{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MGR6YFU7S3N774IIOUH54EKUZZ","short_pith_number":"pith:MGR6YFU7","canonical_record":{"source":{"id":"1803.03135","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-07T01:49:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f81b4cff3d47f7734b0850a4ac395463f173c3c5bf12a9466ec1b84e7e9a1ae7","abstract_canon_sha256":"66285e8e5a3ec51860438ac9333137fedee74c3ab23b8b30244d959aeb8e9e08"},"schema_version":"1.0"},"canonical_sha256":"61a3ec169f96dbfff108750fde1154ce6046356fe02940a12a8f34c164f5bf83","source":{"kind":"arxiv","id":"1803.03135","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03135","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03135v3","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03135","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"MGR6YFU7S3N7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MGR6YFU7S3N774II","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MGR6YFU7","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MGR6YFU7S3N774IIOUH54EKUZZ","target":"record","payload":{"canonical_record":{"source":{"id":"1803.03135","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-07T01:49:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f81b4cff3d47f7734b0850a4ac395463f173c3c5bf12a9466ec1b84e7e9a1ae7","abstract_canon_sha256":"66285e8e5a3ec51860438ac9333137fedee74c3ab23b8b30244d959aeb8e9e08"},"schema_version":"1.0"},"canonical_sha256":"61a3ec169f96dbfff108750fde1154ce6046356fe02940a12a8f34c164f5bf83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:19.425826Z","signature_b64":"emSOiVMOQuHWNXzlSof2Pv4xzPj1XDmBPCJLgoBFq4Jg0pcjWEyCWokgQp6K7BIuEzl1IY0TYtV5B189eTszDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61a3ec169f96dbfff108750fde1154ce6046356fe02940a12a8f34c164f5bf83","last_reissued_at":"2026-05-17T23:58:19.425385Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:19.425385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.03135","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":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jQRL0Lb2U6C43JFi/EuDoAi3ks1eLIpAkJyfDCQOsGiG51QiUXpxuxfnN3/DEpaUKXDvmAqEti1yVtEy6c3/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:09:16.252607Z"},"content_sha256":"916d501198968c5e021a0b9d496b17a6442b330508fab08eb955e6f99367491d","schema_version":"1.0","event_id":"sha256:916d501198968c5e021a0b9d496b17a6442b330508fab08eb955e6f99367491d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MGR6YFU7S3N774IIOUH54EKUZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variations on a Hypergeometric Theme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Michael Milgram","submitted_at":"2018-03-07T01:49:56Z","abstract_excerpt":"The question was asked: Is it possible to express the function \\begin{equation} \\tag{1.1} h(a)\\equiv\\,{_4F_3}(a,a,a,a;2a,a+1,a+1;1) \\label{question} \\end{equation} in closed form? After considerable analysis, the answer appears to be \"no\", but during the attempt to answer this question, a number of interesting (and unexpected) related results were obtained, either as specialized transformations, or as closed-form expressions for several related functions. The purpose of this paper is to record and review both the methods attempted and the related identities obtained (specifically new $_4F_3(1)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03135","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":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NjQHFR0i/TepBKt0ZnX5OBpTmogIgLLic7eOodphcvzCtmLKr0VFvdXPzcVXjVAG5ByA/KOeLVQzZmV3P0uOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:09:16.252951Z"},"content_sha256":"baaeaf24ea06296912842cc5887a9e3fd0982854e1d37ea46076214d6e973110","schema_version":"1.0","event_id":"sha256:baaeaf24ea06296912842cc5887a9e3fd0982854e1d37ea46076214d6e973110"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGR6YFU7S3N774IIOUH54EKUZZ/bundle.json","state_url":"https://pith.science/pith/MGR6YFU7S3N774IIOUH54EKUZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGR6YFU7S3N774IIOUH54EKUZZ/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":"2026-06-27T04:09:16Z","links":{"resolver":"https://pith.science/pith/MGR6YFU7S3N774IIOUH54EKUZZ","bundle":"https://pith.science/pith/MGR6YFU7S3N774IIOUH54EKUZZ/bundle.json","state":"https://pith.science/pith/MGR6YFU7S3N774IIOUH54EKUZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGR6YFU7S3N774IIOUH54EKUZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MGR6YFU7S3N774IIOUH54EKUZZ","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":"66285e8e5a3ec51860438ac9333137fedee74c3ab23b8b30244d959aeb8e9e08","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-07T01:49:56Z","title_canon_sha256":"f81b4cff3d47f7734b0850a4ac395463f173c3c5bf12a9466ec1b84e7e9a1ae7"},"schema_version":"1.0","source":{"id":"1803.03135","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03135","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03135v3","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03135","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"MGR6YFU7S3N7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MGR6YFU7S3N774II","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MGR6YFU7","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:baaeaf24ea06296912842cc5887a9e3fd0982854e1d37ea46076214d6e973110","target":"graph","created_at":"2026-05-17T23:58:19Z","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 question was asked: Is it possible to express the function \\begin{equation} \\tag{1.1} h(a)\\equiv\\,{_4F_3}(a,a,a,a;2a,a+1,a+1;1) \\label{question} \\end{equation} in closed form? After considerable analysis, the answer appears to be \"no\", but during the attempt to answer this question, a number of interesting (and unexpected) related results were obtained, either as specialized transformations, or as closed-form expressions for several related functions. The purpose of this paper is to record and review both the methods attempted and the related identities obtained (specifically new $_4F_3(1)","authors_text":"Michael Milgram","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-07T01:49:56Z","title":"Variations on a Hypergeometric Theme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03135","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":"sha256:916d501198968c5e021a0b9d496b17a6442b330508fab08eb955e6f99367491d","target":"record","created_at":"2026-05-17T23:58:19Z","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":"66285e8e5a3ec51860438ac9333137fedee74c3ab23b8b30244d959aeb8e9e08","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-03-07T01:49:56Z","title_canon_sha256":"f81b4cff3d47f7734b0850a4ac395463f173c3c5bf12a9466ec1b84e7e9a1ae7"},"schema_version":"1.0","source":{"id":"1803.03135","kind":"arxiv","version":3}},"canonical_sha256":"61a3ec169f96dbfff108750fde1154ce6046356fe02940a12a8f34c164f5bf83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61a3ec169f96dbfff108750fde1154ce6046356fe02940a12a8f34c164f5bf83","first_computed_at":"2026-05-17T23:58:19.425385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:19.425385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"emSOiVMOQuHWNXzlSof2Pv4xzPj1XDmBPCJLgoBFq4Jg0pcjWEyCWokgQp6K7BIuEzl1IY0TYtV5B189eTszDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:19.425826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03135","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:916d501198968c5e021a0b9d496b17a6442b330508fab08eb955e6f99367491d","sha256:baaeaf24ea06296912842cc5887a9e3fd0982854e1d37ea46076214d6e973110"],"state_sha256":"0069c837607dd9dfc36bf8f75b319b7e1e22d7552bd9b4ed54a1ff305ff0e9a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O+MSSR87tRak4R5naZVNEko6WYPAh74sqqeIj6MtxQStB3XuMRrB1680bcjV8L2586FLdqg3NWIWoSEyAb3YCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:09:16.254842Z","bundle_sha256":"53439a24aeb6bbba0335d9f050d323dc6013d6d7e6ed680d02c8c6947057889f"}}