{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AQ4L6PZIFGA7G77Z2DID5L5GZJ","short_pith_number":"pith:AQ4L6PZI","canonical_record":{"source":{"id":"1411.3565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-13T14:47:29Z","cross_cats_sorted":["math.CO","math.DG"],"title_canon_sha256":"fc3a862c701fe0064a60517673143359ae3faae8421590ce1057231770b7f46a","abstract_canon_sha256":"024120434d53d300967e563eab05c5a389a4355d836d62f1ef14bfca61a4d71b"},"schema_version":"1.0"},"canonical_sha256":"0438bf3f282981f37ff9d0d03eafa6ca671ad4f94e339f080d4499f406f49296","source":{"kind":"arxiv","id":"1411.3565","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3565","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3565v1","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3565","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"AQ4L6PZIFGA7","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AQ4L6PZIFGA7G77Z","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AQ4L6PZI","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AQ4L6PZIFGA7G77Z2DID5L5GZJ","target":"record","payload":{"canonical_record":{"source":{"id":"1411.3565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-13T14:47:29Z","cross_cats_sorted":["math.CO","math.DG"],"title_canon_sha256":"fc3a862c701fe0064a60517673143359ae3faae8421590ce1057231770b7f46a","abstract_canon_sha256":"024120434d53d300967e563eab05c5a389a4355d836d62f1ef14bfca61a4d71b"},"schema_version":"1.0"},"canonical_sha256":"0438bf3f282981f37ff9d0d03eafa6ca671ad4f94e339f080d4499f406f49296","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:43.441274Z","signature_b64":"a9jpbTPsS7xC52PKgOlLV3syA+1jCF8equwAj6Fiovg0ikiNflFHrgIMu7cN9nPFu7dePsqCnwnzg/HAz5JGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0438bf3f282981f37ff9d0d03eafa6ca671ad4f94e339f080d4499f406f49296","last_reissued_at":"2026-05-18T02:37:43.440889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:43.440889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.3565","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xu+oat0qNQxyu4iR+xEEGApaAwRgPitPwL5jc6dANOqx93uiWt05efCY+o7pH392CqDFLdSx0GDqAC/IrjCbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:32:52.708776Z"},"content_sha256":"93892f916040cc44a75491d5ed8c79311d8d67421b165e2e065126aef5656ff5","schema_version":"1.0","event_id":"sha256:93892f916040cc44a75491d5ed8c79311d8d67421b165e2e065126aef5656ff5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AQ4L6PZIFGA7G77Z2DID5L5GZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chromatic numbers of hyperbolic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DG"],"primary_cat":"math.GT","authors_text":"Camille Petit, Hugo Parlier","submitted_at":"2014-11-13T14:47:29Z","abstract_excerpt":"This article is about chromatic numbers of hyperbolic surfaces. For a metric space, the $d$-chromatic number is the minimum number of colors needed to color the points of the space so that any two points at distance $d$ are of a different color. We prove upper bounds on the $d$-chromatic number of any hyperbolic surface which only depend on $d$. In another direction, we investigate chromatic numbers of closed genus $g$ surfaces and find upper bounds that only depend on $g$ (and not on $d$). For both problems, we construct families of examples that show that our bounds are meaningful."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3565","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m+DokiLHM+Bjsl9cFE/HvWLd5dA40dW6Xn6MBIwWgCiDJO+RoHB2V+hZH3ThFX5gqx2OY3QTBUGoAN2AHP4hCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:32:52.709262Z"},"content_sha256":"de100aa285cf4d754144484b32147b649d8f4e9dce7ad17eb85e4e52cefa268d","schema_version":"1.0","event_id":"sha256:de100aa285cf4d754144484b32147b649d8f4e9dce7ad17eb85e4e52cefa268d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQ4L6PZIFGA7G77Z2DID5L5GZJ/bundle.json","state_url":"https://pith.science/pith/AQ4L6PZIFGA7G77Z2DID5L5GZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQ4L6PZIFGA7G77Z2DID5L5GZJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T21:32:52Z","links":{"resolver":"https://pith.science/pith/AQ4L6PZIFGA7G77Z2DID5L5GZJ","bundle":"https://pith.science/pith/AQ4L6PZIFGA7G77Z2DID5L5GZJ/bundle.json","state":"https://pith.science/pith/AQ4L6PZIFGA7G77Z2DID5L5GZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQ4L6PZIFGA7G77Z2DID5L5GZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AQ4L6PZIFGA7G77Z2DID5L5GZJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"024120434d53d300967e563eab05c5a389a4355d836d62f1ef14bfca61a4d71b","cross_cats_sorted":["math.CO","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-13T14:47:29Z","title_canon_sha256":"fc3a862c701fe0064a60517673143359ae3faae8421590ce1057231770b7f46a"},"schema_version":"1.0","source":{"id":"1411.3565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3565","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3565v1","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3565","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"AQ4L6PZIFGA7","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AQ4L6PZIFGA7G77Z","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AQ4L6PZI","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:de100aa285cf4d754144484b32147b649d8f4e9dce7ad17eb85e4e52cefa268d","target":"graph","created_at":"2026-05-18T02:37:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This article is about chromatic numbers of hyperbolic surfaces. For a metric space, the $d$-chromatic number is the minimum number of colors needed to color the points of the space so that any two points at distance $d$ are of a different color. We prove upper bounds on the $d$-chromatic number of any hyperbolic surface which only depend on $d$. In another direction, we investigate chromatic numbers of closed genus $g$ surfaces and find upper bounds that only depend on $g$ (and not on $d$). For both problems, we construct families of examples that show that our bounds are meaningful.","authors_text":"Camille Petit, Hugo Parlier","cross_cats":["math.CO","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-13T14:47:29Z","title":"Chromatic numbers of hyperbolic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3565","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:93892f916040cc44a75491d5ed8c79311d8d67421b165e2e065126aef5656ff5","target":"record","created_at":"2026-05-18T02:37:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"024120434d53d300967e563eab05c5a389a4355d836d62f1ef14bfca61a4d71b","cross_cats_sorted":["math.CO","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-13T14:47:29Z","title_canon_sha256":"fc3a862c701fe0064a60517673143359ae3faae8421590ce1057231770b7f46a"},"schema_version":"1.0","source":{"id":"1411.3565","kind":"arxiv","version":1}},"canonical_sha256":"0438bf3f282981f37ff9d0d03eafa6ca671ad4f94e339f080d4499f406f49296","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0438bf3f282981f37ff9d0d03eafa6ca671ad4f94e339f080d4499f406f49296","first_computed_at":"2026-05-18T02:37:43.440889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:43.440889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a9jpbTPsS7xC52PKgOlLV3syA+1jCF8equwAj6Fiovg0ikiNflFHrgIMu7cN9nPFu7dePsqCnwnzg/HAz5JGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:43.441274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93892f916040cc44a75491d5ed8c79311d8d67421b165e2e065126aef5656ff5","sha256:de100aa285cf4d754144484b32147b649d8f4e9dce7ad17eb85e4e52cefa268d"],"state_sha256":"7beea2637a88351e92d88f6361c4cea995c3f3cb556a42c88d4a7dd184d85290"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cdjoTA1t56Z6p7kjVT9596ZBlWJlTtLjVjqWmJ4y7AAhKRRUW5mWXhkuUkX6RQu+B+OmgK2MNr94f/UegdxlCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T21:32:52.711522Z","bundle_sha256":"feabe52a2b1b946be8d5783eae4039da6a866d8f3caf789328ea755f70ebb742"}}