{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MVAQ354YEAHB266AS57WGKZBSA","short_pith_number":"pith:MVAQ354Y","schema_version":"1.0","canonical_sha256":"65410df798200e1d7bc0977f632b219037f81bcc5d0ba9d0c883f59b3710f29c","source":{"kind":"arxiv","id":"1710.08859","version":1},"attestation_state":"computed","paper":{"title":"Geometric constructibility of polygons lying on a circular arc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.AG","authors_text":"Delbrin Ahmed, Eszter K. Horv\\'ath, G\\'abor Cz\\'edli","submitted_at":"2017-10-24T15:54:07Z","abstract_excerpt":"For a positive integer $n$, an $n$-sided polygon lying on a circular arc or, shortly, an $n$-fan is a sequence of $n+1$ points on a circle going counterclockwise such that the \"total rotation\" $\\delta$ from the first point to the last one is at most $2\\pi$. We prove that for $n\\geq 3$, the $n$-fan cannot be constructed with straightedge and compass in general from its central angle $\\delta$ and its central distances, which are the distances of the edges from the center of the circle. Also, we prove that for each fixed $\\delta$ in the interval $(0, 2\\pi]$ and for every $n\\geq 5$, there exists a"},"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":"1710.08859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-24T15:54:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"e4d3caea8ec68cd0defb37209db964d6f6cf4afb502737f074d959821520c86b","abstract_canon_sha256":"0c6873cb6bf12c5dc7771cb5b131c6f6477b1cc2d2115cd4dfac1bbb97aeb3ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:03.598794Z","signature_b64":"WQsiDwdXRf4oOcQTEKywOfuT/4Sd0nA4UkqjwdgvMog1O38NxmtRqOPBqzcpdXfpFRiXaupuZ2JmWhDMnhAbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65410df798200e1d7bc0977f632b219037f81bcc5d0ba9d0c883f59b3710f29c","last_reissued_at":"2026-05-18T00:32:03.598223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:03.598223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric constructibility of polygons lying on a circular arc","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.AG","authors_text":"Delbrin Ahmed, Eszter K. Horv\\'ath, G\\'abor Cz\\'edli","submitted_at":"2017-10-24T15:54:07Z","abstract_excerpt":"For a positive integer $n$, an $n$-sided polygon lying on a circular arc or, shortly, an $n$-fan is a sequence of $n+1$ points on a circle going counterclockwise such that the \"total rotation\" $\\delta$ from the first point to the last one is at most $2\\pi$. We prove that for $n\\geq 3$, the $n$-fan cannot be constructed with straightedge and compass in general from its central angle $\\delta$ and its central distances, which are the distances of the edges from the center of the circle. Also, we prove that for each fixed $\\delta$ in the interval $(0, 2\\pi]$ and for every $n\\geq 5$, there exists a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08859","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.08859","created_at":"2026-05-18T00:32:03.598290+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.08859v1","created_at":"2026-05-18T00:32:03.598290+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08859","created_at":"2026-05-18T00:32:03.598290+00:00"},{"alias_kind":"pith_short_12","alias_value":"MVAQ354YEAHB","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MVAQ354YEAHB266A","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MVAQ354Y","created_at":"2026-05-18T12:31:31.346846+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/MVAQ354YEAHB266AS57WGKZBSA","json":"https://pith.science/pith/MVAQ354YEAHB266AS57WGKZBSA.json","graph_json":"https://pith.science/api/pith-number/MVAQ354YEAHB266AS57WGKZBSA/graph.json","events_json":"https://pith.science/api/pith-number/MVAQ354YEAHB266AS57WGKZBSA/events.json","paper":"https://pith.science/paper/MVAQ354Y"},"agent_actions":{"view_html":"https://pith.science/pith/MVAQ354YEAHB266AS57WGKZBSA","download_json":"https://pith.science/pith/MVAQ354YEAHB266AS57WGKZBSA.json","view_paper":"https://pith.science/paper/MVAQ354Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.08859&json=true","fetch_graph":"https://pith.science/api/pith-number/MVAQ354YEAHB266AS57WGKZBSA/graph.json","fetch_events":"https://pith.science/api/pith-number/MVAQ354YEAHB266AS57WGKZBSA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MVAQ354YEAHB266AS57WGKZBSA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MVAQ354YEAHB266AS57WGKZBSA/action/storage_attestation","attest_author":"https://pith.science/pith/MVAQ354YEAHB266AS57WGKZBSA/action/author_attestation","sign_citation":"https://pith.science/pith/MVAQ354YEAHB266AS57WGKZBSA/action/citation_signature","submit_replication":"https://pith.science/pith/MVAQ354YEAHB266AS57WGKZBSA/action/replication_record"}},"created_at":"2026-05-18T00:32:03.598290+00:00","updated_at":"2026-05-18T00:32:03.598290+00:00"}