{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DGLPOK2QN6F24X3GMZCEOA5TIY","short_pith_number":"pith:DGLPOK2Q","canonical_record":{"source":{"id":"2608.12224","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-12T16:22:21Z","cross_cats_sorted":[],"title_canon_sha256":"0335a8a08b836d4d7d75a4e2ce74b5f9d8169fd8db57a271c343364a397d91a3","abstract_canon_sha256":"a37da1730e203f316bf86f3fae0b5506146c9631b62ee94246002a39d8265518"},"schema_version":"1.0"},"canonical_sha256":"1996f72b506f8bae5f6666444703b3463ecedc2bf5c8c6daf7ba1b31c12c39ad","source":{"kind":"arxiv","id":"2608.12224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.12224","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"2608.12224v1","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.12224","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"DGLPOK2QN6F2","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"pith_short_16","alias_value":"DGLPOK2QN6F24X3G","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"pith_short_8","alias_value":"DGLPOK2Q","created_at":"2026-08-13T01:30:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DGLPOK2QN6F24X3GMZCEOA5TIY","target":"record","payload":{"canonical_record":{"source":{"id":"2608.12224","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-12T16:22:21Z","cross_cats_sorted":[],"title_canon_sha256":"0335a8a08b836d4d7d75a4e2ce74b5f9d8169fd8db57a271c343364a397d91a3","abstract_canon_sha256":"a37da1730e203f316bf86f3fae0b5506146c9631b62ee94246002a39d8265518"},"schema_version":"1.0"},"canonical_sha256":"1996f72b506f8bae5f6666444703b3463ecedc2bf5c8c6daf7ba1b31c12c39ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-13T01:30:33.186978Z","signature_b64":"mGYTtFY+UX6HjI8c5MY8JFPxXh4G7Sn95B1sCywJxB/gZRQy4Tz1p/EWumYP8wDAfU06jBAU16Df+ZrXTxSwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1996f72b506f8bae5f6666444703b3463ecedc2bf5c8c6daf7ba1b31c12c39ad","last_reissued_at":"2026-08-13T01:30:33.184476Z","signature_status":"signed_v1","first_computed_at":"2026-08-13T01:30:33.184476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.12224","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":"2026-08-13T01:30:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2TEy5o72dNRRvha7EqAzCo6R06j+LXifGU92VCBPfyMduxMY91tAVoBPAc2PD0kaw4kAWNo4tq1e7GcXKVGtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T03:54:23.331740Z"},"content_sha256":"602a35f9ffa1c93c2180559d033b3c216f71f630b17f9a8b059d76d220b17fc2","schema_version":"1.0","event_id":"sha256:602a35f9ffa1c93c2180559d033b3c216f71f630b17f9a8b059d76d220b17fc2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DGLPOK2QN6F24X3GMZCEOA5TIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster Exponential Algorithms for Multi-Machine Scheduling Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ahmed Ghazy, Anita D\\\"urr, Anubhav Dhar, Jakob Greilhuber, Karol W\\k{e}grzycki","submitted_at":"2026-08-12T16:22:21Z","abstract_excerpt":"Minimizing the weighted completion times ($P \\mid \\mid \\Sigma w_j C_j$) and weighted number of tardy jobs ($P \\mid \\mid \\Sigma w_j U_j$) on multiple identical machines are two classical NP-hard scheduling problems. As shown by Lent\\'e et al. (2014), both problems can be solved in time ${O}^{\\star}(3^n)$. In this paper, we improve these bounds to ${O}(2.755^n)$ and ${O}^{\\star}(2^n)$, respectively. Our algorithm for $P \\mid \\mid \\Sigma w_j C_j$ exploits the meet-in-the-middle paradigm and an efficient data structure answering linear programming queries. Additionally, when the number of machines"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12224","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/2608.12224/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":"2026-08-13T01:30:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PknELq10IuaNOp+qcsmlO77hGpGS8qyxgTbxAU1UbFTdCB2TNG8SZoD7Ipj+KraEkd9nmzwDlGBueD+WFnP9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T03:54:23.332309Z"},"content_sha256":"d25aac0bd79fce6c6d12bf51c5ecd415fabe38e4cb493e533cc6c5b8364a3ad8","schema_version":"1.0","event_id":"sha256:d25aac0bd79fce6c6d12bf51c5ecd415fabe38e4cb493e533cc6c5b8364a3ad8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DGLPOK2QN6F24X3GMZCEOA5TIY/bundle.json","state_url":"https://pith