{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MDAHGPVOA5JNISQYYJHTCV57B5","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":"5032db3480b269e0fca1327ad7172a719ecb68b470ae88a157dc85be73781004","cross_cats_sorted":["math.CV","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-28T15:49:02Z","title_canon_sha256":"f2acdcb4dc591a4ac584fb30e156a9a0c765c43891e1612a644b4c95f54ff71f"},"schema_version":"1.0","source":{"id":"1501.07157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07157","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07157v1","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07157","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"MDAHGPVOA5JN","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MDAHGPVOA5JNISQY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MDAHGPVO","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:36e91f6c3bb80bc124125f390022b805676ccde39defdd3df97afabcebb78b88","target":"graph","created_at":"2026-05-18T02:28:30Z","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 space of quadrilaterals with fixed side lengths is an elliptic curve. Darboux used this to prove a porism on foldings. In this article, the space of oriented quadrilaterals is studied on the base of biquadratic equations between their angles. The space of non-oriented quadrilaterals is also an elliptic curve, doubly covered by the previous one, and is described by a biquadratic relation between the diagonals. The spaces of non-oriented quadrilaterals with the side lengths $(a_1, a_2, a_3, a_4)$ and $(s-a_1, s-a_2, s-a_3, s-a_4)$ turn out to be isomorphic via identification of two quadrilat","authors_text":"Ivan Izmestiev","cross_cats":["math.CV","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-28T15:49:02Z","title":"Deformation of quadrilaterals and addition on elliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07157","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":"sha256:37d7e7ef59a8e851fd53f4291644dcbfeb6eee6a29332c905c7344db4cf01414","target":"record","created_at":"2026-05-18T02:28:30Z","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":"5032db3480b269e0fca1327ad7172a719ecb68b470ae88a157dc85be73781004","cross_cats_sorted":["math.CV","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-28T15:49:02Z","title_canon_sha256":"f2acdcb4dc591a4ac584fb30e156a9a0c765c43891e1612a644b4c95f54ff71f"},"schema_version":"1.0","source":{"id":"1501.07157","kind":"arxiv","version":1}},"canonical_sha256":"60c0733eae0752d44a18c24f3157bf0f78ea8798192ef6b57911fbfad3d684e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60c0733eae0752d44a18c24f3157bf0f78ea8798192ef6b57911fbfad3d684e2","first_computed_at":"2026-05-18T02:28:30.051425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:30.051425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JcveN3Anvc6nGpxp5RVJqHT9G9QRxrYLVfeBlj/uxnoRkeUToSwKRtzgRnBGc/opZ0rGJksVRLKeM60UAC/PBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:30.051865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37d7e7ef59a8e851fd53f4291644dcbfeb6eee6a29332c905c7344db4cf01414","sha256:36e91f6c3bb80bc124125f390022b805676ccde39defdd3df97afabcebb78b88"],"state_sha256":"21f7359f20565074d901cbac05596887b271d3c73ddb936db6e6189e7ccf7468"}