{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:YFHLK54UM2QFIAQPRZP5IRXLTY","short_pith_number":"pith:YFHLK54U","canonical_record":{"source":{"id":"1001.1334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-01-08T18:50:19Z","cross_cats_sorted":[],"title_canon_sha256":"6051e713758d5efb53b1553d49c3faa4c057e513fa9ca1465f0bb59f2d49aeb5","abstract_canon_sha256":"4443d4df6a7e0fcf229a6616215ab48f4bd0979e1a94506dbc73d610f94ea0e2"},"schema_version":"1.0"},"canonical_sha256":"c14eb5779466a054020f8e5fd446eb9e38896d3083f4607c1435d43801ebfd5b","source":{"kind":"arxiv","id":"1001.1334","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1334","created_at":"2026-05-18T04:24:43Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1334v2","created_at":"2026-05-18T04:24:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1334","created_at":"2026-05-18T04:24:43Z"},{"alias_kind":"pith_short_12","alias_value":"YFHLK54UM2QF","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YFHLK54UM2QFIAQP","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YFHLK54U","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:YFHLK54UM2QFIAQPRZP5IRXLTY","target":"record","payload":{"canonical_record":{"source":{"id":"1001.1334","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-01-08T18:50:19Z","cross_cats_sorted":[],"title_canon_sha256":"6051e713758d5efb53b1553d49c3faa4c057e513fa9ca1465f0bb59f2d49aeb5","abstract_canon_sha256":"4443d4df6a7e0fcf229a6616215ab48f4bd0979e1a94506dbc73d610f94ea0e2"},"schema_version":"1.0"},"canonical_sha256":"c14eb5779466a054020f8e5fd446eb9e38896d3083f4607c1435d43801ebfd5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:43.897855Z","signature_b64":"O9NKyWmMGfLW6AVDL6ILZSIVAIBTOdz8uIFlOVEw4z2rao7Yuyuu/WHDDjcL4VRiBFo57PY9nQF4pfWukLA0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c14eb5779466a054020f8e5fd446eb9e38896d3083f4607c1435d43801ebfd5b","last_reissued_at":"2026-05-18T04:24:43.897502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:43.897502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.1334","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":"2026-05-18T04:24:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exe26t7pztwgbQutbBl90XgAYQGo14ODrPBoqWRnmF/2QVMdMT1NDSc60bho1/a4K33FGlX5gkX5XuSl4GZiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:36:07.722468Z"},"content_sha256":"e888f84c843fbc60a48941afb061071d67ead7126ea184b539c44ad98f614521","schema_version":"1.0","event_id":"sha256:e888f84c843fbc60a48941afb061071d67ead7126ea184b539c44ad98f614521"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:YFHLK54UM2QFIAQPRZP5IRXLTY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimum Number of Fox Colors for Small Primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"J. Matias, P. Lopes","submitted_at":"2010-01-08T18:50:19Z","abstract_excerpt":"This article concerns exact results on the minimum number of colors of a Fox coloring over the integers modulo r, of a link with non-null determinant. Specifically, we prove that whenever the least prime divisor of the determinant of such a link and the modulus r is 2, 3, 5, or 7, then the minimum number of colors is 2, 3, 4, or 4 (respectively) and conversely. We are thus led to conjecture that for each prime p there exists a unique positive integer, m, with the following property. For any link L of non-null determinant and any modulus r such that p is the least prime divisor of the determina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1334","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":"2026-05-18T04:24:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CkSPQV5LvkmnH7r9cyVfMaS1MkU7wV5Plxkyn2NI8r+q1ZagzdFAD96dXV8II6uMOAOR73bN4NkoPynOPuYHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:36:07.723182Z"},"content_sha256":"5aab3bc55988a762fda2b459a94466a8e9d51780664782997931a425c03ea756","schema_version":"1.0","event_id":"sha256:5aab3bc55988a762fda2b459a94466a8e9d51780664782997931a425c03ea756"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/bundle.json","state_url":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/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":"2026-05-26T00:36:07Z","links":{"resolver":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY","bundle":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/bundle.json","state":"https://pith.science/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFHLK54UM2QFIAQPRZP5IRXLTY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YFHLK54UM2QFIAQPRZP5IRXLTY","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":"4443d4df6a7e0fcf229a6616215ab48f4bd0979e1a94506dbc73d610f94ea0e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-01-08T18:50:19Z","title_canon_sha256":"6051e713758d5efb53b1553d49c3faa4c057e513fa9ca1465f0bb59f2d49aeb5"},"schema_version":"1.0","source":{"id":"1001.1334","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1334","created_at":"2026-05-18T04:24:43Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1334v2","created_at":"2026-05-18T04:24:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1334","created_at":"2026-05-18T04:24:43Z"},{"alias_kind":"pith_short_12","alias_value":"YFHLK54UM2QF","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YFHLK54UM2QFIAQP","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YFHLK54U","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:5aab3bc55988a762fda2b459a94466a8e9d51780664782997931a425c03ea756","target":"graph","created_at":"2026-05-18T04:24:43Z","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 concerns exact results on the minimum number of colors of a Fox coloring over the integers modulo r, of a link with non-null determinant. Specifically, we prove that whenever the least prime divisor of the determinant of such a link and the modulus r is 2, 3, 5, or 7, then the minimum number of colors is 2, 3, 4, or 4 (respectively) and conversely. We are thus led to conjecture that for each prime p there exists a unique positive integer, m, with the following property. For any link L of non-null determinant and any modulus r such that p is the least prime divisor of the determina","authors_text":"J. Matias, P. Lopes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-01-08T18:50:19Z","title":"Minimum Number of Fox Colors for Small Primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1334","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:e888f84c843fbc60a48941afb061071d67ead7126ea184b539c44ad98f614521","target":"record","created_at":"2026-05-18T04:24:43Z","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":"4443d4df6a7e0fcf229a6616215ab48f4bd0979e1a94506dbc73d610f94ea0e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-01-08T18:50:19Z","title_canon_sha256":"6051e713758d5efb53b1553d49c3faa4c057e513fa9ca1465f0bb59f2d49aeb5"},"schema_version":"1.0","source":{"id":"1001.1334","kind":"arxiv","version":2}},"canonical_sha256":"c14eb5779466a054020f8e5fd446eb9e38896d3083f4607c1435d43801ebfd5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c14eb5779466a054020f8e5fd446eb9e38896d3083f4607c1435d43801ebfd5b","first_computed_at":"2026-05-18T04:24:43.897502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:43.897502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O9NKyWmMGfLW6AVDL6ILZSIVAIBTOdz8uIFlOVEw4z2rao7Yuyuu/WHDDjcL4VRiBFo57PY9nQF4pfWukLA0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:43.897855Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.1334","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e888f84c843fbc60a48941afb061071d67ead7126ea184b539c44ad98f614521","sha256:5aab3bc55988a762fda2b459a94466a8e9d51780664782997931a425c03ea756"],"state_sha256":"1f8d8174d3e3897aada17956ccebe4e52b0d9ab3eca5127dda6c36bc6266e792"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l3lVW/9KtIncpTDdPWGtHr23ckQhWBCGuuBnuZJB4UAlkJGFF3bs/kjw24hWRetUrpezO1s22MnZoTxldLgGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:36:07.726221Z","bundle_sha256":"9dc10173efda5d37fd4af124394bb1856420bad7b78da19f57384f6cac6ea659"}}