{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5P23UKVUIMJP2VKWRGRFL4LBJF","short_pith_number":"pith:5P23UKVU","schema_version":"1.0","canonical_sha256":"ebf5ba2ab44312fd555689a255f16149694057f79fa7856f181d2678b8ce8546","source":{"kind":"arxiv","id":"1907.01229","version":1},"attestation_state":"computed","paper":{"title":"Pairs of Pythagorean triangles with given catheti ratios","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"M. Ska{\\l}ba, M. Ulas","submitted_at":"2019-07-02T08:23:20Z","abstract_excerpt":"In this note we investigate the problem of finding pairs of Pythagorean triangles $(a, b, c), (A, B, C)$, with given catheti ratios $A/a, B/b$. In particular, we prove that there are infinitely many essentially different (\"non-similar\") pairs of Pythagorean triangles $(a, b, c), (A, B, C)$ satisfying given proportions, provided that $Aa\\neq Bb$."},"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":"1907.01229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-02T08:23:20Z","cross_cats_sorted":[],"title_canon_sha256":"f0fecd7e63c4b7b27602051c28fe53e4b8b53846669ca8c8249d2491a06740f5","abstract_canon_sha256":"db50435974a15ddd25b5d4844e44d448e9242e672a36bbdfd010f112e40f8bbb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:40.893372Z","signature_b64":"iD8NAY/I70xzm4ZxTA+VSihEbcpm1wXuoyl8GlaM0EFYPaeYwUPlzawkTsLzX+kro44OnTMeV9jYfDfrVe1rBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebf5ba2ab44312fd555689a255f16149694057f79fa7856f181d2678b8ce8546","last_reissued_at":"2026-05-17T23:41:40.892788Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:40.892788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pairs of Pythagorean triangles with given catheti ratios","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"M. Ska{\\l}ba, M. Ulas","submitted_at":"2019-07-02T08:23:20Z","abstract_excerpt":"In this note we investigate the problem of finding pairs of Pythagorean triangles $(a, b, c), (A, B, C)$, with given catheti ratios $A/a, B/b$. In particular, we prove that there are infinitely many essentially different (\"non-similar\") pairs of Pythagorean triangles $(a, b, c), (A, B, C)$ satisfying given proportions, provided that $Aa\\neq Bb$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01229","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":"1907.01229","created_at":"2026-05-17T23:41:40.892871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.01229v1","created_at":"2026-05-17T23:41:40.892871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01229","created_at":"2026-05-17T23:41:40.892871+00:00"},{"alias_kind":"pith_short_12","alias_value":"5P23UKVUIMJP","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"5P23UKVUIMJP2VKW","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"5P23UKVU","created_at":"2026-05-18T12:33:10.108867+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/5P23UKVUIMJP2VKWRGRFL4LBJF","json":"https://pith.science/pith/5P23UKVUIMJP2VKWRGRFL4LBJF.json","graph_json":"https://pith.science/api/pith-number/5P23UKVUIMJP2VKWRGRFL4LBJF/graph.json","events_json":"https://pith.science/api/pith-number/5P23UKVUIMJP2VKWRGRFL4LBJF/events.json","paper":"https://pith.science/paper/5P23UKVU"},"agent_actions":{"view_html":"https://pith.science/pith/5P23UKVUIMJP2VKWRGRFL4LBJF","download_json":"https://pith.science/pith/5P23UKVUIMJP2VKWRGRFL4LBJF.json","view_paper":"https://pith.science/paper/5P23UKVU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.01229&json=true","fetch_graph":"https://pith.science/api/pith-number/5P23UKVUIMJP2VKWRGRFL4LBJF/graph.json","fetch_events":"https://pith.science/api/pith-number/5P23UKVUIMJP2VKWRGRFL4LBJF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5P23UKVUIMJP2VKWRGRFL4LBJF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5P23UKVUIMJP2VKWRGRFL4LBJF/action/storage_attestation","attest_author":"https://pith.science/pith/5P23UKVUIMJP2VKWRGRFL4LBJF/action/author_attestation","sign_citation":"https://pith.science/pith/5P23UKVUIMJP2VKWRGRFL4LBJF/action/citation_signature","submit_replication":"https://pith.science/pith/5P23UKVUIMJP2VKWRGRFL4LBJF/action/replication_record"}},"created_at":"2026-05-17T23:41:40.892871+00:00","updated_at":"2026-05-17T23:41:40.892871+00:00"}