{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:X4KG4BGHT3EPM3OLMNPLAH4ZZP","short_pith_number":"pith:X4KG4BGH","schema_version":"1.0","canonical_sha256":"bf146e04c79ec8f66dcb635eb01f99cbdd2b0e8ac9c68d3fd89ce3711ae6ffa4","source":{"kind":"arxiv","id":"1109.1078","version":2},"attestation_state":"computed","paper":{"title":"An analogue of Gromov's waist theorem for coloring the cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Roman Karasev","submitted_at":"2011-09-06T06:14:35Z","abstract_excerpt":"It is proved that if we partition a $d$-dimensional cube into $n^d$ small cubes and color the small cubes into $m+1$ colors then there exists a monochromatic connected component consisting of at least $f(d, m) n^{d-m}$ small cubes."},"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":"1109.1078","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-06T06:14:35Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"d372f3a97390bf72341e9d45a026c9f5936cc36bd0f468dcce46cbfc978f300e","abstract_canon_sha256":"05e43b1a6cca721add52c3de6529b55158487057dcbc31ee91c5791b4591a4dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:21.247493Z","signature_b64":"YUQxUn305CNt3x4hGp+0h1wegmK4o16z7rp2uzOmeI/KlIJk7F1oo9iLuyz0P5UDMoo+Th5JofTEJGT4JcbfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf146e04c79ec8f66dcb635eb01f99cbdd2b0e8ac9c68d3fd89ce3711ae6ffa4","last_reissued_at":"2026-05-18T03:15:21.246598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:21.246598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An analogue of Gromov's waist theorem for coloring the cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Roman Karasev","submitted_at":"2011-09-06T06:14:35Z","abstract_excerpt":"It is proved that if we partition a $d$-dimensional cube into $n^d$ small cubes and color the small cubes into $m+1$ colors then there exists a monochromatic connected component consisting of at least $f(d, m) n^{d-m}$ small cubes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1078","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":"1109.1078","created_at":"2026-05-18T03:15:21.246735+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.1078v2","created_at":"2026-05-18T03:15:21.246735+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1078","created_at":"2026-05-18T03:15:21.246735+00:00"},{"alias_kind":"pith_short_12","alias_value":"X4KG4BGHT3EP","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"X4KG4BGHT3EPM3OL","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"X4KG4BGH","created_at":"2026-05-18T12:26:44.992195+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/X4KG4BGHT3EPM3OLMNPLAH4ZZP","json":"https://pith.science/pith/X4KG4BGHT3EPM3OLMNPLAH4ZZP.json","graph_json":"https://pith.science/api/pith-number/X4KG4BGHT3EPM3OLMNPLAH4ZZP/graph.json","events_json":"https://pith.science/api/pith-number/X4KG4BGHT3EPM3OLMNPLAH4ZZP/events.json","paper":"https://pith.science/paper/X4KG4BGH"},"agent_actions":{"view_html":"https://pith.science/pith/X4KG4BGHT3EPM3OLMNPLAH4ZZP","download_json":"https://pith.science/pith/X4KG4BGHT3EPM3OLMNPLAH4ZZP.json","view_paper":"https://pith.science/paper/X4KG4BGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.1078&json=true","fetch_graph":"https://pith.science/api/pith-number/X4KG4BGHT3EPM3OLMNPLAH4ZZP/graph.json","fetch_events":"https://pith.science/api/pith-number/X4KG4BGHT3EPM3OLMNPLAH4ZZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X4KG4BGHT3EPM3OLMNPLAH4ZZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X4KG4BGHT3EPM3OLMNPLAH4ZZP/action/storage_attestation","attest_author":"https://pith.science/pith/X4KG4BGHT3EPM3OLMNPLAH4ZZP/action/author_attestation","sign_citation":"https://pith.science/pith/X4KG4BGHT3EPM3OLMNPLAH4ZZP/action/citation_signature","submit_replication":"https://pith.science/pith/X4KG4BGHT3EPM3OLMNPLAH4ZZP/action/replication_record"}},"created_at":"2026-05-18T03:15:21.246735+00:00","updated_at":"2026-05-18T03:15:21.246735+00:00"}