{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5HZJMFAZFVAFX7WLCEK5WSA3BZ","short_pith_number":"pith:5HZJMFAZ","canonical_record":{"source":{"id":"1506.01064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-02T21:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"0d7f8f399d0a8fab85a25f53dd255d65b2ead0c68bb708ca45d0d4bc90678b55","abstract_canon_sha256":"5d6d984cb95f72b0812fcc5fd0a76726d8d38ddbce7a169dfc1f318e85dad1cb"},"schema_version":"1.0"},"canonical_sha256":"e9f29614192d405bfecb1115db481b0e535c4434adadda2b1266191f8aab9400","source":{"kind":"arxiv","id":"1506.01064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01064","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01064v1","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01064","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"pith_short_12","alias_value":"5HZJMFAZFVAF","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5HZJMFAZFVAFX7WL","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5HZJMFAZ","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5HZJMFAZFVAFX7WLCEK5WSA3BZ","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-02T21:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"0d7f8f399d0a8fab85a25f53dd255d65b2ead0c68bb708ca45d0d4bc90678b55","abstract_canon_sha256":"5d6d984cb95f72b0812fcc5fd0a76726d8d38ddbce7a169dfc1f318e85dad1cb"},"schema_version":"1.0"},"canonical_sha256":"e9f29614192d405bfecb1115db481b0e535c4434adadda2b1266191f8aab9400","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:59.583406Z","signature_b64":"xIPTizOtnSlgVKwLuNPX5lJ8pGF05EbN7ycGM1R2rfwA3Lz2GULCjWUIDF4GKoTUVM53YuyPVcAHu4pRwhovAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9f29614192d405bfecb1115db481b0e535c4434adadda2b1266191f8aab9400","last_reissued_at":"2026-05-18T01:35:59.582761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:59.582761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01064","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":"2026-05-18T01:35:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXDZHCT4P4LXcEoaNUn0ZIDswKyGqcfVuYx9wHull4XPXVoVA0fq3X/Y7BoR4vBefqNy8PgPTZxufmuZyUrkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:05:23.789418Z"},"content_sha256":"1b48b97cd3fccbc189484927f065c0a2846d78a63630afbb75484cd557404cff","schema_version":"1.0","event_id":"sha256:1b48b97cd3fccbc189484927f065c0a2846d78a63630afbb75484cd557404cff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5HZJMFAZFVAFX7WLCEK5WSA3BZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Family of explicitly diagonalizable weighted Hankel matrices generalizing the Hilbert matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Pavel Stovicek, Tomas Kalvoda","submitted_at":"2015-06-02T21:14:57Z","abstract_excerpt":"A three-parameter family $B=B(a,b,c)$ of weighted Hankel matrices is introduced with the entries \\[ B_{j,k}=\\frac{\\Gamma(j+k+a)}{\\Gamma(j+k+b+c)}\\,\\sqrt{\\frac{\\Gamma(j+b)\\Gamma(j+c)\\Gamma(k+b)\\Gamma(k+c)}{\\Gamma(j+a)\\, j!\\,\\Gamma(k+a)\\, k!}}\\,, \\] $j,k\\in\\mathbb{Z}_{+}$, supposing $a$, $b$, $c$ are positive and $a<b+c$, $b<a+c$, $c\\leq a+b$. The famous Hilbert matrix is included as a particular case. The direct sum $B(a,b,c)\\oplus B(a+1,b+1,c)$ is shown to commute with a discrete analog of the dilatation operator. It follows that there exists a three-parameter family of real symmetric Jacobi m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01064","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":"2026-05-18T01:35:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/SLl67YaUXbAfYSir/2MV95gr2lb8PAFmsgUUQnCj5be3HEhBmbuPhhtXwWCvMkkCZtBS/ypTC7iohUyxQCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:05:23.789926Z"},"content_sha256":"4cc07e06f8f6baa65c4f7afbcad990264da8f6b190eb38ecb71fb05ed45345fd","schema_version":"1.0","event_id":"sha256:4cc07e06f8f6baa65c4f7afbcad990264da8f6b190eb38ecb71fb05ed45345fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HZJMFAZFVAFX7WLCEK5WSA3BZ/bundle.json","state_url":"https://pith.science/pith