{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:UCEN6TQVLMYNKRRJNOJTZZ244H","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":"1282f48d2de9baf7804923f03937004f343cb1e0709b1cff14f175ec4b3967af","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.CA","submitted_at":"2006-04-13T14:04:02Z","title_canon_sha256":"18c314011ebda2feb92cafb1ee91d6d96f729e9ada85dfd634f407d68f207ea3"},"schema_version":"1.0","source":{"id":"math/0604312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604312","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604312v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604312","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"UCEN6TQVLMYN","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"UCEN6TQVLMYNKRRJ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"UCEN6TQV","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:94befe8eef01f200a85968af4bd6f8e9058c9529828b5a7d41f3e14fd30e1357","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":"In this paper we show how one can obtain simultaneous rational approximants for $\\zeta_q(1)$ and $\\zeta_q(2)$ with a common denominator by means of Hermite-Pade approximation using multiple little q-Jacobi polynomials and we show that properties of these rational approximants prove that 1, $\\zeta_q(1)$, $\\zeta_q(2)$ are linearly independent over the rationals. In particular this implies that $\\zeta_q(1)$ and $\\zeta_q(2)$ are irrational. Furthermore we give an upper bound for the measure of irrationality.","authors_text":"Kelly Postelmans, Walter Van Assche","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2006-04-13T14:04:02Z","title":"Irrationality of $\\zeta_q(1)$ and $\\zeta_q(2)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604312","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":"sha256:7b163b9d057591681ee99f2f7e16a9ec5302907ab57abc5ae535ff56adc88b20","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":"1282f48d2de9baf7804923f03937004f343cb1e0709b1cff14f175ec4b3967af","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.CA","submitted_at":"2006-04-13T14:04:02Z","title_canon_sha256":"18c314011ebda2feb92cafb1ee91d6d96f729e9ada85dfd634f407d68f207ea3"},"schema_version":"1.0","source":{"id":"math/0604312","kind":"arxiv","version":1}},"canonical_sha256":"a088df4e155b30d546296b933ce75ce1db322c0043e3b61018a74016974d34cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a088df4e155b30d546296b933ce75ce1db322c0043e3b61018a74016974d34cd","first_computed_at":"2026-05-18T03:11:24.441188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:24.441188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NYhIw4X14zulISriBHNmh5umDuFzwZpf6xCjAOP6pbjn6nCqAMFWoz05m1QjSycZf9N0DfyiYVHUGUCQpmYNCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:24.441924Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b163b9d057591681ee99f2f7e16a9ec5302907ab57abc5ae535ff56adc88b20","sha256:94befe8eef01f200a85968af4bd6f8e9058c9529828b5a7d41f3e14fd30e1357"],"state_sha256":"15a37feb3672eaf0c5867bd2ba68471e6d372e77d38ae17c6e6fd2abaf7c355c"}