{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:X3VCZGQH36Z5RRQDWKAM42PF7D","short_pith_number":"pith:X3VCZGQH","schema_version":"1.0","canonical_sha256":"beea2c9a07dfb3d8c603b280ce69e5f8ce4a23edcf4985afcfb19d0b4ac10a15","source":{"kind":"arxiv","id":"1506.08345","version":1},"attestation_state":"computed","paper":{"title":"Color-blind index in graphs of very low degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Charlie Suer, Derrick Stolee, Devon Sigler, Jennifer Diemunsch, Lauren M. Nelsen, Lucas Kramer, Luke L. Nelsen, Nathan Graber, Victor Larsen","submitted_at":"2015-06-28T02:08:56Z","abstract_excerpt":"Let $c:E(G)\\to [k]$ be an edge-coloring of a graph $G$, not necessarily proper. For each vertex $v$, let $\\bar{c}(v)=(a_1,\\ldots,a_k)$, where $a_i$ is the number of edges incident to $v$ with color $i$. Reorder $\\bar{c}(v)$ for every $v$ in $G$ in nonincreasing order to obtain $c^*(v)$, the color-blind partition of $v$. When $c^*$ induces a proper vertex coloring, that is, $c^*(u)\\neq c^*(v)$ for every edge $uv$ in $G$, we say that $c$ is color-blind distinguishing. The minimum $k$ for which there exists a color-blind distinguishing edge coloring $c:E(G)\\to [k]$ is the color-blind index of $G$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.08345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-28T02:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"ecf7725d585345a3aed75a6b3ba334eb1af4cdb493eadcc607bcad1d9f8e0647","abstract_canon_sha256":"01fbed318e3eddded4d42dd4e5d6944d0b22d8b13287ab014c2aa7ede0b88fea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:45.083204Z","signature_b64":"r8u3qPTIkQLI/z/TyrtUFqHcD2O4niVhD1reQOJBQb1DH/enR14kGUdjtngTOvnol66rDT1iWnZ946lHkbGnDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beea2c9a07dfb3d8c603b280ce69e5f8ce4a23edcf4985afcfb19d0b4ac10a15","last_reissued_at":"2026-05-18T00:34:45.082526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:45.082526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Color-blind index in graphs of very low degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Charlie Suer, Derrick Stolee, Devon Sigler, Jennifer Diemunsch, Lauren M. Nelsen, Lucas Kramer, Luke L. Nelsen, Nathan Graber, Victor Larsen","submitted_at":"2015-06-28T02:08:56Z","abstract_excerpt":"Let $c:E(G)\\to [k]$ be an edge-coloring of a graph $G$, not necessarily proper. For each vertex $v$, let $\\bar{c}(v)=(a_1,\\ldots,a_k)$, where $a_i$ is the number of edges incident to $v$ with color $i$. Reorder $\\bar{c}(v)$ for every $v$ in $G$ in nonincreasing order to obtain $c^*(v)$, the color-blind partition of $v$. When $c^*$ induces a proper vertex coloring, that is, $c^*(u)\\neq c^*(v)$ for every edge $uv$ in $G$, we say that $c$ is color-blind distinguishing. The minimum $k$ for which there exists a color-blind distinguishing edge coloring $c:E(G)\\to [k]$ is the color-blind index of $G$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08345","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.08345","created_at":"2026-05-18T00:34:45.082622+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.08345v1","created_at":"2026-05-18T00:34:45.082622+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08345","created_at":"2026-05-18T00:34:45.082622+00:00"},{"alias_kind":"pith_short_12","alias_value":"X3VCZGQH36Z5","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"X3VCZGQH36Z5RRQD","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"X3VCZGQH","created_at":"2026-05-18T12:29:47.479230+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X3VCZGQH36Z5RRQDWKAM42PF7D","json":"https://pith.science/pith/X3VCZGQH36Z5RRQDWKAM42PF7D.json","graph_json":"https://pith.science/api/pith-number/X3VCZGQH36Z5RRQDWKAM42PF7D/graph.json","events_json":"https://pith.science/api/pith-number/X3VCZGQH36Z5RRQDWKAM42PF7D/events.json","paper":"https://pith.science/paper/X3VCZGQH"},"agent_actions":{"view_html":"https://pith.science/pith/X3VCZGQH36Z5RRQDWKAM42PF7D","download_json":"https://pith.science/pith/X3VCZGQH36Z5RRQDWKAM42PF7D.json","view_paper":"https://pith.science/paper/X3VCZGQH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.08345&json=true","fetch_graph":"https://pith.science/api/pith-number/X3VCZGQH36Z5RRQDWKAM42PF7D/graph.json","fetch_events":"https://pith.science/api/pith-number/X3VCZGQH36Z5RRQDWKAM42PF7D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X3VCZGQH36Z5RRQDWKAM42PF7D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X3VCZGQH36Z5RRQDWKAM42PF7D/action/storage_attestation","attest_author":"https://pith.science/pith/X3VCZGQH36Z5RRQDWKAM42PF7D/action/author_attestation","sign_citation":"https://pith.science/pith/X3VCZGQH36Z5RRQDWKAM42PF7D/action/citation_signature","submit_replication":"https://pith.science/pith/X3VCZGQH36Z5RRQDWKAM42PF7D/action/replication_record"}},"created_at":"2026-05-18T00:34:45.082622+00:00","updated_at":"2026-05-18T00:34:45.082622+00:00"}