{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:PQPC5EDWV3P7IWZR5OJTLWXP72","short_pith_number":"pith:PQPC5EDW","canonical_record":{"source":{"id":"math/0101187","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2001-01-23T11:34:32Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e33ac2282afcec9992eaba817210c7a58a1780e87512f81dd5100043aca62d63","abstract_canon_sha256":"b1cf2c5b4677cf983f30b7a7bc562359c6cbd14c4a199a845796fed01ab5ece2"},"schema_version":"1.0"},"canonical_sha256":"7c1e2e9076aedff45b31eb9335daeffea2b80d5d09b913bf6df16fecc9601e7f","source":{"kind":"arxiv","id":"math/0101187","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0101187","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0101187v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101187","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"PQPC5EDWV3P7","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"PQPC5EDWV3P7IWZR","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"PQPC5EDW","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:PQPC5EDWV3P7IWZR5OJTLWXP72","target":"record","payload":{"canonical_record":{"source":{"id":"math/0101187","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2001-01-23T11:34:32Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e33ac2282afcec9992eaba817210c7a58a1780e87512f81dd5100043aca62d63","abstract_canon_sha256":"b1cf2c5b4677cf983f30b7a7bc562359c6cbd14c4a199a845796fed01ab5ece2"},"schema_version":"1.0"},"canonical_sha256":"7c1e2e9076aedff45b31eb9335daeffea2b80d5d09b913bf6df16fecc9601e7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:24.610045Z","signature_b64":"VTKyIEwCWzf1MXUZSOJ38C4ZhshEwBwSpbgIPJeG57FMB3isd3malyNGjD61Uvs6YepjMoEDSxLi62yFITR2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c1e2e9076aedff45b31eb9335daeffea2b80d5d09b913bf6df16fecc9601e7f","last_reissued_at":"2026-05-18T03:11:24.609465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:24.609465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0101187","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":"2026-05-18T03:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RPuo1IPXuwgatLxRpC+GYdMFejyp8ThWI6b66uxN5ptY7TbsDgWhwP8fHY/JzIb/7pE3lWb98PXgt1BvS5+sBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:26:50.165446Z"},"content_sha256":"cb8da7ec3ea8f7314874de7d0678df8f1dab8a1f02ffc6faaa259a4e335137a1","schema_version":"1.0","event_id":"sha256:cb8da7ec3ea8f7314874de7d0678df8f1dab8a1f02ffc6faaa259a4e335137a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:PQPC5EDWV3P7IWZR5OJTLWXP72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Little q-Legendre polynomials and irrationality of certain Lambert series","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Walter Van Assche","submitted_at":"2001-01-23T11:34:32Z","abstract_excerpt":"We show how one can obtain rational approximants for $q$-extensions of the harmonic series and the logarithm (and many other similar quantities) by Pad\\'e approximation using little $q$-Legendre polynomials and we show that properties of these orthogonal polynomials indeed prove the irrationality, with an upper bound of the measure of irrationality which is as sharp as the upper bound given by Bundschuh and V\\\"a\\\"an\\\"anen for the harmonic series and a better upper bound than the one given by Matala-aho and V\\\"a\\\"an\\\"anen for the logarithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101187","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":"2026-05-18T03:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WwNBRKTd7w+FJ4iKkrooe0DaCLiJOg7AhO/HMB49/lgjiYx3zI9kPwi2on/uA4b0UgtdfRPJ/iNMDDw9rSqHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:26:50.165798Z"},"content_sha256":"21a30d7f2d0cf10a47da00f4ddff1a758505ff6bd60b3f6ce8c28843dce8c646","schema_version":"1.0","event_id":"sha256:21a30d7f2d0cf10a47da00f4ddff1a758505ff6bd60b3f6ce8c28843dce8c646"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQPC5EDWV3P7IWZR5OJTLWXP72/bundle.json","state_url":"https://pith.science/pith