{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:S2XI5YLK3QHVNSNAZ5YIXIOECO","short_pith_number":"pith:S2XI5YLK","schema_version":"1.0","canonical_sha256":"96ae8ee16adc0f56c9a0cf708ba1c4139c7d089b13eb04d50b07a08577f81a81","source":{"kind":"arxiv","id":"1009.3061","version":1},"attestation_state":"computed","paper":{"title":"Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Young, Andrew Marchese, Daniel Champion, Jacob Miller","submitted_at":"2010-09-15T23:30:25Z","abstract_excerpt":"In [7], a notion of constant scalar curvature metrics on piecewise flat manifolds is defined. Such metrics are candidates for canonical metrics on discrete manifolds. In this paper, we define a class of vertex transitive metrics on certain triangulations of $\\mathbb{S}^3$; namely, the boundary complexes of cyclic polytopes. We use combinatorial properties of cyclic polytopes to show that, for any number of vertices, these metrics have constant scalar curvature."},"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":"1009.3061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-15T23:30:25Z","cross_cats_sorted":[],"title_canon_sha256":"38c19614113c02c3c48ab2910f53e522ebd674db03fd4e414af04899ce4c3aa6","abstract_canon_sha256":"7ff020e60a4e0b6cb2d02fa2953a4401c893ee38e01f01a8c8f0f6ce2d05a727"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:54.263100Z","signature_b64":"cmTPOdqrD4ynhmtjetTUUGYYohPXrabcE3OnXwCasdV9v4Wt7QiMhN0oULF49onEluepCghgUR1jOnkPRgbZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96ae8ee16adc0f56c9a0cf708ba1c4139c7d089b13eb04d50b07a08577f81a81","last_reissued_at":"2026-05-18T04:40:54.262430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:54.262430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Young, Andrew Marchese, Daniel Champion, Jacob Miller","submitted_at":"2010-09-15T23:30:25Z","abstract_excerpt":"In [7], a notion of constant scalar curvature metrics on piecewise flat manifolds is defined. Such metrics are candidates for canonical metrics on discrete manifolds. In this paper, we define a class of vertex transitive metrics on certain triangulations of $\\mathbb{S}^3$; namely, the boundary complexes of cyclic polytopes. We use combinatorial properties of cyclic polytopes to show that, for any number of vertices, these metrics have constant scalar curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3061","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":"1009.3061","created_at":"2026-05-18T04:40:54.262542+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3061v1","created_at":"2026-05-18T04:40:54.262542+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3061","created_at":"2026-05-18T04:40:54.262542+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2XI5YLK3QHV","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2XI5YLK3QHVNSNA","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2XI5YLK","created_at":"2026-05-18T12:26:13.927090+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/S2XI5YLK3QHVNSNAZ5YIXIOECO","json":"https://pith.science/pith/S2XI5YLK3QHVNSNAZ5YIXIOECO.json","graph_json":"https://pith.science/api/pith-number/S2XI5YLK3QHVNSNAZ5YIXIOECO/graph.json","events_json":"https://pith.science/api/pith-number/S2XI5YLK3QHVNSNAZ5YIXIOECO/events.json","paper":"https://pith.science/paper/S2XI5YLK"},"agent_actions":{"view_html":"https://pith.science/pith/S2XI5YLK3QHVNSNAZ5YIXIOECO","download_json":"https://pith.science/pith/S2XI5YLK3QHVNSNAZ5YIXIOECO.json","view_paper":"https://pith.science/paper/S2XI5YLK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3061&json=true","fetch_graph":"https://pith.science/api/pith-number/S2XI5YLK3QHVNSNAZ5YIXIOECO/graph.json","fetch_events":"https://pith.science/api/pith-number/S2XI5YLK3QHVNSNAZ5YIXIOECO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2XI5YLK3QHVNSNAZ5YIXIOECO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2XI5YLK3QHVNSNAZ5YIXIOECO/action/storage_attestation","attest_author":"https://pith.science/pith/S2XI5YLK3QHVNSNAZ5YIXIOECO/action/author_attestation","sign_citation":"https://pith.science/pith/S2XI5YLK3QHVNSNAZ5YIXIOECO/action/citation_signature","submit_replication":"https://pith.science/pith/S2XI5YLK3QHVNSNAZ5YIXIOECO/action/replication_record"}},"created_at":"2026-05-18T04:40:54.262542+00:00","updated_at":"2026-05-18T04:40:54.262542+00:00"}