{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JRNQ2FZHFKBE5BFY55SI7PPR3R","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":"1bc8b1b8e1431cd40b855dc229c574475380e88306785c093a52691ff8384768","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-01-31T02:40:54Z","title_canon_sha256":"89a157219827587d842e14ec5f5c8ddc55bcfce463e82378d74eed19e7e3d79a"},"schema_version":"1.0","source":{"id":"1201.6421","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6421","created_at":"2026-05-18T04:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6421v1","created_at":"2026-05-18T04:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6421","created_at":"2026-05-18T04:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"JRNQ2FZHFKBE","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JRNQ2FZHFKBE5BFY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JRNQ2FZH","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:0728b8bfffe3939c6f9ef0cd7e56b96df0d801296e1f2e00a57f9e47b220e933","target":"graph","created_at":"2026-05-18T04:03:31Z","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":"Given a graph G and integers b and w. The black-and-white coloring problem asks if there exist disjoint sets of vertices B and W with |B|=b and |W|=w such that no vertex in B is adjacent to any vertex in W. In this paper we show that the problem is polynomial when restricted to permutation graphs.","authors_text":"Ton Kloks","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-01-31T02:40:54Z","title":"The black-and-white coloring problem on permutation graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6421","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:c05f4425d1889bf2a246249c1a9d5845e26cef35152b9fbc007ac1853b4ab42c","target":"record","created_at":"2026-05-18T04:03:31Z","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":"1bc8b1b8e1431cd40b855dc229c574475380e88306785c093a52691ff8384768","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-01-31T02:40:54Z","title_canon_sha256":"89a157219827587d842e14ec5f5c8ddc55bcfce463e82378d74eed19e7e3d79a"},"schema_version":"1.0","source":{"id":"1201.6421","kind":"arxiv","version":1}},"canonical_sha256":"4c5b0d17272a824e84b8ef648fbdf1dc5c499c01c934cb19aeb9c5070db7f7c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c5b0d17272a824e84b8ef648fbdf1dc5c499c01c934cb19aeb9c5070db7f7c6","first_computed_at":"2026-05-18T04:03:31.557771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:31.557771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AeIvfSSdXGGGk/cAag0EyGCU+7fXyENQVLCFnQJ3ondovEp4hsf81chLZ5Cf1Qtt68ZPwnSBAH9GB7jdCZJxBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:31.558579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6421","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c05f4425d1889bf2a246249c1a9d5845e26cef35152b9fbc007ac1853b4ab42c","sha256:0728b8bfffe3939c6f9ef0cd7e56b96df0d801296e1f2e00a57f9e47b220e933"],"state_sha256":"5e33a7aa7f3b08ebbb9bab555f3d56a52b107ed6703f045638b5d7667e0e8089"}