{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2VRCZCVLBFEXNGDXWLZGGZE5II","short_pith_number":"pith:2VRCZCVL","canonical_record":{"source":{"id":"1705.04283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-11T16:53:32Z","cross_cats_sorted":[],"title_canon_sha256":"662ed7f7775b6743cb801c9e27624b2402700fa33ffaee089bda5dd4be044849","abstract_canon_sha256":"ed9a8ee5161a36d97ab35977a12c56f902dcd7e4ca90b35a8bb3a0e0a8d4b400"},"schema_version":"1.0"},"canonical_sha256":"d5622c8aab0949769877b2f263649d420d7072f18b856c3a7ea8ae7b215445d2","source":{"kind":"arxiv","id":"1705.04283","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04283","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04283v2","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04283","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"pith_short_12","alias_value":"2VRCZCVLBFEX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2VRCZCVLBFEXNGDX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2VRCZCVL","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2VRCZCVLBFEXNGDXWLZGGZE5II","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-11T16:53:32Z","cross_cats_sorted":[],"title_canon_sha256":"662ed7f7775b6743cb801c9e27624b2402700fa33ffaee089bda5dd4be044849","abstract_canon_sha256":"ed9a8ee5161a36d97ab35977a12c56f902dcd7e4ca90b35a8bb3a0e0a8d4b400"},"schema_version":"1.0"},"canonical_sha256":"d5622c8aab0949769877b2f263649d420d7072f18b856c3a7ea8ae7b215445d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:51.265876Z","signature_b64":"E+p2u+9HEWMzD/ADGbQgSvuh/E4bdPqpqdAwXbJch5abTHd7WgAEwmWTyNTRg8HsfxyOOVgbx/JQhxgNvc2NBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5622c8aab0949769877b2f263649d420d7072f18b856c3a7ea8ae7b215445d2","last_reissued_at":"2026-05-18T00:35:51.265367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:51.265367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04283","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eX1XVE2hTKxuxwC7C05iOsMVs8FD4sI2hjYBvW0jTpiZotj57nTEbtBMDwmul9DDnR+7T/5/UtJdKZ7wWZirDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:00:20.826159Z"},"content_sha256":"a869a38d02747cea1353fa56f566e4382bef7bd821ccd54dd5c3ba2342afebfe","schema_version":"1.0","event_id":"sha256:a869a38d02747cea1353fa56f566e4382bef7bd821ccd54dd5c3ba2342afebfe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2VRCZCVLBFEXNGDXWLZGGZE5II","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Completely $p$-primitive binary quadratic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Byeong-Kweon Oh, Hoseog Yu","submitted_at":"2017-05-11T16:53:32Z","abstract_excerpt":"Let $f(x,y)=ax^2+bxy+cy^2$ be a binary quadratic form with integer coefficients. For a prime $p$ not dividing the discriminant of $f$, we say $f$ is completely $p$-primitive if for any non-zero integer $N$, the diophantine equation $f(x,y)=N$ has always an integer solution $(x,y)=(m,n)$ with $(m,n,p)=1$ whenever it has an integer solution. In this article, we study various properties of completely $p$-primitive binary quadratic forms. In particular, we give a necessary and sufficient condition for a definite binary quadratic form $f$ to be completely $p$-primitive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04283","kind":"arxiv","version":2},"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":"2026-05-18T00:35:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K+w5xtJyJqqFdOjEnF55o/mA/n0UgOJvIVcNJsvgWtn6gydlHcva3MVb4xgreu2pUEpZjimymjz+YEIImIGACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:00:20.826532Z"},"content_sha256":"7e914fc5a9c8713cc2d8ab273934057c9058bd1fd46f72223855e390c319efbf","schema_version":"1.0","event_id":"sha256:7e914fc5a9c8713cc2d8ab273934057c9058bd1fd46f72223855e390c319efbf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2VRCZCVLBFEXNGDXWLZGGZE5II/bundle.json","state_url":"https://pith.science/pith/2VRCZCVLBFEXNGDXWLZGGZE5II/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