{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:TKOGJO7DGARMERRZB6TPLJOSXW","short_pith_number":"pith:TKOGJO7D","canonical_record":{"source":{"id":"2502.13631","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-02-19T11:09:35Z","cross_cats_sorted":[],"title_canon_sha256":"6233b4694bb95d1319a06a5770397178d9b247ef0d603a307425c674f287f458","abstract_canon_sha256":"9197b67236bd9db2fad08487f5839d5a8426c5bf8e6e9dc9a663cedc0e18ea80"},"schema_version":"1.0"},"canonical_sha256":"9a9c64bbe33022c246390fa6f5a5d2bda50f3cd8b275bb5fb7b6844917d3334c","source":{"kind":"arxiv","id":"2502.13631","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.13631","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"2502.13631v1","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13631","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"TKOGJO7DGARM","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"pith_short_16","alias_value":"TKOGJO7DGARMERRZ","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"pith_short_8","alias_value":"TKOGJO7D","created_at":"2026-07-05T10:16:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:TKOGJO7DGARMERRZB6TPLJOSXW","target":"record","payload":{"canonical_record":{"source":{"id":"2502.13631","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-02-19T11:09:35Z","cross_cats_sorted":[],"title_canon_sha256":"6233b4694bb95d1319a06a5770397178d9b247ef0d603a307425c674f287f458","abstract_canon_sha256":"9197b67236bd9db2fad08487f5839d5a8426c5bf8e6e9dc9a663cedc0e18ea80"},"schema_version":"1.0"},"canonical_sha256":"9a9c64bbe33022c246390fa6f5a5d2bda50f3cd8b275bb5fb7b6844917d3334c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:16:50.461223Z","signature_b64":"fo0SH5bKawjMVG0dG/Y875b9wAXFi3V3r82zVKVP1i2cG/ZpBPZd/KMCPb0seqcJJozTkfNfWWqoaOKDKtuVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a9c64bbe33022c246390fa6f5a5d2bda50f3cd8b275bb5fb7b6844917d3334c","last_reissued_at":"2026-07-05T10:16:50.460610Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:16:50.460610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.13631","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":"2026-07-05T10:16:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aNjEWgyJEgljWjSrnhwJIB3LSxBmqIAK5JJ/AM+0blDmmuowLKUD6fQ20s2LnQjPUlURJTJTQA+g9CrLyVq/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T07:55:32.802362Z"},"content_sha256":"67e7f04f9499845f172bef53bb84db9e0eb07b1262a2578d347c6659db8caddb","schema_version":"1.0","event_id":"sha256:67e7f04f9499845f172bef53bb84db9e0eb07b1262a2578d347c6659db8caddb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:TKOGJO7DGARMERRZB6TPLJOSXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster Minimization of Total Weighted Completion Time on Parallel Machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Danny Hermelin, Dvir Shabtay, Tomohiro Koana","submitted_at":"2025-02-19T11:09:35Z","abstract_excerpt":"We study the classical problem of minimizing the total weighted completion time on a fixed set of $m$ identical machines working in parallel, the $Pm||\\sum w_jC_j$ problem in the standard three field notation for scheduling problems. This problem is well known to be NP-hard, but only in the ordinary sense, and appears as one of the fundamental problems in any scheduling textbook. In particular, the problem served as a proof of concept for applying pseudo-polynomial time algorithms and approximation schemes to scheduling problems. The fastest known pseudo-polynomial time algorithm for $Pm||\\sum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13631","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.13631/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:16:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9+X5dijC7s/PwyaLpvLno2H4O1/CT+VmwEyqPN9gRu/5R3PYwvGZzMOm3Lm8RHHNThGUZF+qqK7xA3/sxxyfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T07:55:32.802912Z"},"content_sha256":"3efcaa9f19929b2247dd1d9b4e276d705b9c3b157cbbc7c6bb25be18c20f9efa","schema_version":"1.0","event_id":"sha256:3efcaa9f19929b2247dd1d9b4e276d705b9c3b157cbbc7c6bb25be18c20f9efa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKOGJO7DGARMERRZB6TPLJOSXW/bundle.json","state_url":"https://pith.science