{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HCD5PFBN4RVGCE2NBWTOUN5EAY","short_pith_number":"pith:HCD5PFBN","schema_version":"1.0","canonical_sha256":"3887d7942de46a61134d0da6ea37a40621edf4a7c22a7bb1c6fcdae2e913ea72","source":{"kind":"arxiv","id":"1810.01819","version":1},"attestation_state":"computed","paper":{"title":"Solving binomial Thue equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Istv\\'an Ga\\'al, L\\'aszl\\'o Remete","submitted_at":"2018-09-27T08:46:59Z","abstract_excerpt":"We consider binomial Thue equations of type $x^n-my^n=\\pm 1$ in $x,y\\in Z$. Optimizing the method of Peth\\H o we perform an extensive calculation by a high performance computer to determine all solutions with $\\max(|x|,|y|)<10^{500}$ of binomial Thue equations for $m<10^7$ for exponents $n=3,4,5,7,11,13,17,19,23,29$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.01819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-27T08:46:59Z","cross_cats_sorted":[],"title_canon_sha256":"c359d2006f8451f774b0908fd58aa5fc17dc0f8bab9f9249f6edc5c84119de7b","abstract_canon_sha256":"83ce4188511b81148023c8de6c1cda0e00b18b4545f08a66d3145917562be782"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:10.887958Z","signature_b64":"Bn5x8p3miYh1VeBmUxsDw7bm/C/C5CGqsXXIcFXQt+XlQMX6JOhrm9e3h44/3aoijKlw/Mf3+LRRE7MdeQU2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3887d7942de46a61134d0da6ea37a40621edf4a7c22a7bb1c6fcdae2e913ea72","last_reissued_at":"2026-05-18T00:04:10.887330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:10.887330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solving binomial Thue equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Istv\\'an Ga\\'al, L\\'aszl\\'o Remete","submitted_at":"2018-09-27T08:46:59Z","abstract_excerpt":"We consider binomial Thue equations of type $x^n-my^n=\\pm 1$ in $x,y\\in Z$. Optimizing the method of Peth\\H o we perform an extensive calculation by a high performance computer to determine all solutions with $\\max(|x|,|y|)<10^{500}$ of binomial Thue equations for $m<10^7$ for exponents $n=3,4,5,7,11,13,17,19,23,29$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01819","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.01819","created_at":"2026-05-18T00:04:10.887416+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.01819v1","created_at":"2026-05-18T00:04:10.887416+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01819","created_at":"2026-05-18T00:04:10.887416+00:00"},{"alias_kind":"pith_short_12","alias_value":"HCD5PFBN4RVG","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HCD5PFBN4RVGCE2N","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HCD5PFBN","created_at":"2026-05-18T12:32:28.185984+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HCD5PFBN4RVGCE2NBWTOUN5EAY","json":"https://pith.science/pith/HCD5PFBN4RVGCE2NBWTOUN5EAY.json","graph_json":"https://pith.science/api/pith-number/HCD5PFBN4RVGCE2NBWTOUN5EAY/graph.json","events_json":"https://pith.science/api/pith-number/HCD5PFBN4RVGCE2NBWTOUN5EAY/events.json","paper":"https://pith.science/paper/HCD5PFBN"},"agent_actions":{"view_html":"https://pith.science/pith/HCD5PFBN4RVGCE2NBWTOUN5EAY","download_json":"https://pith.science/pith/HCD5PFBN4RVGCE2NBWTOUN5EAY.json","view_paper":"https://pith.science/paper/HCD5PFBN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.01819&json=true","fetch_graph":"https://pith.science/api/pith-number/HCD5PFBN4RVGCE2NBWTOUN5EAY/graph.json","fetch_events":"https://pith.science/api/pith-number/HCD5PFBN4RVGCE2NBWTOUN5EAY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HCD5PFBN4RVGCE2NBWTOUN5EAY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HCD5PFBN4RVGCE2NBWTOUN5EAY/action/storage_attestation","attest_author":"https://pith.science/pith/HCD5PFBN4RVGCE2NBWTOUN5EAY/action/author_attestation","sign_citation":"https://pith.science/pith/HCD5PFBN4RVGCE2NBWTOUN5EAY/action/citation_signature","submit_replication":"https://pith.science/pith/HCD5PFBN4RVGCE2NBWTOUN5EAY/action/replication_record"}},"created_at":"2026-05-18T00:04:10.887416+00:00","updated_at":"2026-05-18T00:04:10.887416+00:00"}