.science/pith/DGLPOK2QN6F24X3GMZCEOA5TIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DGLPOK2QN6F24X3GMZCEOA5TIY/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":"2026-08-19T03:54:23Z","links":{"resolver":"https://pith.science/pith/DGLPOK2QN6F24X3GMZCEOA5TIY","bundle":"https://pith.science/pith/DGLPOK2QN6F24X3GMZCEOA5TIY/bundle.json","state":"https://pith.science/pith/DGLPOK2QN6F24X3GMZCEOA5TIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DGLPOK2QN6F24X3GMZCEOA5TIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DGLPOK2QN6F24X3GMZCEOA5TIY","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":"a37da1730e203f316bf86f3fae0b5506146c9631b62ee94246002a39d8265518","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-12T16:22:21Z","title_canon_sha256":"0335a8a08b836d4d7d75a4e2ce74b5f9d8169fd8db57a271c343364a397d91a3"},"schema_version":"1.0","source":{"id":"2608.12224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.12224","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"2608.12224v1","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.12224","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"DGLPOK2QN6F2","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"pith_short_16","alias_value":"DGLPOK2QN6F24X3G","created_at":"2026-08-13T01:30:33Z"},{"alias_kind":"pith_short_8","alias_value":"DGLPOK2Q","created_at":"2026-08-13T01:30:33Z"}],"graph_snapshots":[{"event_id":"sha256:d25aac0bd79fce6c6d12bf51c5ecd415fabe38e4cb493e533cc6c5b8364a3ad8","target":"graph","created_at":"2026-08-13T01:30:33Z","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/2608.12224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Minimizing the weighted completion times ($P \\mid \\mid \\Sigma w_j C_j$) and weighted number of tardy jobs ($P \\mid \\mid \\Sigma w_j U_j$) on multiple identical machines are two classical NP-hard scheduling problems. As shown by Lent\\'e et al. (2014), both problems can be solved in time ${O}^{\\star}(3^n)$. In this paper, we improve these bounds to ${O}(2.755^n)$ and ${O}^{\\star}(2^n)$, respectively. Our algorithm for $P \\mid \\mid \\Sigma w_j C_j$ exploits the meet-in-the-middle paradigm and an efficient data structure answering linear programming queries. Additionally, when the number of machines","authors_text":"Ahmed Ghazy, Anita D\\\"urr, Anubhav Dhar, Jakob Greilhuber, Karol W\\k{e}grzycki","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-12T16:22:21Z","title":"Faster Exponential Algorithms for Multi-Machine Scheduling Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12224","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":"sha256:602a35f9ffa1c93c2180559d033b3c216f71f630b17f9a8b059d76d220b17fc2","target":"record","created_at":"2026-08-13T01:30:33Z","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":"a37da1730e203f316bf86f3fae0b5506146c9631b62ee94246002a39d8265518","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-12T16:22:21Z","title_canon_sha256":"0335a8a08b836d4d7d75a4e2ce74b5f9d8169fd8db57a271c343364a397d91a3"},"schema_version":"1.0","source":{"id":"2608.12224","kind":"arxiv","version":1}},"canonical_sha256":"1996f72b506f8bae5f6666444703b3463ecedc2bf5c8c6daf7ba1b31c12c39ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1996f72b506f8bae5f6666444703b3463ecedc2bf5c8c6daf7ba1b31c12c39ad","first_computed_at":"2026-08-13T01:30:33.184476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-13T01:30:33.184476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mGYTtFY+UX6HjI8c5MY8JFPxXh4G7Sn95B1sCywJxB/gZRQy4Tz1p/EWumYP8wDAfU06jBAU16Df+ZrXTxSwBw==","signature_status":"signed_v1","signed_at":"2026-08-13T01:30:33.186978Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.12224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:602a35f9ffa1c93c2180559d033b3c216f71f630b17f9a8b059d76d220b17fc2","sha256:d25aac0bd79fce6c6d12bf51c5ecd415fabe38e4cb493e533cc6c5b8364a3ad8"],"state_sha256":"e3dbd22572e57309dbd5876cbf0470be1da7f9866c0f349681ae691dbbfdb51e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cqNGLlGmDgZwDV26FpRSEaYdMwDY3T3rm9ZNQNOyL3BU1pkekhPrDSlam7KUMlRk/LszRVM5ODBmMDa0U07uDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T03:54:23.336256Z","bundle_sha256":"d85203803a2bd5f73b8c47539ddf73317de284a3a518721c43a1e43f983c896f"}}