{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JR4FCPTTPTO5H3PWCR66L22DNE","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":"973cc5616fa4d6b151cf5dbfded21448d7f4777bb77cd2ee7a567bc0295a728b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-24T01:53:30Z","title_canon_sha256":"cc61e362a6aa4bf16d79b1ce1e91894fa129dd940c0a7f742183c8a1b14451c3"},"schema_version":"1.0","source":{"id":"1308.5278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5278","created_at":"2026-05-18T03:15:07Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5278v1","created_at":"2026-05-18T03:15:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5278","created_at":"2026-05-18T03:15:07Z"},{"alias_kind":"pith_short_12","alias_value":"JR4FCPTTPTO5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JR4FCPTTPTO5H3PW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JR4FCPTT","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:ab849c6e6270983bc99aba3cf2f70a5dcba7e38004a5260052cfe24d2879897e","target":"graph","created_at":"2026-05-18T03:15:07Z","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 prove that if a link admits non-trivial (2k+1)-colorings, with prime 2k+1>7, it also admits non-trivial (2k+1)-colorings not involving colors 2k, 2k-1, nor k.","authors_text":"Pedro Lopes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-24T01:53:30Z","title":"Removing Colors 2k, 2k-1, and k"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5278","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:f9338488239a2e15a4d73df7fa47e376bcee6e733265550c44cf3780d3ab0f54","target":"record","created_at":"2026-05-18T03:15:07Z","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":"973cc5616fa4d6b151cf5dbfded21448d7f4777bb77cd2ee7a567bc0295a728b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-24T01:53:30Z","title_canon_sha256":"cc61e362a6aa4bf16d79b1ce1e91894fa129dd940c0a7f742183c8a1b14451c3"},"schema_version":"1.0","source":{"id":"1308.5278","kind":"arxiv","version":1}},"canonical_sha256":"4c78513e737cddd3edf6147de5eb43691905448cdd35092e334971d5de106b7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c78513e737cddd3edf6147de5eb43691905448cdd35092e334971d5de106b7b","first_computed_at":"2026-05-18T03:15:07.223274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:07.223274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aiXjQqhKQhRvRbOsf8/GhJsnm3pF/i7lV+MWw+fC091Ly4x/P06O0hYJGAtF8jGCnKS5Iob57GaAEnsFZRFQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:07.223998Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9338488239a2e15a4d73df7fa47e376bcee6e733265550c44cf3780d3ab0f54","sha256:ab849c6e6270983bc99aba3cf2f70a5dcba7e38004a5260052cfe24d2879897e"],"state_sha256":"ced08246252d19e7c6f95e5a9012fdecf534341cc372d6fec0e8e34604e24c48"}