{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:U4VMNLSE67OJ5IMIGOBIQGYRTM","short_pith_number":"pith:U4VMNLSE","canonical_record":{"source":{"id":"1907.05540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-12T01:20:57Z","cross_cats_sorted":[],"title_canon_sha256":"164f5954665c349d807cc5e6e2db5c06a78a7e6e164b435cd16da99f271cd8bf","abstract_canon_sha256":"9bc683529f32510a3d7c9c4cbed6bb7fea599c524401a1f9e6a9801f81237d4b"},"schema_version":"1.0"},"canonical_sha256":"a72ac6ae44f7dc9ea1883382881b119b2fe2d2b7f4b3455a5ef8bd2b9dba253b","source":{"kind":"arxiv","id":"1907.05540","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05540","created_at":"2026-05-17T23:40:48Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05540v1","created_at":"2026-05-17T23:40:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05540","created_at":"2026-05-17T23:40:48Z"},{"alias_kind":"pith_short_12","alias_value":"U4VMNLSE67OJ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U4VMNLSE67OJ5IMI","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U4VMNLSE","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:U4VMNLSE67OJ5IMIGOBIQGYRTM","target":"record","payload":{"canonical_record":{"source":{"id":"1907.05540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-12T01:20:57Z","cross_cats_sorted":[],"title_canon_sha256":"164f5954665c349d807cc5e6e2db5c06a78a7e6e164b435cd16da99f271cd8bf","abstract_canon_sha256":"9bc683529f32510a3d7c9c4cbed6bb7fea599c524401a1f9e6a9801f81237d4b"},"schema_version":"1.0"},"canonical_sha256":"a72ac6ae44f7dc9ea1883382881b119b2fe2d2b7f4b3455a5ef8bd2b9dba253b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:48.008518Z","signature_b64":"aCPdYzoobm1Tp+DTHJRJJqSykt/STYXJUlzYCTXGoxNuaIsJ9jMjxi5L37tZNB1qkAlWJoKmIHn62+r6I48xCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a72ac6ae44f7dc9ea1883382881b119b2fe2d2b7f4b3455a5ef8bd2b9dba253b","last_reissued_at":"2026-05-17T23:40:48.007944Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:48.007944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.05540","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BeVykLClaDN1SjF2SQuBjv6k0OzjADZXshQHaP/9ckkB+0QxUthOuMB76XjpioqiHRtD9URvePhWj4lYRFgNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:44:16.157074Z"},"content_sha256":"f7a5c0889556184ed689a22d49bad5924575e264f6830e369d7487f6312124b0","schema_version":"1.0","event_id":"sha256:f7a5c0889556184ed689a22d49bad5924575e264f6830e369d7487f6312124b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:U4VMNLSE67OJ5IMIGOBIQGYRTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric and algebraic interpretation of primitive Pythagorean triples parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Natalia Aleshkevich","submitted_at":"2019-07-12T01:20:57Z","abstract_excerpt":"The paper found a geometric and algebraic interpretation of the parameters m and n from the formulas for obtaining primitive Pythagorean triples, which are solutions of the equation ${x^2+y^2=z^2}$, namely: ${x=m^2-n^2}$, ${y=2mn}$, ${z=m^2+n^2}$. The study was based on the process of building figurate numbers using gnomons. The paper discusses the process of building squares. The addition of the gnomon U to the original square leads to a larger square: ${x^2+U=z^2}$. The first stage of the investigation was the construction of the gnomon U, which is equal to the area of a square ${y^2}$. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05540","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZlBZOsmJmv0S5oP6F/5aBSnHyq0wTetZHSjgP4ItPJyThKlnZroeokFwHSyCLsgIlpuJpAK4SvTkJOdbIacDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:44:16.157430Z"},"content_sha256":"bfc9012c013e4bd1bc4273be9784e65a00a08345d3781ca613e019593bb1741b","schema_version":"1.0","event_id":"sha256:bfc9012c013e4bd1bc4273be9784e65a00a08345d3781ca613e019593bb1741b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4VMNLSE67OJ5IMIGOBIQGYRTM/bundle.json","state_url":"https://pith.science/pith/U4VMNLSE67OJ5IMIGOBIQGYRTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