{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HRX4YHDBSR5XQDYUHLNAXPRSZ2","short_pith_number":"pith:HRX4YHDB","canonical_record":{"source":{"id":"1308.6665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-08-30T07:29:15Z","cross_cats_sorted":[],"title_canon_sha256":"7720213d33134c9e0690d1a13363aa3bf2c6fb7037c5ffc9656bbfd0c74ec762","abstract_canon_sha256":"d85f0b166e6cef94152d2cd40aa62d4faf95e9115e35b387bafe0a925c95509e"},"schema_version":"1.0"},"canonical_sha256":"3c6fcc1c61947b780f143ada0bbe32cea5867e30aef68f34ed7bcbf8679d9cd3","source":{"kind":"arxiv","id":"1308.6665","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6665","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6665v1","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6665","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"HRX4YHDBSR5X","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HRX4YHDBSR5XQDYU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HRX4YHDB","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HRX4YHDBSR5XQDYUHLNAXPRSZ2","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-08-30T07:29:15Z","cross_cats_sorted":[],"title_canon_sha256":"7720213d33134c9e0690d1a13363aa3bf2c6fb7037c5ffc9656bbfd0c74ec762","abstract_canon_sha256":"d85f0b166e6cef94152d2cd40aa62d4faf95e9115e35b387bafe0a925c95509e"},"schema_version":"1.0"},"canonical_sha256":"3c6fcc1c61947b780f143ada0bbe32cea5867e30aef68f34ed7bcbf8679d9cd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:47.630847Z","signature_b64":"u6mf1OnokUa8pHnU8NfqoOPUbKf8b3YNZipLxffgIUyks6sThEpwFU/XJIOmreOINZ6qpvdJG6lhH0vy2426Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c6fcc1c61947b780f143ada0bbe32cea5867e30aef68f34ed7bcbf8679d9cd3","last_reissued_at":"2026-05-18T01:37:47.630491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:47.630491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6665","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":"2026-05-18T01:37:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Goe4MKkDzxFXYUTXcu+BXAUmmsWAbMpMIj0lkHuPgJ/IPKX6jiR0YKUGTqNSjeyydvH1DFb7LYQxhtjZAendDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:09:37.436178Z"},"content_sha256":"e1639240e5608e94c091053056000442b20b771af4e9e1a0ce992f5896cedc32","schema_version":"1.0","event_id":"sha256:e1639240e5608e94c091053056000442b20b771af4e9e1a0ce992f5896cedc32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HRX4YHDBSR5XQDYUHLNAXPRSZ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ramanujan's $_1\\psi_1$ summation theorem --- perspective, announcement of bilateral $q$-Dixon--Anderson and $q$-Selberg integral extensions, and context","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Masahiko Ito, Peter J. Forrester","submitted_at":"2013-08-30T07:29:15Z","abstract_excerpt":"The Ramanujan $_1\\psi_1$ summation theorem in studied from the perspective of $q$-Jackson integrals, $q$-difference equations and connection formulas. This is an approach which has previously been shown to yield Bailey's very-well-poised $_6\\psi_6$ summation. Bilateral Jackson integral generalizations of the Dixon--Anderson and Selberg integrals relating to the type $A$ root system are identified as natural candidates for multidimensional generalizations of the Ramanujan $_1\\psi_1$ summation theorem. New results of this type are announced, and furthermore they are put into context by reviewing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6665","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":"2026-05-18T01:37:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cbaiVbEzZZp+aVnls6Jjq7vQbSdTjiUZx/Vaf7mIs3J9OO8reoblI6UMYv0yEJwQJUmDm3s1CChMngcuvFofBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:09:37.436550Z"},"content_sha256":"69608879eee4b9551cf1833121ce704892dd48303fc42a045e8e083c27b21bae","schema_version":"1.0","event_id":"sha256:69608879eee4b9551cf1833121ce704892dd48303fc42a045e8e083c27b21bae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HRX4YHDBSR5XQDYUHLNAXPRSZ2/bundle.json","state_url":"https://pith.science/pith/HRX4YHDBSR5XQDYUHLNAXPRSZ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HRX4YHDBSR5XQDYUHLNAXPRSZ2/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":"2026-05-28T09:09:37Z","links":{"resolver":"https://pith.science/pith/HRX4YHDBSR5XQDYUHLNAXPRSZ2","bundle":"https://pith.science/pith/HRX4YHDBSR5XQDYUHLNAXPRSZ2/bundle.json","state":"https://pith.science/pith/HRX4YHDBSR5XQDYUHLNAXPRSZ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HRX4YHDBSR5XQDYUHLNAXPRSZ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HRX4YHDBSR5XQDYUHLNAXPRSZ2","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":"d85f0b166e6cef94152d2cd40aa62d4faf95e9115e35b387bafe0a925c95509e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-08-30T07:29:15Z","title_canon_sha256":"7720213d33134c9e0690d1a13363aa3bf2c6fb7037c5ffc9656bbfd0c74ec762"},"schema_version":"1.0","source":{"id":"1308.6665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6665","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6665v1","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6665","created_at":"2026-05-18T01:37:47Z"},{"alias_kind":"pith_short_12","alias_value":"HRX4YHDBSR5X","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HRX4YHDBSR5XQDYU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HRX4YHDB","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:69608879eee4b9551cf1833121ce704892dd48303fc42a045e8e083c27b21bae","target":"graph","created_at":"2026-05-18T01:37:47Z","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 Ramanujan $_1\\psi_1$ summation theorem in studied from the perspective of $q$-Jackson integrals, $q$-difference equations and connection formulas. This is an approach which has previously been shown to yield Bailey's very-well-poised $_6\\psi_6$ summation. Bilateral Jackson integral generalizations of the Dixon--Anderson and Selberg integrals relating to the type $A$ root system are identified as natural candidates for multidimensional generalizations of the Ramanujan $_1\\psi_1$ summation theorem. New results of this type are announced, and furthermore they are put into context by reviewing","authors_text":"Masahiko Ito, Peter J. Forrester","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-08-30T07:29:15Z","title":"Ramanujan's $_1\\psi_1$ summation theorem --- perspective, announcement of bilateral $q$-Dixon--Anderson and $q$-Selberg integral extensions, and context"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6665","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:e1639240e5608e94c091053056000442b20b771af4e9e1a0ce992f5896cedc32","target":"record","created_at":"2026-05-18T01:37:47Z","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":"d85f0b166e6cef94152d2cd40aa62d4faf95e9115e35b387bafe0a925c95509e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-08-30T07:29:15Z","title_canon_sha256":"7720213d33134c9e0690d1a13363aa3bf2c6fb7037c5ffc9656bbfd0c74ec762"},"schema_version":"1.0","source":{"id":"1308.6665","kind":"arxiv","version":1}},"canonical_sha256":"3c6fcc1c61947b780f143ada0bbe32cea5867e30aef68f34ed7bcbf8679d9cd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c6fcc1c61947b780f143ada0bbe32cea5867e30aef68f34ed7bcbf8679d9cd3","first_computed_at":"2026-05-18T01:37:47.630491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:47.630491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u6mf1OnokUa8pHnU8NfqoOPUbKf8b3YNZipLxffgIUyks6sThEpwFU/XJIOmreOINZ6qpvdJG6lhH0vy2426Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:47.630847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1639240e5608e94c091053056000442b20b771af4e9e1a0ce992f5896cedc32","sha256:69608879eee4b9551cf1833121ce704892dd48303fc42a045e8e083c27b21bae"],"state_sha256":"b9faa542b7ef7424c45ffd9e92ef218758451e716918e8dafd1f035222e108e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nyzq6IuUwMtLdNy79BDhfm737UHGa1pIUtfeTDsX+xtZUn1GdoCyzvJmterxFkQx9D6BZMq02+AWtKeDNdT+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:09:37.438524Z","bundle_sha256":"e188198b90cf9abb2b6ae73d66e4b09aee714275b5eae2f0b10395e695d92c0e"}}