{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BFNLU6ZPXST7YLZ6EHLKTOKXHE","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":"e81f2e295c3bb9f19256c69deedce6ca9ec2c4ed39a5532ae72ad5e2f5e59a91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-02T14:43:59Z","title_canon_sha256":"2de02e1072ccdef56f6021a7dea959061d432a2bcd7fa16c3529f0ae4d442a01"},"schema_version":"1.0","source":{"id":"1510.00614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00614","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00614v1","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00614","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"BFNLU6ZPXST7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BFNLU6ZPXST7YLZ6","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BFNLU6ZP","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:4b3c4ef9d854465fc83b21ffc99e3b85f36e59de06094d12c3bee741ad623cff","target":"graph","created_at":"2026-05-18T01:31:12Z","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":"The chromatic number $\\chi((G,\\sigma))$ of a signed graph $(G,\\sigma)$ is the smallest number $k$ for which there is a function $c : V(G) \\rightarrow \\mathbb{Z}_k$ such that $c(v) \\not= \\sigma(e) c(w)$ for every edge $e = vw$. Let $\\Sigma(G)$ be the set of all signatures of $G$. We study the chromatic spectrum $\\Sigma_{\\chi}(G) = \\{\\chi((G,\\sigma))\\colon\\ \\sigma \\in \\Sigma(G)\\}$ of $(G,\\sigma)$. Let $M_{\\chi}(G) = \\max\\{\\chi((G,\\sigma))\\colon\\ \\sigma \\in \\Sigma(G)\\}$, and $m_{\\chi}(G) = \\min\\{\\chi((G,\\sigma))\\colon\\ \\sigma \\in \\Sigma(G)\\}$. We show that $\\Sigma_{\\chi}(G) = \\{k : m_{\\chi}(G) \\l","authors_text":"Eckhard Steffen, Yingli Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-02T14:43:59Z","title":"The chromatic spectrum of signed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00614","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":"sha256:423c3bbbd353780345743641ce6b13274de9535652c03529e78ad3f048984451","target":"record","created_at":"2026-05-18T01:31:12Z","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":"e81f2e295c3bb9f19256c69deedce6ca9ec2c4ed39a5532ae72ad5e2f5e59a91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-02T14:43:59Z","title_canon_sha256":"2de02e1072ccdef56f6021a7dea959061d432a2bcd7fa16c3529f0ae4d442a01"},"schema_version":"1.0","source":{"id":"1510.00614","kind":"arxiv","version":1}},"canonical_sha256":"095aba7b2fbca7fc2f3e21d6a9b957393182793db10961dc9a0b120a49f44273","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"095aba7b2fbca7fc2f3e21d6a9b957393182793db10961dc9a0b120a49f44273","first_computed_at":"2026-05-18T01:31:12.495093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:12.495093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"STOGZgcNyA6rhqe5HwI8gUMzUeia/fLWKhRqQJTtV3PfMjuDukbQOD6DlfuuR/Tv8kClO6bAiAdq6bv6j63fAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:12.495756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:423c3bbbd353780345743641ce6b13274de9535652c03529e78ad3f048984451","sha256:4b3c4ef9d854465fc83b21ffc99e3b85f36e59de06094d12c3bee741ad623cff"],"state_sha256":"93fcbbb47daf0d1ae66c48f1b2113745b0736227748e937b9fb6f37f247bc9d0"}