{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JSNHYNXP3XP3JCWQRR7ZGHJ74P","short_pith_number":"pith:JSNHYNXP","schema_version":"1.0","canonical_sha256":"4c9a7c36efdddfb48ad08c7f931d3fe3cd721c7785b38cc993c165f0357d9312","source":{"kind":"arxiv","id":"1611.08339","version":1},"attestation_state":"computed","paper":{"title":"Sperner's colorings and optimal partitioning of the simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan Vondrak, Maryam Mirzakhani","submitted_at":"2016-11-25T02:41:41Z","abstract_excerpt":"We discuss coloring and partitioning questions related to Sperner's Lemma, originally motivated by an application in hardness of approximation. Informally, we call a partitioning of the $(k-1)$-dimensional simplex into $k$ parts, or a labeling of a lattice inside the simplex by $k$ colors, \"Sperner-admissible\" if color $i$ avoids the face opposite to vertex $i$. The questions we study are of the following flavor: What is the Sperner-admissible labeling/partitioning that makes the total area of the boundary between different colors/parts as small as possible?\n  First, for a natural arrangement "},"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":"1611.08339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-25T02:41:41Z","cross_cats_sorted":[],"title_canon_sha256":"63945b0f871d628ec01d379ec8a924bee33c253d1554babc6555c7803b25dba1","abstract_canon_sha256":"37baa6869e8593f9a7b80715a5dcd3a5750e2617b6470f94d55bb223b2fa6041"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:39.363936Z","signature_b64":"t+za1xhweBxFc1BYtSpOe5gkfETw0sYyW88UWCM4o/4ee6BNu+Ee/oIOwhrfhh8UQsrxG+kjwd2SZYLz0CWXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c9a7c36efdddfb48ad08c7f931d3fe3cd721c7785b38cc993c165f0357d9312","last_reissued_at":"2026-05-18T00:56:39.363300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:39.363300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sperner's colorings and optimal partitioning of the simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan Vondrak, Maryam Mirzakhani","submitted_at":"2016-11-25T02:41:41Z","abstract_excerpt":"We discuss coloring and partitioning questions related to Sperner's Lemma, originally motivated by an application in hardness of approximation. Informally, we call a partitioning of the $(k-1)$-dimensional simplex into $k$ parts, or a labeling of a lattice inside the simplex by $k$ colors, \"Sperner-admissible\" if color $i$ avoids the face opposite to vertex $i$. The questions we study are of the following flavor: What is the Sperner-admissible labeling/partitioning that makes the total area of the boundary between different colors/parts as small as possible?\n  First, for a natural arrangement "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08339","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":"1611.08339","created_at":"2026-05-18T00:56:39.363425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.08339v1","created_at":"2026-05-18T00:56:39.363425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08339","created_at":"2026-05-18T00:56:39.363425+00:00"},{"alias_kind":"pith_short_12","alias_value":"JSNHYNXP3XP3","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JSNHYNXP3XP3JCWQ","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JSNHYNXP","created_at":"2026-05-18T12:30:25.849896+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/JSNHYNXP3XP3JCWQRR7ZGHJ74P","json":"https://pith.science/pith/JSNHYNXP3XP3JCWQRR7ZGHJ74P.json","graph_json":"https://pith.science/api/pith-number/JSNHYNXP3XP3JCWQRR7ZGHJ74P/graph.json","events_json":"https://pith.science/api/pith-number/JSNHYNXP3XP3JCWQRR7ZGHJ74P/events.json","paper":"https://pith.science/paper/JSNHYNXP"},"agent_actions":{"view_html":"https://pith.science/pith/JSNHYNXP3XP3JCWQRR7ZGHJ74P","download_json":"https://pith.science/pith/JSNHYNXP3XP3JCWQRR7ZGHJ74P.json","view_paper":"https://pith.science/paper/JSNHYNXP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.08339&json=true","fetch_graph":"https://pith.science/api/pith-number/JSNHYNXP3XP3JCWQRR7ZGHJ74P/graph.json","fetch_events":"https://pith.science/api/pith-number/JSNHYNXP3XP3JCWQRR7ZGHJ74P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JSNHYNXP3XP3JCWQRR7ZGHJ74P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JSNHYNXP3XP3JCWQRR7ZGHJ74P/action/storage_attestation","attest_author":"https://pith.science/pith/JSNHYNXP3XP3JCWQRR7ZGHJ74P/action/author_attestation","sign_citation":"https://pith.science/pith/JSNHYNXP3XP3JCWQRR7ZGHJ74P/action/citation_signature","submit_replication":"https://pith.science/pith/JSNHYNXP3XP3JCWQRR7ZGHJ74P/action/replication_record"}},"created_at":"2026-05-18T00:56:39.363425+00:00","updated_at":"2026-05-18T00:56:39.363425+00:00"}