/5HZJMFAZFVAFX7WLCEK5WSA3BZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HZJMFAZFVAFX7WLCEK5WSA3BZ/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":"2026-06-22T22:05:23Z","links":{"resolver":"https://pith.science/pith/5HZJMFAZFVAFX7WLCEK5WSA3BZ","bundle":"https://pith.science/pith/5HZJMFAZFVAFX7WLCEK5WSA3BZ/bundle.json","state":"https://pith.science/pith/5HZJMFAZFVAFX7WLCEK5WSA3BZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HZJMFAZFVAFX7WLCEK5WSA3BZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5HZJMFAZFVAFX7WLCEK5WSA3BZ","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":"5d6d984cb95f72b0812fcc5fd0a76726d8d38ddbce7a169dfc1f318e85dad1cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-02T21:14:57Z","title_canon_sha256":"0d7f8f399d0a8fab85a25f53dd255d65b2ead0c68bb708ca45d0d4bc90678b55"},"schema_version":"1.0","source":{"id":"1506.01064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01064","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01064v1","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01064","created_at":"2026-05-18T01:35:59Z"},{"alias_kind":"pith_short_12","alias_value":"5HZJMFAZFVAF","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5HZJMFAZFVAFX7WL","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5HZJMFAZ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:4cc07e06f8f6baa65c4f7afbcad990264da8f6b190eb38ecb71fb05ed45345fd","target":"graph","created_at":"2026-05-18T01:35:59Z","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":"A three-parameter family $B=B(a,b,c)$ of weighted Hankel matrices is introduced with the entries \\[ B_{j,k}=\\frac{\\Gamma(j+k+a)}{\\Gamma(j+k+b+c)}\\,\\sqrt{\\frac{\\Gamma(j+b)\\Gamma(j+c)\\Gamma(k+b)\\Gamma(k+c)}{\\Gamma(j+a)\\, j!\\,\\Gamma(k+a)\\, k!}}\\,, \\] $j,k\\in\\mathbb{Z}_{+}$, supposing $a$, $b$, $c$ are positive and $a<b+c$, $b<a+c$, $c\\leq a+b$. The famous Hilbert matrix is included as a particular case. The direct sum $B(a,b,c)\\oplus B(a+1,b+1,c)$ is shown to commute with a discrete analog of the dilatation operator. It follows that there exists a three-parameter family of real symmetric Jacobi m","authors_text":"Pavel Stovicek, Tomas Kalvoda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-02T21:14:57Z","title":"Family of explicitly diagonalizable weighted Hankel matrices generalizing the Hilbert matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01064","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":"sha256:1b48b97cd3fccbc189484927f065c0a2846d78a63630afbb75484cd557404cff","target":"record","created_at":"2026-05-18T01:35:59Z","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":"5d6d984cb95f72b0812fcc5fd0a76726d8d38ddbce7a169dfc1f318e85dad1cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-02T21:14:57Z","title_canon_sha256":"0d7f8f399d0a8fab85a25f53dd255d65b2ead0c68bb708ca45d0d4bc90678b55"},"schema_version":"1.0","source":{"id":"1506.01064","kind":"arxiv","version":1}},"canonical_sha256":"e9f29614192d405bfecb1115db481b0e535c4434adadda2b1266191f8aab9400","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9f29614192d405bfecb1115db481b0e535c4434adadda2b1266191f8aab9400","first_computed_at":"2026-05-18T01:35:59.582761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:59.582761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xIPTizOtnSlgVKwLuNPX5lJ8pGF05EbN7ycGM1R2rfwA3Lz2GULCjWUIDF4GKoTUVM53YuyPVcAHu4pRwhovAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:59.583406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b48b97cd3fccbc189484927f065c0a2846d78a63630afbb75484cd557404cff","sha256:4cc07e06f8f6baa65c4f7afbcad990264da8f6b190eb38ecb71fb05ed45345fd"],"state_sha256":"0e144315ae2a941062f90be43c992a020b34df2e716ad18d5d445fceab5323ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"INoLr6GkZUouNEUfcyMokR4Cyj+mwi0vBM7h4zZ6AvqCcpRp5fD3/9+lubAEVlJXrBdsYozonOkTbLvpeVW2BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:05:23.792206Z","bundle_sha256":"a912cc5c021418e2d24ab2e758cd762a267000f6b2b62d20515b11e7581cfe0a"}}