4VMNLSE67OJ5IMIGOBIQGYRTM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-28T15:44:16Z","links":{"resolver":"https://pith.science/pith/U4VMNLSE67OJ5IMIGOBIQGYRTM","bundle":"https://pith.science/pith/U4VMNLSE67OJ5IMIGOBIQGYRTM/bundle.json","state":"https://pith.science/pith/U4VMNLSE67OJ5IMIGOBIQGYRTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4VMNLSE67OJ5IMIGOBIQGYRTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:U4VMNLSE67OJ5IMIGOBIQGYRTM","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":"9bc683529f32510a3d7c9c4cbed6bb7fea599c524401a1f9e6a9801f81237d4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-12T01:20:57Z","title_canon_sha256":"164f5954665c349d807cc5e6e2db5c06a78a7e6e164b435cd16da99f271cd8bf"},"schema_version":"1.0","source":{"id":"1907.05540","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05540","created_at":"2026-05-17T23:40:48Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05540v1","created_at":"2026-05-17T23:40:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05540","created_at":"2026-05-17T23:40:48Z"},{"alias_kind":"pith_short_12","alias_value":"U4VMNLSE67OJ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U4VMNLSE67OJ5IMI","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U4VMNLSE","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:bfc9012c013e4bd1bc4273be9784e65a00a08345d3781ca613e019593bb1741b","target":"graph","created_at":"2026-05-17T23:40:48Z","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":"The paper found a geometric and algebraic interpretation of the parameters m and n from the formulas for obtaining primitive Pythagorean triples, which are solutions of the equation ${x^2+y^2=z^2}$, namely: ${x=m^2-n^2}$, ${y=2mn}$, ${z=m^2+n^2}$. The study was based on the process of building figurate numbers using gnomons. The paper discusses the process of building squares. The addition of the gnomon U to the original square leads to a larger square: ${x^2+U=z^2}$. The first stage of the investigation was the construction of the gnomon U, which is equal to the area of a square ${y^2}$. The ","authors_text":"Natalia Aleshkevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-12T01:20:57Z","title":"Geometric and algebraic interpretation of primitive Pythagorean triples parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05540","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:f7a5c0889556184ed689a22d49bad5924575e264f6830e369d7487f6312124b0","target":"record","created_at":"2026-05-17T23:40:48Z","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":"9bc683529f32510a3d7c9c4cbed6bb7fea599c524401a1f9e6a9801f81237d4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-12T01:20:57Z","title_canon_sha256":"164f5954665c349d807cc5e6e2db5c06a78a7e6e164b435cd16da99f271cd8bf"},"schema_version":"1.0","source":{"id":"1907.05540","kind":"arxiv","version":1}},"canonical_sha256":"a72ac6ae44f7dc9ea1883382881b119b2fe2d2b7f4b3455a5ef8bd2b9dba253b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a72ac6ae44f7dc9ea1883382881b119b2fe2d2b7f4b3455a5ef8bd2b9dba253b","first_computed_at":"2026-05-17T23:40:48.007944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:48.007944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aCPdYzoobm1Tp+DTHJRJJqSykt/STYXJUlzYCTXGoxNuaIsJ9jMjxi5L37tZNB1qkAlWJoKmIHn62+r6I48xCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:48.008518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.05540","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7a5c0889556184ed689a22d49bad5924575e264f6830e369d7487f6312124b0","sha256:bfc9012c013e4bd1bc4273be9784e65a00a08345d3781ca613e019593bb1741b"],"state_sha256":"fcbd63285a797378f1559cb75cc370942fa1ef252b55c8602f70e7128918360f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9hcxv5gejB9XTCZGK67U7GqvdQZHKggzHKYTcWRevWtqrQlTf3MGrjoWOy1zzFRPEDFKECiY+5q9M9OMmUrhBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T15:44:16.159294Z","bundle_sha256":"a5326867e3c9c64771c130f0d395e39690ac456428ff7b7ac012548ef9cd4b32"}}