{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ERYXN4W232GO7FG3NWVLR7EQQ6","short_pith_number":"pith:ERYXN4W2","schema_version":"1.0","canonical_sha256":"247176f2dade8cef94db6daab8fc9087a94d790440148df57e540de9bbc4d060","source":{"kind":"arxiv","id":"1602.04637","version":2},"attestation_state":"computed","paper":{"title":"Incircular nets and confocal conics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Alexander I. Bobenko, Arseniy Akopyan","submitted_at":"2016-02-15T11:36:40Z","abstract_excerpt":"We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics.\n  Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite natur"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.04637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-15T11:36:40Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"8635f19256bd622894a624bc450f00562d1661925fdd0c6ccb837fdb81b5b48b","abstract_canon_sha256":"2f05d68e16da2fa61929b0f45043978144c08758491b1935b50e3246ce3e6b6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:56.253650Z","signature_b64":"yLfouh+JKPNMf7JBj4D/dCOjvkn6bAQcPQuwRzaMX8/vy8knpLAGgR2ACcQfnrB3H6SrenV1/UGPAbr/+ey/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"247176f2dade8cef94db6daab8fc9087a94d790440148df57e540de9bbc4d060","last_reissued_at":"2026-05-18T00:31:56.253171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:56.253171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incircular nets and confocal conics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Alexander I. Bobenko, Arseniy Akopyan","submitted_at":"2016-02-15T11:36:40Z","abstract_excerpt":"We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics.\n  Our main new results are on checkerboard IC-nets in the plane. These are congruences of straight lines in the plane with the combinatorics of the square grid, combinatorially colored as a checkerboard, such that all black coordinate quadrilaterals possess inscribed circles. We show how this larger class of IC-nets appears quite natur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04637","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.04637","created_at":"2026-05-18T00:31:56.253255+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.04637v2","created_at":"2026-05-18T00:31:56.253255+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04637","created_at":"2026-05-18T00:31:56.253255+00:00"},{"alias_kind":"pith_short_12","alias_value":"ERYXN4W232GO","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"ERYXN4W232GO7FG3","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"ERYXN4W2","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6","json":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6.json","graph_json":"https://pith.science/api/pith-number/ERYXN4W232GO7FG3NWVLR7EQQ6/graph.json","events_json":"https://pith.science/api/pith-number/ERYXN4W232GO7FG3NWVLR7EQQ6/events.json","paper":"https://pith.science/paper/ERYXN4W2"},"agent_actions":{"view_html":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6","download_json":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6.json","view_paper":"https://pith.science/paper/ERYXN4W2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.04637&json=true","fetch_graph":"https://pith.science/api/pith-number/ERYXN4W232GO7FG3NWVLR7EQQ6/graph.json","fetch_events":"https://pith.science/api/pith-number/ERYXN4W232GO7FG3NWVLR7EQQ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/action/storage_attestation","attest_author":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/action/author_attestation","sign_citation":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/action/citation_signature","submit_replication":"https://pith.science/pith/ERYXN4W232GO7FG3NWVLR7EQQ6/action/replication_record"}},"created_at":"2026-05-18T00:31:56.253255+00:00","updated_at":"2026-05-18T00:31:56.253255+00:00"}