{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3A3CKTIBCQLVGCVNVLCVTXQEA6","short_pith_number":"pith:3A3CKTIB","canonical_record":{"source":{"id":"1305.5229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-22T18:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"5a6593fe1256197e69a967d1d82a20998c798c99ff511bf4db0b686a38a91dbc","abstract_canon_sha256":"8346fd2c9e8c22f2f90a1361dcabab35fcffffc63020c3e4841b8bfc8128d424"},"schema_version":"1.0"},"canonical_sha256":"d836254d011417530aadaac559de0407b6cb2467f1c7dd62b108dcf06c2b17d4","source":{"kind":"arxiv","id":"1305.5229","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5229","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5229v2","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5229","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"3A3CKTIBCQLV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3A3CKTIBCQLVGCVN","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3A3CKTIB","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3A3CKTIBCQLVGCVNVLCVTXQEA6","target":"record","payload":{"canonical_record":{"source":{"id":"1305.5229","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-22T18:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"5a6593fe1256197e69a967d1d82a20998c798c99ff511bf4db0b686a38a91dbc","abstract_canon_sha256":"8346fd2c9e8c22f2f90a1361dcabab35fcffffc63020c3e4841b8bfc8128d424"},"schema_version":"1.0"},"canonical_sha256":"d836254d011417530aadaac559de0407b6cb2467f1c7dd62b108dcf06c2b17d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:33.941809Z","signature_b64":"v4vqCCSfFrbQZ5p5xhS9TNf7U4au03RVWiBKO74occN2J2ZPWAm/ihwoA8hORy6/jGTDGJh1V6DlVTqR33O5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d836254d011417530aadaac559de0407b6cb2467f1c7dd62b108dcf06c2b17d4","last_reissued_at":"2026-05-18T02:30:33.941413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:33.941413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.5229","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RLHrGClGbw5CXi7GA0FQ7WaLm1P7JEkK5auOY6IFudja4CyBRXJE9MUqCw74Bdpq6m1x2uymnhNfkXP137eNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:26:24.129183Z"},"content_sha256":"ea85047076c9593ae4ac349249aa9f43f4aa1246d507fae08727f7cc305b3398","schema_version":"1.0","event_id":"sha256:ea85047076c9593ae4ac349249aa9f43f4aa1246d507fae08727f7cc305b3398"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3A3CKTIBCQLVGCVNVLCVTXQEA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Radial Colorings of Annuli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jacob Manske, Jeremy F. Alm","submitted_at":"2013-05-22T18:53:44Z","abstract_excerpt":"We consider the chromatic numbers of unit-distance graphs of various annuli. In particular, we consider radial colorings, which are \"nice\" colorings, and completely determine the radial chromatic numbers of various annuli."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5229","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XC20jDf2vgtxG+MDClVyYQL4h/K6M49yQx2Ovu3nZgXMJw9HBgJr4olGliIxPc3FaEaHlgRz4mgwhhZ9lDlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:26:24.129599Z"},"content_sha256":"ca23e7f8b24796bfb8fa80e6b2e4cc0bf2ca8f5d8ba441b9d95359d3e806d77b","schema_version":"1.0","event_id":"sha256:ca23e7f8b24796bfb8fa80e6b2e4cc0bf2ca8f5d8ba441b9d95359d3e806d77b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3A3CKTIBCQLVGCVNVLCVTXQEA6/bundle.json","state_url":"https://pith.science/pith/3A3CKTIBCQLVGCVNVLCVTXQEA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3A3CKTIBCQLVGCVNVLCVTXQEA6/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":"2026-06-02T17:26:24Z","links":{"resolver":"https://pith.science/pith/3A3CKTIBCQLVGCVNVLCVTXQEA6","bundle":"https://pith.science/pith/3A3CKTIBCQLVGCVNVLCVTXQEA6/bundle.json","state":"https://pith.science/pith/3A3CKTIBCQLVGCVNVLCVTXQEA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3A3CKTIBCQLVGCVNVLCVTXQEA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3A3CKTIBCQLVGCVNVLCVTXQEA6","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":"8346fd2c9e8c22f2f90a1361dcabab35fcffffc63020c3e4841b8bfc8128d424","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-22T18:53:44Z","title_canon_sha256":"5a6593fe1256197e69a967d1d82a20998c798c99ff511bf4db0b686a38a91dbc"},"schema_version":"1.0","source":{"id":"1305.5229","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5229","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5229v2","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5229","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"3A3CKTIBCQLV","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3A3CKTIBCQLVGCVN","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3A3CKTIB","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:ca23e7f8b24796bfb8fa80e6b2e4cc0bf2ca8f5d8ba441b9d95359d3e806d77b","target":"graph","created_at":"2026-05-18T02:30:33Z","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":"We consider the chromatic numbers of unit-distance graphs of various annuli. In particular, we consider radial colorings, which are \"nice\" colorings, and completely determine the radial chromatic numbers of various annuli.","authors_text":"Jacob Manske, Jeremy F. Alm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-22T18:53:44Z","title":"On Radial Colorings of Annuli"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5229","kind":"arxiv","version":2},"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:ea85047076c9593ae4ac349249aa9f43f4aa1246d507fae08727f7cc305b3398","target":"record","created_at":"2026-05-18T02:30:33Z","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":"8346fd2c9e8c22f2f90a1361dcabab35fcffffc63020c3e4841b8bfc8128d424","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-22T18:53:44Z","title_canon_sha256":"5a6593fe1256197e69a967d1d82a20998c798c99ff511bf4db0b686a38a91dbc"},"schema_version":"1.0","source":{"id":"1305.5229","kind":"arxiv","version":2}},"canonical_sha256":"d836254d011417530aadaac559de0407b6cb2467f1c7dd62b108dcf06c2b17d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d836254d011417530aadaac559de0407b6cb2467f1c7dd62b108dcf06c2b17d4","first_computed_at":"2026-05-18T02:30:33.941413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:33.941413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v4vqCCSfFrbQZ5p5xhS9TNf7U4au03RVWiBKO74occN2J2ZPWAm/ihwoA8hORy6/jGTDGJh1V6DlVTqR33O5DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:33.941809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5229","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea85047076c9593ae4ac349249aa9f43f4aa1246d507fae08727f7cc305b3398","sha256:ca23e7f8b24796bfb8fa80e6b2e4cc0bf2ca8f5d8ba441b9d95359d3e806d77b"],"state_sha256":"93897fc1a5fff3b20d34a0dd37aaeef69f1a4a340125bf1ef47fad2c0cbb1999"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQRpZYzYRqy+jBSmLThF6ZfFcg6ZABq8myrpbgtk2R4gaVzuwhge4+jjrTYWLCFnh+KWwMXYrJVc8VTXE6EFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:26:24.132184Z","bundle_sha256":"4e689281042ec41ac235f3f2a3ee493a74ff26951f8ad36df2feac7ad90aad90"}}