{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A7SRCSXWFLELX3QIPOGJDGHILC","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":"e4205a4f83d314ddd4b219d3f2cb3b6586364bb47fcc1dd8d2bc01a5c95ab874","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-09T22:48:46Z","title_canon_sha256":"5a35a4cab75762495c57c1cd61223a07fc40f1b61328be47e4e3bb6d9fdb485b"},"schema_version":"1.0","source":{"id":"1406.2378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2378","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2378v1","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2378","created_at":"2026-05-18T02:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"A7SRCSXWFLEL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A7SRCSXWFLELX3QI","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A7SRCSXW","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:bfb8f0f20ad90bd4cbbb002ddcaf630e3ded63bfc19e01ab44802efda0108f22","target":"graph","created_at":"2026-05-18T02:50:01Z","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":"A link diagram is said to be lune-free if, when viewed as a 4-regular plane graph it does not have multiple edges between any pair of nodes. We prove that any colored link diagram is equivalent to a colored lune-free diagram with the same number of colors. Thus any colored link diagram with a minimum number of colors (known as a minimal diagram) is equivalent to a colored lune-free diagram with that same number of colors. We call the passage from a link diagram to an equivalent lune-free diagram its delunification process.\n  We then introduce a notion of grey sets in order to obtain higher low","authors_text":"Louis Kauffman, Pedro Lopes, Slavik Jablan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-09T22:48:46Z","title":"The Delunification Process and Minimal Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2378","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:f32560bd54802875c1aa5ceebe141b63c01a5cf179c4f929108df5193c3587fd","target":"record","created_at":"2026-05-18T02:50:01Z","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":"e4205a4f83d314ddd4b219d3f2cb3b6586364bb47fcc1dd8d2bc01a5c95ab874","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-09T22:48:46Z","title_canon_sha256":"5a35a4cab75762495c57c1cd61223a07fc40f1b61328be47e4e3bb6d9fdb485b"},"schema_version":"1.0","source":{"id":"1406.2378","kind":"arxiv","version":1}},"canonical_sha256":"07e5114af62ac8bbee087b8c9198e8588c4dbf96dd0eef1ac7e4c2344555ba06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07e5114af62ac8bbee087b8c9198e8588c4dbf96dd0eef1ac7e4c2344555ba06","first_computed_at":"2026-05-18T02:50:01.811472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:01.811472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L+9ZNTLtrNkqsr9GLBgg0sYy04TLDZKKsK0r+fLL5hm0pMp2JHg9gN9VaPpYwQzMXuDB8n/ZLNFld/Mrl87qAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:01.811981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f32560bd54802875c1aa5ceebe141b63c01a5cf179c4f929108df5193c3587fd","sha256:bfb8f0f20ad90bd4cbbb002ddcaf630e3ded63bfc19e01ab44802efda0108f22"],"state_sha256":"9b5c7a37fa1c6f1d3d7c3d342632ec06d01b066f751ec445640127693e42bf2e"}