{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:M43G7PRCDISKZFRE7XBYXW3Q76","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":"57edf05c1c4882d3ee51c40ade5f21277b8d513d667112ca89f15e76b7d7b2b0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-11T05:18:12Z","title_canon_sha256":"52a2e9d97736c74988b60008af52b5c5508bd9c0a358df5aec911da369fd873f"},"schema_version":"1.0","source":{"id":"1706.08837","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08837","created_at":"2026-05-18T00:41:30Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08837v1","created_at":"2026-05-18T00:41:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08837","created_at":"2026-05-18T00:41:30Z"},{"alias_kind":"pith_short_12","alias_value":"M43G7PRCDISK","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"M43G7PRCDISKZFRE","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"M43G7PRC","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:198355dd5cb851dccffc5fbdd40694bbb1c6297d9801d38db1e39a789262224c","target":"graph","created_at":"2026-05-18T00:41:30Z","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":"K. Ichihara and E. Matsudo introduced the notions of $\\mathbb{Z}$-colorable links and the minimal coloring number for $\\mathbb{Z}$-colorable links, which is one of invariants for links. They proved that the lower bound of minimal coloring number of a non-splittable $\\mathbb{Z}$-colorable link is 4. In this paper, we show the minimal coloring number of any non-splittable $\\mathbb{Z}$-colorable link is exactly 4.","authors_text":"Meiqiao Zhang, Qingying Deng, Xian'an Jin","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-11T05:18:12Z","title":"The Minimal Coloring Number Of Any Non-splittable $\\mathbb{Z}$-colorable Link Is Four"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08837","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":"sha256:4c7fe77da98d9737e2e72c02fb295ad017be894f5bbf69680cde2c7e6335dea1","target":"record","created_at":"2026-05-18T00:41:30Z","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":"57edf05c1c4882d3ee51c40ade5f21277b8d513d667112ca89f15e76b7d7b2b0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-11T05:18:12Z","title_canon_sha256":"52a2e9d97736c74988b60008af52b5c5508bd9c0a358df5aec911da369fd873f"},"schema_version":"1.0","source":{"id":"1706.08837","kind":"arxiv","version":1}},"canonical_sha256":"67366fbe221a24ac9624fdc38bdb70ffb9578f4dce1b1648848ab7630c2f097d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67366fbe221a24ac9624fdc38bdb70ffb9578f4dce1b1648848ab7630c2f097d","first_computed_at":"2026-05-18T00:41:30.879471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:30.879471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cIePiVoBqgKL9WdIHcCiV1WhFfTZwrozpLaxc3Fe0SuZFx54Sj+57LJMMpWUH/1Y8CA/nfEovYsIbOMwUH8KDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:30.880145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08837","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c7fe77da98d9737e2e72c02fb295ad017be894f5bbf69680cde2c7e6335dea1","sha256:198355dd5cb851dccffc5fbdd40694bbb1c6297d9801d38db1e39a789262224c"],"state_sha256":"2ee03038f6452859dc0e437cd5befbe1c5115032cf34245789af73e58c529fff"}