{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HQAGD3NYPARHWEKLWZWIYL3FU7","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":"f7c9c766fc66c38ff0e5cd0a15aa86de04a52ff1297756cd42efc2dbdf07167c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GM","submitted_at":"2012-03-28T21:13:22Z","title_canon_sha256":"4456ea49a64a5769aa949291cbbd7d0a825823cb39245f44b486ab5a8c433c1b"},"schema_version":"1.0","source":{"id":"1203.6380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6380","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6380v1","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6380","created_at":"2026-05-18T03:59:02Z"},{"alias_kind":"pith_short_12","alias_value":"HQAGD3NYPARH","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HQAGD3NYPARHWEKL","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HQAGD3NY","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:ab5012cd4932464ac84e75318877d92634c14dfc166089ccd1e4b76f9abc5af5","target":"graph","created_at":"2026-05-18T03:59:02Z","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 the fall 2011 issue of the Journal'Mathematics and Computer Education', author Unal Hasan, in the one page article \"Proof without Words\", gives a purely geometric proof of the equality, arctan(1/3)+ arctan(1/7) = arctan(1/2) (1) (See reference [1]) Now consider the two-variable diophantine equation(x and y being positive integer variables), arctan(1/x) + arctan(m/y) = arctan(1/k) (2), where m and k are given or fixed positive integers with gcd(m,k^2+1)=1;and also with gcd(m,y)=1. Equality (1) then says that the pair (3,7)is a positive integer solution to (2) in the case m=1=k. We prove, in ","authors_text":"Konstantine Zelator","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GM","submitted_at":"2012-03-28T21:13:22Z","title":"The Diophantine Equation arctan(1/x)+arctan(m/y)= arctan(1/k)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6380","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":"sha256:5d7d6f13cffaca2cd248de549faaaa4d46d10dface24bfefd6f8e6529737ee7a","target":"record","created_at":"2026-05-18T03:59:02Z","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":"f7c9c766fc66c38ff0e5cd0a15aa86de04a52ff1297756cd42efc2dbdf07167c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GM","submitted_at":"2012-03-28T21:13:22Z","title_canon_sha256":"4456ea49a64a5769aa949291cbbd7d0a825823cb39245f44b486ab5a8c433c1b"},"schema_version":"1.0","source":{"id":"1203.6380","kind":"arxiv","version":1}},"canonical_sha256":"3c0061edb878227b114bb66c8c2f65a7d60a1f13a04d920ababfa1e491b073f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c0061edb878227b114bb66c8c2f65a7d60a1f13a04d920ababfa1e491b073f2","first_computed_at":"2026-05-18T03:59:02.668401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:02.668401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v6TXwXJQl2SmVwG8FPUKzgb97DIl0X/WTchh/NcvPgLAZQ4Mb/nX7LIPO2KW1Q4UHxsByHwBKOBm8lwWZOzOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:02.669130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d7d6f13cffaca2cd248de549faaaa4d46d10dface24bfefd6f8e6529737ee7a","sha256:ab5012cd4932464ac84e75318877d92634c14dfc166089ccd1e4b76f9abc5af5"],"state_sha256":"6e1b2f67e183d71f06b4eadc81e65a76f58792e513861ae59a940e1335223fcf"}