/PQPC5EDWV3P7IWZR5OJTLWXP72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQPC5EDWV3P7IWZR5OJTLWXP72/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":"2026-06-05T02:26:50Z","links":{"resolver":"https://pith.science/pith/PQPC5EDWV3P7IWZR5OJTLWXP72","bundle":"https://pith.science/pith/PQPC5EDWV3P7IWZR5OJTLWXP72/bundle.json","state":"https://pith.science/pith/PQPC5EDWV3P7IWZR5OJTLWXP72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQPC5EDWV3P7IWZR5OJTLWXP72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:PQPC5EDWV3P7IWZR5OJTLWXP72","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":"b1cf2c5b4677cf983f30b7a7bc562359c6cbd14c4a199a845796fed01ab5ece2","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.CA","submitted_at":"2001-01-23T11:34:32Z","title_canon_sha256":"e33ac2282afcec9992eaba817210c7a58a1780e87512f81dd5100043aca62d63"},"schema_version":"1.0","source":{"id":"math/0101187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0101187","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0101187v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101187","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"PQPC5EDWV3P7","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"PQPC5EDWV3P7IWZR","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"PQPC5EDW","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:21a30d7f2d0cf10a47da00f4ddff1a758505ff6bd60b3f6ce8c28843dce8c646","target":"graph","created_at":"2026-05-18T03:11:24Z","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 obtain rational approximants for $q$-extensions of the harmonic series and the logarithm (and many other similar quantities) by Pad\\'e approximation using little $q$-Legendre polynomials and we show that properties of these orthogonal polynomials indeed prove the irrationality, with an upper bound of the measure of irrationality which is as sharp as the upper bound given by Bundschuh and V\\\"a\\\"an\\\"anen for the harmonic series and a better upper bound than the one given by Matala-aho and V\\\"a\\\"an\\\"anen for the logarithm.","authors_text":"Walter Van Assche","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2001-01-23T11:34:32Z","title":"Little q-Legendre polynomials and irrationality of certain Lambert series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101187","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:cb8da7ec3ea8f7314874de7d0678df8f1dab8a1f02ffc6faaa259a4e335137a1","target":"record","created_at":"2026-05-18T03:11:24Z","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":"b1cf2c5b4677cf983f30b7a7bc562359c6cbd14c4a199a845796fed01ab5ece2","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.CA","submitted_at":"2001-01-23T11:34:32Z","title_canon_sha256":"e33ac2282afcec9992eaba817210c7a58a1780e87512f81dd5100043aca62d63"},"schema_version":"1.0","source":{"id":"math/0101187","kind":"arxiv","version":1}},"canonical_sha256":"7c1e2e9076aedff45b31eb9335daeffea2b80d5d09b913bf6df16fecc9601e7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c1e2e9076aedff45b31eb9335daeffea2b80d5d09b913bf6df16fecc9601e7f","first_computed_at":"2026-05-18T03:11:24.609465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:24.609465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VTKyIEwCWzf1MXUZSOJ38C4ZhshEwBwSpbgIPJeG57FMB3isd3malyNGjD61Uvs6YepjMoEDSxLi62yFITR2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:24.610045Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0101187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb8da7ec3ea8f7314874de7d0678df8f1dab8a1f02ffc6faaa259a4e335137a1","sha256:21a30d7f2d0cf10a47da00f4ddff1a758505ff6bd60b3f6ce8c28843dce8c646"],"state_sha256":"8530bf2a14a028c0b401c2191f3c6f2e75acff26d9e0d885fc04e34ca6bc83f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rmPaOuU9imEYcq0kE9IeDJqIJyCfNkayQsTTDDArEpGvpZItdSnFeFR3PzQ00+QwE+wF+PelEuR190Wsstr9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:26:50.167802Z","bundle_sha256":"5551504279e0820aef08c61dcde658a6c8b04ac97a683e45720a0598b0fe2b6e"}}