{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:2SKWCTGQMX22H4G6LIZ7OTSDLD","short_pith_number":"pith:2SKWCTGQ","canonical_record":{"source":{"id":"0809.2501","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-15T12:14:36Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7f4dfeefb9c6b570a78c7c89a0264fcbc7429e55823961e5f5c62bcd3b4dea77","abstract_canon_sha256":"e0e066727034cba4bb6fb6c930a09efe154a17377f747084ffc3f3761ddb3eee"},"schema_version":"1.0"},"canonical_sha256":"d495614cd065f5a3f0de5a33f74e4358c930e1077ab3c35f43c1c1c4a473ceeb","source":{"kind":"arxiv","id":"0809.2501","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.2501","created_at":"2026-05-18T02:15:34Z"},{"alias_kind":"arxiv_version","alias_value":"0809.2501v3","created_at":"2026-05-18T02:15:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.2501","created_at":"2026-05-18T02:15:34Z"},{"alias_kind":"pith_short_12","alias_value":"2SKWCTGQMX22","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"2SKWCTGQMX22H4G6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"2SKWCTGQ","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:2SKWCTGQMX22H4G6LIZ7OTSDLD","target":"record","payload":{"canonical_record":{"source":{"id":"0809.2501","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-15T12:14:36Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7f4dfeefb9c6b570a78c7c89a0264fcbc7429e55823961e5f5c62bcd3b4dea77","abstract_canon_sha256":"e0e066727034cba4bb6fb6c930a09efe154a17377f747084ffc3f3761ddb3eee"},"schema_version":"1.0"},"canonical_sha256":"d495614cd065f5a3f0de5a33f74e4358c930e1077ab3c35f43c1c1c4a473ceeb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:34.621410Z","signature_b64":"EiOyVQOAnrzjOpz6kJjKKe1F6Leb4G1jsVJoCPMGtaRa60GHJ7Y7G/lVnR6Qj8DOwqUWcEOuItaMpuJSXy+GAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d495614cd065f5a3f0de5a33f74e4358c930e1077ab3c35f43c1c1c4a473ceeb","last_reissued_at":"2026-05-18T02:15:34.620780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:34.620780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.2501","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":"2026-05-18T02:15:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J0AoLc0rGHyXo4AlxcymDn5kPH4B4Pl7MqCfTgCipSIElDcW50TOwan9j5JxaVWkm7BQy+7HCZ6nsdSP1dNFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:16:59.226770Z"},"content_sha256":"9e9af1182b51677782cffd2f6be7dc8074b11b8ddc56b68c5c7b1526e5298c85","schema_version":"1.0","event_id":"sha256:9e9af1182b51677782cffd2f6be7dc8074b11b8ddc56b68c5c7b1526e5298c85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:2SKWCTGQMX22H4G6LIZ7OTSDLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Irrationality proof of a $q$-extension of $\\zeta(2)$ using little $q$-Jacobi polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Christophe Smet, Walter Van Assche","submitted_at":"2008-09-15T12:14:36Z","abstract_excerpt":"We show how one can use Hermite-Pad\\'{e} approximation and little $q$-Jacobi polynomials to construct rational approximants for $\\zeta_q(2)$. These numbers are $q$-analogues of the well known $\\zeta(2)$. Here $q=\\frac{1}{p}$, with $p$ an integer greater than one. These approximants are good enough to show the irrationality of $\\zeta_q(2)$ and they allow us to calculate an upper bound for its measure of irrationality: $\\mu(\\zeta_q(2))\\leq 10\\pi^2/(5\\pi^2-24) \\approx 3.8936$. This is sharper than the upper bound given by Zudilin (\\textit{On the irrationality measure for a $q$-analogue of $\\zeta("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.2501","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":"2026-05-18T02:15:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MfEbKOqZvr6yIzgr7PxP6gQtP64IJ/4WO20cHvKtCUf8Geh5lpf6dN4x2n550uqKdAfT3ax53zsYcoi6aoMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:16:59.227115Z"},"content_sha256":"959b9906e3ed055b348ad9fb172fe11c2eb5b1b65b1a625ef8f562291feae255","schema_version":"1.0","event_id":"sha256:959b9906e3ed055b348ad9fb172fe11c2eb5b1b65b1a625ef8f562291feae255"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2SKWCTGQMX22H4G6LIZ7OTSDLD/bundle.json","state_url":"https://pith.science