{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5YEIWKNDF4ZAK6OFBT3CB7CHDP","short_pith_number":"pith:5YEIWKND","schema_version":"1.0","canonical_sha256":"ee088b29a32f320579c50cf620fc471bc47c85b1f575917681294a344d9a5c76","source":{"kind":"arxiv","id":"1609.01266","version":3},"attestation_state":"computed","paper":{"title":"Minimal and minimum unit circular-arc models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Francisco J. Soulignac, Pablo Terlisky","submitted_at":"2016-09-05T19:44:02Z","abstract_excerpt":"A proper circular-arc (PCA) model is a pair ${\\cal M} = (C, \\cal A)$ where $C$ is a circle and $\\cal A$ is a family of inclusion-free arcs on $C$ in which no two arcs of $\\cal A$ cover $C$. A PCA model $\\cal U = (C,\\cal A)$ is a $(c, \\ell)$-CA model when $C$ has circumference $c$, all the arcs in $\\cal A$ have length $\\ell$, and all the extremes of the arcs in $\\cal A$ are at a distance at least $1$. If $c \\leq c'$ and $\\ell \\leq \\ell'$ for every $(c', \\ell')$-CA model equivalent (resp. isomorphic) to $\\cal U$, then $\\cal U$ is minimal (resp. minimum). In this article we prove that every PCA m"},"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":"1609.01266","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-09-05T19:44:02Z","cross_cats_sorted":[],"title_canon_sha256":"8180765487f0578803db14b578916ae0e547108453b35b7323885f355a65f609","abstract_canon_sha256":"1b716c764761f4bdeab2eec2449e9370a7bac451273568b1ab7be967a26d23e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:23.086902Z","signature_b64":"zjwkYfj9d+0T1PKrWH6F5UBPVQ2PxY25uS048huI77G+MZoyjUHg/36e9ok3lRkpCTfJ1g2Q97jgxZ0hBNEmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee088b29a32f320579c50cf620fc471bc47c85b1f575917681294a344d9a5c76","last_reissued_at":"2026-05-18T00:33:23.086164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:23.086164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal and minimum unit circular-arc models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Francisco J. Soulignac, Pablo Terlisky","submitted_at":"2016-09-05T19:44:02Z","abstract_excerpt":"A proper circular-arc (PCA) model is a pair ${\\cal M} = (C, \\cal A)$ where $C$ is a circle and $\\cal A$ is a family of inclusion-free arcs on $C$ in which no two arcs of $\\cal A$ cover $C$. A PCA model $\\cal U = (C,\\cal A)$ is a $(c, \\ell)$-CA model when $C$ has circumference $c$, all the arcs in $\\cal A$ have length $\\ell$, and all the extremes of the arcs in $\\cal A$ are at a distance at least $1$. If $c \\leq c'$ and $\\ell \\leq \\ell'$ for every $(c', \\ell')$-CA model equivalent (resp. isomorphic) to $\\cal U$, then $\\cal U$ is minimal (resp. minimum). In this article we prove that every PCA m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01266","kind":"arxiv","version":3},"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":"1609.01266","created_at":"2026-05-18T00:33:23.086293+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.01266v3","created_at":"2026-05-18T00:33:23.086293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01266","created_at":"2026-05-18T00:33:23.086293+00:00"},{"alias_kind":"pith_short_12","alias_value":"5YEIWKNDF4ZA","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5YEIWKNDF4ZAK6OF","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5YEIWKND","created_at":"2026-05-18T12:30:01.593930+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/5YEIWKNDF4ZAK6OFBT3CB7CHDP","json":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP.json","graph_json":"https://pith.science/api/pith-number/5YEIWKNDF4ZAK6OFBT3CB7CHDP/graph.json","events_json":"https://pith.science/api/pith-number/5YEIWKNDF4ZAK6OFBT3CB7CHDP/events.json","paper":"https://pith.science/paper/5YEIWKND"},"agent_actions":{"view_html":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP","download_json":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP.json","view_paper":"https://pith.science/paper/5YEIWKND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.01266&json=true","fetch_graph":"https://pith.science/api/pith-number/5YEIWKNDF4ZAK6OFBT3CB7CHDP/graph.json","fetch_events":"https://pith.science/api/pith-number/5YEIWKNDF4ZAK6OFBT3CB7CHDP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/action/storage_attestation","attest_author":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/action/author_attestation","sign_citation":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/action/citation_signature","submit_replication":"https://pith.science/pith/5YEIWKNDF4ZAK6OFBT3CB7CHDP/action/replication_record"}},"created_at":"2026-05-18T00:33:23.086293+00:00","updated_at":"2026-05-18T00:33:23.086293+00:00"}