{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DRB4YI7OVY4GUOLLBPBYMFSH3F","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":"565340a919f539adc3d65fdad4296637c597998dc1cd929eac3ad51ff1c05e50","cross_cats_sorted":["cs.GT","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-03-18T14:52:26Z","title_canon_sha256":"3fd18ac834acdb1ca5d4199407f129128f2a8381c99208d3406fb3b7352fdc31"},"schema_version":"1.0","source":{"id":"1804.01567","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01567","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01567v1","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01567","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"pith_short_12","alias_value":"DRB4YI7OVY4G","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DRB4YI7OVY4GUOLL","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DRB4YI7O","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:3f24714845904027ff722a0597826f5502df7be19f48198abaaad292779e6d89","target":"graph","created_at":"2026-05-18T00:19:10Z","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":"An on-line chain partitioning algorithm receives the points of the poset from some externally determined list. Being presented with a new point the algorithm learns the comparability status of this new point to all previously presented ones. As each point is received, the algorithm assigns this new point to a chain in an irrevocable manner and this assignment is made without knowledge of future points. Kierstead presented an algorithm using $(5^w-1)/4$ chains to cover each poset of width $w$. Felsner proved that width $2$ posets can be partitioned on-line into $5$ chains. We present an algorit","authors_text":"Bart{\\l}omiej Bosek","cross_cats":["cs.GT","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-03-18T14:52:26Z","title":"On-line Chain Partitioning Approach to Scheduling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01567","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":"sha256:4c28d5e2e1fed127c36db86f97b0c3cea229288d59602a7bb1bfdbff0e8687e8","target":"record","created_at":"2026-05-18T00:19:10Z","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":"565340a919f539adc3d65fdad4296637c597998dc1cd929eac3ad51ff1c05e50","cross_cats_sorted":["cs.GT","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-03-18T14:52:26Z","title_canon_sha256":"3fd18ac834acdb1ca5d4199407f129128f2a8381c99208d3406fb3b7352fdc31"},"schema_version":"1.0","source":{"id":"1804.01567","kind":"arxiv","version":1}},"canonical_sha256":"1c43cc23eeae386a396b0bc3861647d97b5761e8be20a1cc6c049cdbcec4b9a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c43cc23eeae386a396b0bc3861647d97b5761e8be20a1cc6c049cdbcec4b9a3","first_computed_at":"2026-05-18T00:19:10.876879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:10.876879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZARdhwk+jTN73+d5KBtW7Fa/PsExiJLt6+s7NtaypPILzc3tn9c4nwqsYv97z4IIgedGZ3Yf25UCntlWBpCeBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:10.877590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01567","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c28d5e2e1fed127c36db86f97b0c3cea229288d59602a7bb1bfdbff0e8687e8","sha256:3f24714845904027ff722a0597826f5502df7be19f48198abaaad292779e6d89"],"state_sha256":"cd0b869245145d8425e30e1f390850464aee8cfa70ab6fca2dc5e58e21830a76"}