{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UPITT3J2XSYONWWGPXKJ2A553V","short_pith_number":"pith:UPITT3J2","canonical_record":{"source":{"id":"1604.02104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-07T18:36:51Z","cross_cats_sorted":[],"title_canon_sha256":"899d9b8ea86602c92667991ca0a7aae7f5a636dcb7856f4093b0a10004bbf919","abstract_canon_sha256":"b4b4e84e63dbfbaa6202a54df3e54ebfba0579e2b89378bb234ef767ac710c28"},"schema_version":"1.0"},"canonical_sha256":"a3d139ed3abcb0e6dac67dd49d03bddd7b52ede216d54817063d29d593ae28a0","source":{"kind":"arxiv","id":"1604.02104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02104","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02104v1","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02104","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"UPITT3J2XSYO","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UPITT3J2XSYONWWG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UPITT3J2","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UPITT3J2XSYONWWGPXKJ2A553V","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-07T18:36:51Z","cross_cats_sorted":[],"title_canon_sha256":"899d9b8ea86602c92667991ca0a7aae7f5a636dcb7856f4093b0a10004bbf919","abstract_canon_sha256":"b4b4e84e63dbfbaa6202a54df3e54ebfba0579e2b89378bb234ef767ac710c28"},"schema_version":"1.0"},"canonical_sha256":"a3d139ed3abcb0e6dac67dd49d03bddd7b52ede216d54817063d29d593ae28a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:31.271519Z","signature_b64":"XFhb49WUAbrSwFklsok6tThVBFiFEWJftAKhcl1kDnsh/p7opQc2dKKZ8FA1TZnVBkm09OmPt3XiRGHM3yqrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3d139ed3abcb0e6dac67dd49d03bddd7b52ede216d54817063d29d593ae28a0","last_reissued_at":"2026-05-18T01:17:31.270795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:31.270795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02104","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":"2026-05-18T01:17:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UVUs8NWujgOCe2JNhgej5S/ZYqw/MJfJWC9AL2f2N4+dU2XQEhiAeHxjxFtG54pVDJ5+KyAk6Hf2pgivhzooCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:32:36.313053Z"},"content_sha256":"a3dc67bd8cea7a3c1f5b7ca5c78792099ccd3ab64208177f7f851da9053b5bcf","schema_version":"1.0","event_id":"sha256:a3dc67bd8cea7a3c1f5b7ca5c78792099ccd3ab64208177f7f851da9053b5bcf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UPITT3J2XSYONWWGPXKJ2A553V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Parametric Spaces of Bicentric Quadrilaterals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Allan J. MacLeod, Arman Shamsi Zargar, Farzali Izadi, Foad Khoshnam","submitted_at":"2016-04-07T18:36:51Z","abstract_excerpt":"In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both a circumcircle passing through the four vertices and an incircle having the four sides as tangents. Consider a bicentric quadrilateral with rational sides. We discuss the problem of finding such quadrilaterals where the ratio of the radii of the circumcircle and incircle is rational. We show that this problem can be formulated in terms of a family of elliptic curves given by $E_a:y^2=x^3+(a^4-4a^3-2a^2-4a+1)x^2+16a^4x$ which have, in general, \\(\\mathbb Z/8\\mathbb Z\\), and in rare cases \\(\\mathbb Z/2\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02104","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":"2026-05-18T01:17:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pVAbEHiF55CBqpnRkJ6iLThKkz1E/D0mBDx/noef1LCabC0ea2SvkHfywWtjVWE3Pq+Ees4Sl0V4ZK9CTgkYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:32:36.313419Z"},"content_sha256":"f9f4ba55145e93108c36952c70c19c3b2913622f99c6121fe64a4b074427c584","schema_version":"1.0","event_id":"sha256:f9f4ba55145e93108c36952c70c19c3b2913622f99c6121fe64a4b074427c584"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPITT3J2XSYONWWGPXKJ2A553V/bundle.json","state_url":"https://pith.science/pith/UPITT3J2XSYONWWGPXKJ2A553V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPITT3J2XSYONWWGPXKJ2A553V/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":"2026-06-25T05:32:36Z","links":{"resolver":"https://pith.science/pith/UPITT3J2XSYONWWGPXKJ2A553V","bundle":"https://pith.science/pith/UPITT3J2XSYONWWGPXKJ2A553V/bundle.json","state":"https://pith.science/pith/UPITT3J2XSYONWWGPXKJ2A553V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPITT3J2XSYONWWGPXKJ2A553V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UPITT3J2XSYONWWGPXKJ2A553V","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":"b4b4e84e63dbfbaa6202a54df3e54ebfba0579e2b89378bb234ef767ac710c28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-07T18:36:51Z","title_canon_sha256":"899d9b8ea86602c92667991ca0a7aae7f5a636dcb7856f4093b0a10004bbf919"},"schema_version":"1.0","source":{"id":"1604.02104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02104","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02104v1","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02104","created_at":"2026-05-18T01:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"UPITT3J2XSYO","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UPITT3J2XSYONWWG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UPITT3J2","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:f9f4ba55145e93108c36952c70c19c3b2913622f99c6121fe64a4b074427c584","target":"graph","created_at":"2026-05-18T01:17:31Z","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 Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both a circumcircle passing through the four vertices and an incircle having the four sides as tangents. Consider a bicentric quadrilateral with rational sides. We discuss the problem of finding such quadrilaterals where the ratio of the radii of the circumcircle and incircle is rational. We show that this problem can be formulated in terms of a family of elliptic curves given by $E_a:y^2=x^3+(a^4-4a^3-2a^2-4a+1)x^2+16a^4x$ which have, in general, \\(\\mathbb Z/8\\mathbb Z\\), and in rare cases \\(\\mathbb Z/2\\mathbb","authors_text":"Allan J. MacLeod, Arman Shamsi Zargar, Farzali Izadi, Foad Khoshnam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-07T18:36:51Z","title":"On Parametric Spaces of Bicentric Quadrilaterals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02104","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:a3dc67bd8cea7a3c1f5b7ca5c78792099ccd3ab64208177f7f851da9053b5bcf","target":"record","created_at":"2026-05-18T01:17:31Z","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":"b4b4e84e63dbfbaa6202a54df3e54ebfba0579e2b89378bb234ef767ac710c28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-07T18:36:51Z","title_canon_sha256":"899d9b8ea86602c92667991ca0a7aae7f5a636dcb7856f4093b0a10004bbf919"},"schema_version":"1.0","source":{"id":"1604.02104","kind":"arxiv","version":1}},"canonical_sha256":"a3d139ed3abcb0e6dac67dd49d03bddd7b52ede216d54817063d29d593ae28a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3d139ed3abcb0e6dac67dd49d03bddd7b52ede216d54817063d29d593ae28a0","first_computed_at":"2026-05-18T01:17:31.270795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:31.270795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFhb49WUAbrSwFklsok6tThVBFiFEWJftAKhcl1kDnsh/p7opQc2dKKZ8FA1TZnVBkm09OmPt3XiRGHM3yqrDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:31.271519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3dc67bd8cea7a3c1f5b7ca5c78792099ccd3ab64208177f7f851da9053b5bcf","sha256:f9f4ba55145e93108c36952c70c19c3b2913622f99c6121fe64a4b074427c584"],"state_sha256":"242053955ce5f6f332c48d50fd2e98266128a6b13de7b25520feccd5f992d81d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1C817S3KUhxTMuLrJ7TZSFHLNAeL2TvywtNi2DM4zwveHllCSasA4VSvhM6d0Xn5KCB6kYzRCnFawzOfqeMpAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:32:36.315549Z","bundle_sha256":"6dc49ea30648ebaf10294551af73721026c8e1a4340f397c53e3d2f53ed8660a"}}