03qaeZVf/jOquyKOSac429IZhFJQnf4lQuYzaGWbjnPI4JTJlJDKBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:23.986141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5830","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:041ffe1db809618674a97a6fd71d4147570d146814c654c2e95c833623e86c7f","sha256:ff74c120804c4571e302b766b4de65a2c6ac94123155c2ac7fe75d34e548881e"],"state_sha256":"bab6d990393a72c51c93fc06e8c0af67f05b78d957ce59e9d12d3bb056b5ad56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5HRpEMdozChaTpyjofZcV6vtvsOWTJZMbYnPClobkekqIHeVfSbyezwPuTSLQamhUZmUDjP/AGls/h7LTs0KCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:42:11.752620Z","bundle_sha256":"efb439504eb3ed42c40e23c43747a7e88fd047ec1eca259247a72eb45b8164f2"}}