{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7X6JEQZUU4OCRNUK2BOHOW5GQI","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":"59080dde0bac892ea4ee6b2d66f196d556d929a218ef15b13a4d301b9523290d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-02T11:56:06Z","title_canon_sha256":"5a772a29ee1e3eefec6b31a22fa8d2f6f74a9912872cf3f5eccf15b6ec9e5294"},"schema_version":"1.0","source":{"id":"1805.00750","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00750","created_at":"2026-05-18T00:16:57Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00750v1","created_at":"2026-05-18T00:16:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00750","created_at":"2026-05-18T00:16:57Z"},{"alias_kind":"pith_short_12","alias_value":"7X6JEQZUU4OC","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7X6JEQZUU4OCRNUK","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7X6JEQZU","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:0bbe753851397d81d78d8857490f6906840d3312f101d4d8551d6d3c70cb116c","target":"graph","created_at":"2026-05-18T00:16:57Z","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":"Pad\\'e approximations and Siegel's lemma are widely used tools in Diophantine approximation theory. This work has evolved from the attempts to improve Baker-type linear independence measures, either by using the Bombieri-Vaaler version of Siegel's lemma to sharpen the estimates of Pad\\'e-type approximations, or by finding completely explicit expressions for the yet unknown 'twin type' Hermite-Pad\\'e approximations. The appropriate homogeneous matrix equation representing both methods has an $M \\times (L+1)$ coefficient matrix, where $M \\le L$. The homogeneous solution vectors of this matrix eq","authors_text":"Louna Sepp\\\"al\\\"a, Tapani Matala-aho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-02T11:56:06Z","title":"Hermite-Thue equation: Pad\\'e approximations and Siegel's lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00750","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:f462c8bff042ef1bebe91e369d9cff4aa4428d62e3bc1065b02dc51bc5794e31","target":"record","created_at":"2026-05-18T00:16:57Z","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":"59080dde0bac892ea4ee6b2d66f196d556d929a218ef15b13a4d301b9523290d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-02T11:56:06Z","title_canon_sha256":"5a772a29ee1e3eefec6b31a22fa8d2f6f74a9912872cf3f5eccf15b6ec9e5294"},"schema_version":"1.0","source":{"id":"1805.00750","kind":"arxiv","version":1}},"canonical_sha256":"fdfc924334a71c28b68ad05c775ba68229677175bf07f0906155b762a01616e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdfc924334a71c28b68ad05c775ba68229677175bf07f0906155b762a01616e9","first_computed_at":"2026-05-18T00:16:57.859691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:57.859691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4SEJxE1WmStocFWaR3ImMAvfWKqYAy5By+Qadfr0rw19ZPxRNVjkLfV+T0KUVZ4nC6XPqNha7sM8kGhaH79LDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:57.860469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00750","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f462c8bff042ef1bebe91e369d9cff4aa4428d62e3bc1065b02dc51bc5794e31","sha256:0bbe753851397d81d78d8857490f6906840d3312f101d4d8551d6d3c70cb116c"],"state_sha256":"c88062593cd7abfa79e298606deea84bdbc6d90e6cacdc1b23a94e10d80e210e"}