{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5PCVB5KA6XVJ4TDCWL4YEBTZCM","short_pith_number":"pith:5PCVB5KA","canonical_record":{"source":{"id":"1507.00748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-02T20:22:22Z","cross_cats_sorted":[],"title_canon_sha256":"9902491c8d7cfc2839e651fc93516ffb4f2d019b6d54a8fb6a13f1e78aef267e","abstract_canon_sha256":"de5e30bcfcbb41450c62a14dcacd5aad9c44feaa56789de81e749596f32a2514"},"schema_version":"1.0"},"canonical_sha256":"ebc550f540f5ea9e4c62b2f9820679133a463d885b4542b1976dfddf5e2b27bc","source":{"kind":"arxiv","id":"1507.00748","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00748","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00748v1","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00748","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"pith_short_12","alias_value":"5PCVB5KA6XVJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5PCVB5KA6XVJ4TDC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5PCVB5KA","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5PCVB5KA6XVJ4TDCWL4YEBTZCM","target":"record","payload":{"canonical_record":{"source":{"id":"1507.00748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-02T20:22:22Z","cross_cats_sorted":[],"title_canon_sha256":"9902491c8d7cfc2839e651fc93516ffb4f2d019b6d54a8fb6a13f1e78aef267e","abstract_canon_sha256":"de5e30bcfcbb41450c62a14dcacd5aad9c44feaa56789de81e749596f32a2514"},"schema_version":"1.0"},"canonical_sha256":"ebc550f540f5ea9e4c62b2f9820679133a463d885b4542b1976dfddf5e2b27bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:22.808090Z","signature_b64":"HDdt7YdcghJUkGZlYZgeFMOrdyN2aD7iLx+1BnfBEDjtCLLKADMz23TXBCZdaAx2BToSlMYV4/V7XltSHFB5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebc550f540f5ea9e4c62b2f9820679133a463d885b4542b1976dfddf5e2b27bc","last_reissued_at":"2026-05-18T01:37:22.807414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:22.807414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.00748","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":"2026-05-18T01:37:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YP8esH+wU6pbU/pWyRQ5ZJjh5nla/pkBkzTEey5sfAf35a02PtnJa9jaIFO48nNNwiLXpfOvbGC1DtdvcCsAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:46:26.712863Z"},"content_sha256":"7d0f760fb7e09a3dd06bdfe9d18abbc66bfcced64e85fc6fd3e9eee2968078e5","schema_version":"1.0","event_id":"sha256:7d0f760fb7e09a3dd06bdfe9d18abbc66bfcced64e85fc6fd3e9eee2968078e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5PCVB5KA6XVJ4TDCWL4YEBTZCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Deadline-Scheduling with Precedence Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David Malec, Hamid Mahini, Hossein Efsandiari, Jochen Koenemann, Laura Sanita, MohammadTaghi Hajiaghyi","submitted_at":"2015-07-02T20:22:22Z","abstract_excerpt":"We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00748","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":"2026-05-18T01:37:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x48V7oNbQtuI/3H2xb8JZE98RbPm+amr7MABBKZ17OrbL7JDO/WXAb4IzQPr49BnrL/9v7j5Y60YkRByOt9IDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:46:26.713490Z"},"content_sha256":"0f6a29e1224d2ce8735829248a8e4c98c0ad54132735ffc3bf3cab3741b48e4d","schema_version":"1.0","event_id":"sha256:0f6a29e1224d2ce8735829248a8e4c98c0ad54132735ffc3bf3cab3741b48e4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PCVB5KA6XVJ4TDCWL4YEBTZCM/bundle.json","state_url":"https://pith.science/pith/5PCVB5KA6XVJ4TDCWL4YEBTZCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PCVB5KA6XVJ4TDCWL4YEBTZCM/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":"2026-05-30T22:46:26Z","links":{"resolver":"https://pith.science/pith/5PCVB5KA6XVJ4TDCWL4YEBTZCM","bundle":"https://pith.science/pith/5PCVB5KA6XVJ4TDCWL4YEBTZCM/bundle.json","state":"https://pith.science/pith/5PCVB5KA6XVJ4TDCWL4YEBTZCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PCVB5KA6XVJ4TDCWL4YEBTZCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5PCVB5KA6XVJ4TDCWL4YEBTZCM","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":"de5e30bcfcbb41450c62a14dcacd5aad9c44feaa56789de81e749596f32a2514","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-02T20:22:22Z","title_canon_sha256":"9902491c8d7cfc2839e651fc93516ffb4f2d019b6d54a8fb6a13f1e78aef267e"},"schema_version":"1.0","source":{"id":"1507.00748","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00748","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00748v1","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00748","created_at":"2026-05-18T01:37:22Z"},{"alias_kind":"pith_short_12","alias_value":"5PCVB5KA6XVJ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5PCVB5KA6XVJ4TDC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5PCVB5KA","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:0f6a29e1224d2ce8735829248a8e4c98c0ad54132735ffc3bf3cab3741b48e4d","target":"graph","created_at":"2026-05-18T01:37:22Z","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 the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result ","authors_text":"David Malec, Hamid Mahini, Hossein Efsandiari, Jochen Koenemann, Laura Sanita, MohammadTaghi Hajiaghyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-02T20:22:22Z","title":"Approximate Deadline-Scheduling with Precedence Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00748","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":"sha256:7d0f760fb7e09a3dd06bdfe9d18abbc66bfcced64e85fc6fd3e9eee2968078e5","target":"record","created_at":"2026-05-18T01:37:22Z","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":"de5e30bcfcbb41450c62a14dcacd5aad9c44feaa56789de81e749596f32a2514","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-02T20:22:22Z","title_canon_sha256":"9902491c8d7cfc2839e651fc93516ffb4f2d019b6d54a8fb6a13f1e78aef267e"},"schema_version":"1.0","source":{"id":"1507.00748","kind":"arxiv","version":1}},"canonical_sha256":"ebc550f540f5ea9e4c62b2f9820679133a463d885b4542b1976dfddf5e2b27bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebc550f540f5ea9e4c62b2f9820679133a463d885b4542b1976dfddf5e2b27bc","first_computed_at":"2026-05-18T01:37:22.807414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:22.807414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HDdt7YdcghJUkGZlYZgeFMOrdyN2aD7iLx+1BnfBEDjtCLLKADMz23TXBCZdaAx2BToSlMYV4/V7XltSHFB5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:22.808090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00748","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d0f760fb7e09a3dd06bdfe9d18abbc66bfcced64e85fc6fd3e9eee2968078e5","sha256:0f6a29e1224d2ce8735829248a8e4c98c0ad54132735ffc3bf3cab3741b48e4d"],"state_sha256":"7d0b6b7e217606fa69a6d7e3f54db73c3397177ddf43e73a341ac4aecad7c723"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8yPguaL+Knzrl7xiDUkKXkGUhulWxqyNKTkiQ5JzyE0z6L3AKsv4+jN3lNpoo+N3Ppw8W+oqranHjphauQRKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:46:26.716891Z","bundle_sha256":"46d1b4295459c42c3050ec76cdeb67f513f0b09ffac37ef57b6e73745babda1e"}}