{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:J73TCOF2N2YBAVZIADSUEW3UWY","short_pith_number":"pith:J73TCOF2","schema_version":"1.0","canonical_sha256":"4ff73138ba6eb010572800e5425b74b61343e13eba73f71f06a2afc3ff59ce11","source":{"kind":"arxiv","id":"1412.2091","version":1},"attestation_state":"computed","paper":{"title":"Measurable Chromatic Number of Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Greg Malen","submitted_at":"2014-12-05T18:24:01Z","abstract_excerpt":"We examine the measurable chromatic number of distance colorings on the surface of 2-dimensional spheres of varying radii, showing in particular that similar arguments to those used to raise lower bounds in the plane work for all but a countable set of radii. Furthermore, we show that measurable chromatic number as a function of the radius, or more generally the curvature, is not monotonic."},"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":"1412.2091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-05T18:24:01Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"5c04383aa95552a1edc7375cc45714e0ebb868771dc91c255c0a16b796b627a9","abstract_canon_sha256":"7abe8bac9f8fd33cffe368966e0d5ab45f7dcb52457c688798f4320f0bc37281"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:05.387302Z","signature_b64":"oW01/WGYsc9MGZ7BKL/wjowdJVhfa0+xwDfZjAySgxvf+RHo8BN3uweSfAtS0YLU7uhx8CnXFYzZefXL8IUuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ff73138ba6eb010572800e5425b74b61343e13eba73f71f06a2afc3ff59ce11","last_reissued_at":"2026-05-18T02:32:05.386938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:05.386938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Measurable Chromatic Number of Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Greg Malen","submitted_at":"2014-12-05T18:24:01Z","abstract_excerpt":"We examine the measurable chromatic number of distance colorings on the surface of 2-dimensional spheres of varying radii, showing in particular that similar arguments to those used to raise lower bounds in the plane work for all but a countable set of radii. Furthermore, we show that measurable chromatic number as a function of the radius, or more generally the curvature, is not monotonic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2091","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":"1412.2091","created_at":"2026-05-18T02:32:05.387003+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.2091v1","created_at":"2026-05-18T02:32:05.387003+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2091","created_at":"2026-05-18T02:32:05.387003+00:00"},{"alias_kind":"pith_short_12","alias_value":"J73TCOF2N2YB","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"J73TCOF2N2YBAVZI","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"J73TCOF2","created_at":"2026-05-18T12:28:33.132498+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/J73TCOF2N2YBAVZIADSUEW3UWY","json":"https://pith.science/pith/J73TCOF2N2YBAVZIADSUEW3UWY.json","graph_json":"https://pith.science/api/pith-number/J73TCOF2N2YBAVZIADSUEW3UWY/graph.json","events_json":"https://pith.science/api/pith-number/J73TCOF2N2YBAVZIADSUEW3UWY/events.json","paper":"https://pith.science/paper/J73TCOF2"},"agent_actions":{"view_html":"https://pith.science/pith/J73TCOF2N2YBAVZIADSUEW3UWY","download_json":"https://pith.science/pith/J73TCOF2N2YBAVZIADSUEW3UWY.json","view_paper":"https://pith.science/paper/J73TCOF2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.2091&json=true","fetch_graph":"https://pith.science/api/pith-number/J73TCOF2N2YBAVZIADSUEW3UWY/graph.json","fetch_events":"https://pith.science/api/pith-number/J73TCOF2N2YBAVZIADSUEW3UWY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J73TCOF2N2YBAVZIADSUEW3UWY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J73TCOF2N2YBAVZIADSUEW3UWY/action/storage_attestation","attest_author":"https://pith.science/pith/J73TCOF2N2YBAVZIADSUEW3UWY/action/author_attestation","sign_citation":"https://pith.science/pith/J73TCOF2N2YBAVZIADSUEW3UWY/action/citation_signature","submit_replication":"https://pith.science/pith/J73TCOF2N2YBAVZIADSUEW3UWY/action/replication_record"}},"created_at":"2026-05-18T02:32:05.387003+00:00","updated_at":"2026-05-18T02:32:05.387003+00:00"}