/pith/2SKWCTGQMX22H4G6LIZ7OTSDLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2SKWCTGQMX22H4G6LIZ7OTSDLD/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":"2026-06-02T22:16:59Z","links":{"resolver":"https://pith.science/pith/2SKWCTGQMX22H4G6LIZ7OTSDLD","bundle":"https://pith.science/pith/2SKWCTGQMX22H4G6LIZ7OTSDLD/bundle.json","state":"https://pith.science/pith/2SKWCTGQMX22H4G6LIZ7OTSDLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2SKWCTGQMX22H4G6LIZ7OTSDLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:2SKWCTGQMX22H4G6LIZ7OTSDLD","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":"e0e066727034cba4bb6fb6c930a09efe154a17377f747084ffc3f3761ddb3eee","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-15T12:14:36Z","title_canon_sha256":"7f4dfeefb9c6b570a78c7c89a0264fcbc7429e55823961e5f5c62bcd3b4dea77"},"schema_version":"1.0","source":{"id":"0809.2501","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.2501","created_at":"2026-05-18T02:15:34Z"},{"alias_kind":"arxiv_version","alias_value":"0809.2501v3","created_at":"2026-05-18T02:15:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.2501","created_at":"2026-05-18T02:15:34Z"},{"alias_kind":"pith_short_12","alias_value":"2SKWCTGQMX22","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"2SKWCTGQMX22H4G6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"2SKWCTGQ","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:959b9906e3ed055b348ad9fb172fe11c2eb5b1b65b1a625ef8f562291feae255","target":"graph","created_at":"2026-05-18T02:15:34Z","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":"We show how one can use Hermite-Pad\\'{e} approximation and little $q$-Jacobi polynomials to construct rational approximants for $\\zeta_q(2)$. These numbers are $q$-analogues of the well known $\\zeta(2)$. Here $q=\\frac{1}{p}$, with $p$ an integer greater than one. These approximants are good enough to show the irrationality of $\\zeta_q(2)$ and they allow us to calculate an upper bound for its measure of irrationality: $\\mu(\\zeta_q(2))\\leq 10\\pi^2/(5\\pi^2-24) \\approx 3.8936$. This is sharper than the upper bound given by Zudilin (\\textit{On the irrationality measure for a $q$-analogue of $\\zeta(","authors_text":"Christophe Smet, Walter Van Assche","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-15T12:14:36Z","title":"Irrationality proof of a $q$-extension of $\\zeta(2)$ using little $q$-Jacobi polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.2501","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":"sha256:9e9af1182b51677782cffd2f6be7dc8074b11b8ddc56b68c5c7b1526e5298c85","target":"record","created_at":"2026-05-18T02:15:34Z","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":"e0e066727034cba4bb6fb6c930a09efe154a17377f747084ffc3f3761ddb3eee","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-15T12:14:36Z","title_canon_sha256":"7f4dfeefb9c6b570a78c7c89a0264fcbc7429e55823961e5f5c62bcd3b4dea77"},"schema_version":"1.0","source":{"id":"0809.2501","kind":"arxiv","version":3}},"canonical_sha256":"d495614cd065f5a3f0de5a33f74e4358c930e1077ab3c35f43c1c1c4a473ceeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d495614cd065f5a3f0de5a33f74e4358c930e1077ab3c35f43c1c1c4a473ceeb","first_computed_at":"2026-05-18T02:15:34.620780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:34.620780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EiOyVQOAnrzjOpz6kJjKKe1F6Leb4G1jsVJoCPMGtaRa60GHJ7Y7G/lVnR6Qj8DOwqUWcEOuItaMpuJSXy+GAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:34.621410Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.2501","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e9af1182b51677782cffd2f6be7dc8074b11b8ddc56b68c5c7b1526e5298c85","sha256:959b9906e3ed055b348ad9fb172fe11c2eb5b1b65b1a625ef8f562291feae255"],"state_sha256":"849d955af0e835341b7f5caac211a5eae59638140dab6475e5aad1ee645107e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lYc2d/763bfY6os/8beZRVmpyvUfQZ6EUA51izkDENDfUKRZYz+zFus99AvRnbLH8Ztvhy8ywLIgMENbTpK3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:16:59.229179Z","bundle_sha256":"ac5e93bbf3e56c2bf29baaa7986408fa600089e5f8e9e27a2d1b0ae1626b15ba"}}