{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3PVQSLND7NUYY2D6ARCOQWBNB7","short_pith_number":"pith:3PVQSLND","schema_version":"1.0","canonical_sha256":"dbeb092da3fb698c687e0444e8582d0ff20fa4beaa1b5e84000442b4ec2d4a38","source":{"kind":"arxiv","id":"1701.08648","version":1},"attestation_state":"computed","paper":{"title":"Chromatic numbers for the hyperbolic plane and discrete analogs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Camille Petit, Hugo Parlier","submitted_at":"2017-01-30T15:21:29Z","abstract_excerpt":"We study colorings of the hyperbolic plane, analogously to the Hadwiger-Nelson problem for the Euclidean plane. The idea is to color points using the minimum number of colors such that no two points at distance exactly $d$ are of the same color. The problem depends on $d$ and, following a strategy of Kloeckner, we show linear upper bounds on the necessary number of colors. In parallel, we study the same problem on $q$-regular trees and show analogous results. For both settings, we also consider a variant which consists in replacing $d$ with an interval of distances."},"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":"1701.08648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T15:21:29Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"2b59e0da7aca2e10c417d5111d81f1bfd221b52ac1b5040852f4932bcd9aaeb3","abstract_canon_sha256":"ee7a7450ab905a6b4a8e29fc809da9e77145e4b4bfc197990a816a25072c51e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:53.402466Z","signature_b64":"N91ug2b30FT34CSz9fFcbCirbJ1G/N6tJiuTGSLK7p4EEyGsxqV5YoKX9oEgkZJ2RSzcNt6qcwSIXNSuPHWVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbeb092da3fb698c687e0444e8582d0ff20fa4beaa1b5e84000442b4ec2d4a38","last_reissued_at":"2026-05-18T00:51:53.401852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:53.401852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chromatic numbers for the hyperbolic plane and discrete analogs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Camille Petit, Hugo Parlier","submitted_at":"2017-01-30T15:21:29Z","abstract_excerpt":"We study colorings of the hyperbolic plane, analogously to the Hadwiger-Nelson problem for the Euclidean plane. The idea is to color points using the minimum number of colors such that no two points at distance exactly $d$ are of the same color. The problem depends on $d$ and, following a strategy of Kloeckner, we show linear upper bounds on the necessary number of colors. In parallel, we study the same problem on $q$-regular trees and show analogous results. For both settings, we also consider a variant which consists in replacing $d$ with an interval of distances."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08648","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":"1701.08648","created_at":"2026-05-18T00:51:53.401941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.08648v1","created_at":"2026-05-18T00:51:53.401941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08648","created_at":"2026-05-18T00:51:53.401941+00:00"},{"alias_kind":"pith_short_12","alias_value":"3PVQSLND7NUY","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"3PVQSLND7NUYY2D6","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"3PVQSLND","created_at":"2026-05-18T12:30:58.224056+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/3PVQSLND7NUYY2D6ARCOQWBNB7","json":"https://pith.science/pith/3PVQSLND7NUYY2D6ARCOQWBNB7.json","graph_json":"https://pith.science/api/pith-number/3PVQSLND7NUYY2D6ARCOQWBNB7/graph.json","events_json":"https://pith.science/api/pith-number/3PVQSLND7NUYY2D6ARCOQWBNB7/events.json","paper":"https://pith.science/paper/3PVQSLND"},"agent_actions":{"view_html":"https://pith.science/pith/3PVQSLND7NUYY2D6ARCOQWBNB7","download_json":"https://pith.science/pith/3PVQSLND7NUYY2D6ARCOQWBNB7.json","view_paper":"https://pith.science/paper/3PVQSLND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.08648&json=true","fetch_graph":"https://pith.science/api/pith-number/3PVQSLND7NUYY2D6ARCOQWBNB7/graph.json","fetch_events":"https://pith.science/api/pith-number/3PVQSLND7NUYY2D6ARCOQWBNB7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3PVQSLND7NUYY2D6ARCOQWBNB7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3PVQSLND7NUYY2D6ARCOQWBNB7/action/storage_attestation","attest_author":"https://pith.science/pith/3PVQSLND7NUYY2D6ARCOQWBNB7/action/author_attestation","sign_citation":"https://pith.science/pith/3PVQSLND7NUYY2D6ARCOQWBNB7/action/citation_signature","submit_replication":"https://pith.science/pith/3PVQSLND7NUYY2D6ARCOQWBNB7/action/replication_record"}},"created_at":"2026-05-18T00:51:53.401941+00:00","updated_at":"2026-05-18T00:51:53.401941+00:00"}