2VRCZCVLBFEXNGDXWLZGGZE5II/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":"2026-06-05T10:00:20Z","links":{"resolver":"https://pith.science/pith/2VRCZCVLBFEXNGDXWLZGGZE5II","bundle":"https://pith.science/pith/2VRCZCVLBFEXNGDXWLZGGZE5II/bundle.json","state":"https://pith.science/pith/2VRCZCVLBFEXNGDXWLZGGZE5II/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2VRCZCVLBFEXNGDXWLZGGZE5II/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2VRCZCVLBFEXNGDXWLZGGZE5II","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":"ed9a8ee5161a36d97ab35977a12c56f902dcd7e4ca90b35a8bb3a0e0a8d4b400","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-11T16:53:32Z","title_canon_sha256":"662ed7f7775b6743cb801c9e27624b2402700fa33ffaee089bda5dd4be044849"},"schema_version":"1.0","source":{"id":"1705.04283","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04283","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04283v2","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04283","created_at":"2026-05-18T00:35:51Z"},{"alias_kind":"pith_short_12","alias_value":"2VRCZCVLBFEX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2VRCZCVLBFEXNGDX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2VRCZCVL","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:7e914fc5a9c8713cc2d8ab273934057c9058bd1fd46f72223855e390c319efbf","target":"graph","created_at":"2026-05-18T00:35:51Z","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":"Let $f(x,y)=ax^2+bxy+cy^2$ be a binary quadratic form with integer coefficients. For a prime $p$ not dividing the discriminant of $f$, we say $f$ is completely $p$-primitive if for any non-zero integer $N$, the diophantine equation $f(x,y)=N$ has always an integer solution $(x,y)=(m,n)$ with $(m,n,p)=1$ whenever it has an integer solution. In this article, we study various properties of completely $p$-primitive binary quadratic forms. In particular, we give a necessary and sufficient condition for a definite binary quadratic form $f$ to be completely $p$-primitive.","authors_text":"Byeong-Kweon Oh, Hoseog Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-11T16:53:32Z","title":"Completely $p$-primitive binary quadratic forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04283","kind":"arxiv","version":2},"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:a869a38d02747cea1353fa56f566e4382bef7bd821ccd54dd5c3ba2342afebfe","target":"record","created_at":"2026-05-18T00:35:51Z","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":"ed9a8ee5161a36d97ab35977a12c56f902dcd7e4ca90b35a8bb3a0e0a8d4b400","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-05-11T16:53:32Z","title_canon_sha256":"662ed7f7775b6743cb801c9e27624b2402700fa33ffaee089bda5dd4be044849"},"schema_version":"1.0","source":{"id":"1705.04283","kind":"arxiv","version":2}},"canonical_sha256":"d5622c8aab0949769877b2f263649d420d7072f18b856c3a7ea8ae7b215445d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5622c8aab0949769877b2f263649d420d7072f18b856c3a7ea8ae7b215445d2","first_computed_at":"2026-05-18T00:35:51.265367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:51.265367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E+p2u+9HEWMzD/ADGbQgSvuh/E4bdPqpqdAwXbJch5abTHd7WgAEwmWTyNTRg8HsfxyOOVgbx/JQhxgNvc2NBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:51.265876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04283","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a869a38d02747cea1353fa56f566e4382bef7bd821ccd54dd5c3ba2342afebfe","sha256:7e914fc5a9c8713cc2d8ab273934057c9058bd1fd46f72223855e390c319efbf"],"state_sha256":"c756fb8b2cf90a4f9739fb6b9e6baf6f410bd5c0f2ec37d253dfbb3d19ab911e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OX5LXqeDow80mmZuEUomHeZhK2msPRalMY7a9cLqJl0G2ECVm6HrIlJD/sQr6mYyRaPirRgLkCZQVCnXGYJHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:00:20.828390Z","bundle_sha256":"ee34eb51bf1b07a043f6bb9d40374128ffd5dcbac8a1602682f710c4c889e16b"}}