{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:W5JJHQI4NPSTFD2Q3JYSFQVDBT","short_pith_number":"pith:W5JJHQI4","canonical_record":{"source":{"id":"1811.12657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-30T07:57:40Z","cross_cats_sorted":[],"title_canon_sha256":"3bd0dbf46088ab768a8833ab66ced35a7956fb6097482f1141abd8acc87b46df","abstract_canon_sha256":"90413da3f51f33fb81050cab947c7c79f74ba54c56ee9e357619551b34938e8a"},"schema_version":"1.0"},"canonical_sha256":"b75293c11c6be5328f50da7122c2a30cf111e5d28d7c9b10ba9a1623bce72f75","source":{"kind":"arxiv","id":"1811.12657","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12657","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12657v1","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12657","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"W5JJHQI4NPST","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W5JJHQI4NPSTFD2Q","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W5JJHQI4","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:W5JJHQI4NPSTFD2Q3JYSFQVDBT","target":"record","payload":{"canonical_record":{"source":{"id":"1811.12657","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-30T07:57:40Z","cross_cats_sorted":[],"title_canon_sha256":"3bd0dbf46088ab768a8833ab66ced35a7956fb6097482f1141abd8acc87b46df","abstract_canon_sha256":"90413da3f51f33fb81050cab947c7c79f74ba54c56ee9e357619551b34938e8a"},"schema_version":"1.0"},"canonical_sha256":"b75293c11c6be5328f50da7122c2a30cf111e5d28d7c9b10ba9a1623bce72f75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:28.923209Z","signature_b64":"RLxbsxKRD6wRYGbaM16mLpKnzf0wck4MeA//wzQC4ID0P7oZAD8hFINMh6iA4qxrhudC35w5iR2gOJsHBUbFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b75293c11c6be5328f50da7122c2a30cf111e5d28d7c9b10ba9a1623bce72f75","last_reissued_at":"2026-05-17T23:59:28.922707Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:28.922707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.12657","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uwKUB71gtCivV4HXsk+yAfEwWX3QpZTLHoN1sln6oe+nPmGGN31ExVVO9GADFUZXcNhEJltsUnTgIGYFx5xGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:24:48.667501Z"},"content_sha256":"54d257e0a32cca87f6c52738e341365c1a1dc9d0ba8689844ac6009e1aeb9ded","schema_version":"1.0","event_id":"sha256:54d257e0a32cca87f6c52738e341365c1a1dc9d0ba8689844ac6009e1aeb9ded"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:W5JJHQI4NPSTFD2Q3JYSFQVDBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Algorithms for Scheduling under Time-of-Use Tariffs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jos\\'e Verschae, Leen Stougie, Lin Chen, Nicole Megow, Roman Rischke","submitted_at":"2018-11-30T07:57:40Z","abstract_excerpt":"We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling objectives of minimizing the makespan and the sum of (weighted) completion times. It is not difficult to derive a polynomial-time algorithm for preemptive scheduling to minimize the makespan on unrelated machines. The problem of minimizing the total (weighted) completion time is considerably harder, even on a single machine. We present a polynomial-time algori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12657","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ufizIVV/DlYeX8kg51taBCF3ISBXkkz8cnEHqTNjLSvvXwbvaSNeXhLjdLw325KhGAPWU+tY98qGWemiW0d3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:24:48.668200Z"},"content_sha256":"7fa6ed3dfa805eba48f42b7233dafb511b4b52465786bf6f213032b4691b1b19","schema_version":"1.0","event_id":"sha256:7fa6ed3dfa805eba48f42b7233dafb511b4b52465786bf6f213032b4691b1b19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W5JJHQI4NPSTFD2Q3JYSFQVDBT/bundle.json","state_url":"https://pith.science/pith/W5JJHQI4NPSTFD2Q3JYSFQVDBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W5JJHQI4NPSTFD2Q3JYSFQVDBT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T17:24:48Z","links":{"resolver":"https://pith.science/pith/W5JJHQI4NPSTFD2Q3JYSFQVDBT","bundle":"https://pith.science/pith/W5JJHQI4NPSTFD2Q3JYSFQVDBT/bundle.json","state":"https://pith.science/pith/W5JJHQI4NPSTFD2Q3JYSFQVDBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W5JJHQI4NPSTFD2Q3JYSFQVDBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:W5JJHQI4NPSTFD2Q3JYSFQVDBT","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":"90413da3f51f33fb81050cab947c7c79f74ba54c56ee9e357619551b34938e8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-30T07:57:40Z","title_canon_sha256":"3bd0dbf46088ab768a8833ab66ced35a7956fb6097482f1141abd8acc87b46df"},"schema_version":"1.0","source":{"id":"1811.12657","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12657","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12657v1","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12657","created_at":"2026-05-17T23:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"W5JJHQI4NPST","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"W5JJHQI4NPSTFD2Q","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"W5JJHQI4","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:7fa6ed3dfa805eba48f42b7233dafb511b4b52465786bf6f213032b4691b1b19","target":"graph","created_at":"2026-05-17T23:59:28Z","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":"We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling objectives of minimizing the makespan and the sum of (weighted) completion times. It is not difficult to derive a polynomial-time algorithm for preemptive scheduling to minimize the makespan on unrelated machines. The problem of minimizing the total (weighted) completion time is considerably harder, even on a single machine. We present a polynomial-time algori","authors_text":"Jos\\'e Verschae, Leen Stougie, Lin Chen, Nicole Megow, Roman Rischke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-30T07:57:40Z","title":"Optimal Algorithms for Scheduling under Time-of-Use Tariffs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12657","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":"sha256:54d257e0a32cca87f6c52738e341365c1a1dc9d0ba8689844ac6009e1aeb9ded","target":"record","created_at":"2026-05-17T23:59:28Z","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":"90413da3f51f33fb81050cab947c7c79f74ba54c56ee9e357619551b34938e8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-30T07:57:40Z","title_canon_sha256":"3bd0dbf46088ab768a8833ab66ced35a7956fb6097482f1141abd8acc87b46df"},"schema_version":"1.0","source":{"id":"1811.12657","kind":"arxiv","version":1}},"canonical_sha256":"b75293c11c6be5328f50da7122c2a30cf111e5d28d7c9b10ba9a1623bce72f75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b75293c11c6be5328f50da7122c2a30cf111e5d28d7c9b10ba9a1623bce72f75","first_computed_at":"2026-05-17T23:59:28.922707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:28.922707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RLxbsxKRD6wRYGbaM16mLpKnzf0wck4MeA//wzQC4ID0P7oZAD8hFINMh6iA4qxrhudC35w5iR2gOJsHBUbFBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:28.923209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12657","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54d257e0a32cca87f6c52738e341365c1a1dc9d0ba8689844ac6009e1aeb9ded","sha256:7fa6ed3dfa805eba48f42b7233dafb511b4b52465786bf6f213032b4691b1b19"],"state_sha256":"6530782022c3ec7d46c5317acd32c264ce010d84b4cf5b31354033f1613a8d89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tGmYV5nBv2IRFJdnGksyMchK5rSRcSJu1lVRH+vl/qaZZicjt456V5Y7gmKa7IGZSOZ3PzWG9S0+dtczp2a2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:24:48.671932Z","bundle_sha256":"fb628df7fbe22d5f6a8fb1dff0cb936bd7293abe95a51b4f9dfb53f6d9a08bb4"}}