{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SY36A3AS2PSVFGQ4GGIEP3FI4D","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":"c0cfcda9b9de474fc307ace9c53829eaa139510e08526d17f16a8d6881faa3e8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-17T12:44:23Z","title_canon_sha256":"9004a6b76c39d20a517645225ffbe6b2315027b505619e5059e0341779d48d67"},"schema_version":"1.0","source":{"id":"1701.04648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04648","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04648v1","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04648","created_at":"2026-05-18T00:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"SY36A3AS2PSV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SY36A3AS2PSVFGQ4","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SY36A3AS","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:41de27382c93a1083a4c6673ec1a51eb112a1c1c5921e0aac9659805ff2042d3","target":"graph","created_at":"2026-05-18T00:52:43Z","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":"With any (not necessarily proper) edge $k$-colouring $\\gamma:E(G)\\longrightarrow\\{1,\\dots,k\\}$ of a graph $G$,one can associate a vertex colouring $\\sigma\\_{\\gamma}$ given by $\\sigma\\_{\\gamma}(v)=\\sum\\_{e\\ni v}\\gamma(e)$.A neighbour-sum-distinguishing edge $k$-colouring is an edge colouring whose associated vertex colouring is proper.The neighbour-sum-distinguishing index of a graph $G$ is then the smallest $k$ for which $G$ admitsa neighbour-sum-distinguishing edge $k$-colouring.These notions naturally extends to total colourings of graphs that assign colours to both vertices and edges.We stu","authors_text":"Eric Sopena (LaBRI), Jakub Przybylo, Mariusz Wozniak, Mohammed Senhaji (LaBRI), Monika Pilsniak, Olivier Baudon (LaBRI)","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-17T12:44:23Z","title":"Equitable neighbour-sum-distinguishing edge and total colourings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04648","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:a3bce1969fe4aa370fe873a2b0e9baa84bcc87298dccf222833b84fbe8023991","target":"record","created_at":"2026-05-18T00:52:43Z","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":"c0cfcda9b9de474fc307ace9c53829eaa139510e08526d17f16a8d6881faa3e8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-17T12:44:23Z","title_canon_sha256":"9004a6b76c39d20a517645225ffbe6b2315027b505619e5059e0341779d48d67"},"schema_version":"1.0","source":{"id":"1701.04648","kind":"arxiv","version":1}},"canonical_sha256":"9637e06c12d3e5529a1c319047eca8e0e698ff19044186f90eab57db4695143b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9637e06c12d3e5529a1c319047eca8e0e698ff19044186f90eab57db4695143b","first_computed_at":"2026-05-18T00:52:43.011651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:43.011651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IO+Kui8h/xBAAsMpJhdifvukb3yBLK/c5n/inIhRy5xxLjNGMMNFSlSbWFWvDr25VNlAqKzlAH+sWfGfUNTmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:43.012196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3bce1969fe4aa370fe873a2b0e9baa84bcc87298dccf222833b84fbe8023991","sha256:41de27382c93a1083a4c6673ec1a51eb112a1c1c5921e0aac9659805ff2042d3"],"state_sha256":"b3db399c92dbd31c21c7b89df257568e4a389c5ac3a04e4dbd446411e73a4897"}