/pith/TKOGJO7DGARMERRZB6TPLJOSXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKOGJO7DGARMERRZB6TPLJOSXW/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":"2026-08-19T07:55:32Z","links":{"resolver":"https://pith.science/pith/TKOGJO7DGARMERRZB6TPLJOSXW","bundle":"https://pith.science/pith/TKOGJO7DGARMERRZB6TPLJOSXW/bundle.json","state":"https://pith.science/pith/TKOGJO7DGARMERRZB6TPLJOSXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKOGJO7DGARMERRZB6TPLJOSXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TKOGJO7DGARMERRZB6TPLJOSXW","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":"9197b67236bd9db2fad08487f5839d5a8426c5bf8e6e9dc9a663cedc0e18ea80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-02-19T11:09:35Z","title_canon_sha256":"6233b4694bb95d1319a06a5770397178d9b247ef0d603a307425c674f287f458"},"schema_version":"1.0","source":{"id":"2502.13631","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.13631","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"2502.13631v1","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13631","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"TKOGJO7DGARM","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"pith_short_16","alias_value":"TKOGJO7DGARMERRZ","created_at":"2026-07-05T10:16:50Z"},{"alias_kind":"pith_short_8","alias_value":"TKOGJO7D","created_at":"2026-07-05T10:16:50Z"}],"graph_snapshots":[{"event_id":"sha256:3efcaa9f19929b2247dd1d9b4e276d705b9c3b157cbbc7c6bb25be18c20f9efa","target":"graph","created_at":"2026-07-05T10:16:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.13631/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the classical problem of minimizing the total weighted completion time on a fixed set of $m$ identical machines working in parallel, the $Pm||\\sum w_jC_j$ problem in the standard three field notation for scheduling problems. This problem is well known to be NP-hard, but only in the ordinary sense, and appears as one of the fundamental problems in any scheduling textbook. In particular, the problem served as a proof of concept for applying pseudo-polynomial time algorithms and approximation schemes to scheduling problems. The fastest known pseudo-polynomial time algorithm for $Pm||\\sum","authors_text":"Danny Hermelin, Dvir Shabtay, Tomohiro Koana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-02-19T11:09:35Z","title":"Faster Minimization of Total Weighted Completion Time on Parallel Machines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13631","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":"sha256:67e7f04f9499845f172bef53bb84db9e0eb07b1262a2578d347c6659db8caddb","target":"record","created_at":"2026-07-05T10:16:50Z","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":"9197b67236bd9db2fad08487f5839d5a8426c5bf8e6e9dc9a663cedc0e18ea80","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2025-02-19T11:09:35Z","title_canon_sha256":"6233b4694bb95d1319a06a5770397178d9b247ef0d603a307425c674f287f458"},"schema_version":"1.0","source":{"id":"2502.13631","kind":"arxiv","version":1}},"canonical_sha256":"9a9c64bbe33022c246390fa6f5a5d2bda50f3cd8b275bb5fb7b6844917d3334c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a9c64bbe33022c246390fa6f5a5d2bda50f3cd8b275bb5fb7b6844917d3334c","first_computed_at":"2026-07-05T10:16:50.460610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:16:50.460610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fo0SH5bKawjMVG0dG/Y875b9wAXFi3V3r82zVKVP1i2cG/ZpBPZd/KMCPb0seqcJJozTkfNfWWqoaOKDKtuVAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:16:50.461223Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.13631","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67e7f04f9499845f172bef53bb84db9e0eb07b1262a2578d347c6659db8caddb","sha256:3efcaa9f19929b2247dd1d9b4e276d705b9c3b157cbbc7c6bb25be18c20f9efa"],"state_sha256":"746719230eb852a741a640e04f6af964492affbec9d9a5d3243053bf8bb68772"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"29t8ZYLJX7+h+DpbskNlCqntXxfA0Jgw+TaFW6SI4n6xzTIrk0p8xfr6j62lV8ne/PyosiOrbKk6aX1BZMoXBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T07:55:32.807487Z","bundle_sha256":"8c5098c1b9dee9f191528808cacadd78695bf96b1e9865bd26385522f26691e0"}}