{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PL2JM6X2KTARESPIDNHL3ZM4CB","short_pith_number":"pith:PL2JM6X2","schema_version":"1.0","canonical_sha256":"7af4967afa54c11249e81b4ebde59c1057eb1b6da6a4f6bc0320cc3f5dfe0025","source":{"kind":"arxiv","id":"2407.10146","version":1},"attestation_state":"computed","paper":{"title":"Fine Grained Lower Bounds for Multidimensional Knapsack","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ariel Kulik, Ilan Doron-Arad, Pasin Manurangsi","submitted_at":"2024-07-14T10:35:08Z","abstract_excerpt":"We study the $d$-dimensional knapsack problem. We are given a set of items, each with a $d$-dimensional cost vector and a profit, along with a $d$-dimensional budget vector. The goal is to select a set of items that do not exceed the budget in all dimensions and maximize the total profit. A PTAS with running time $n^{\\Theta(d/\\varepsilon)}$ has long been known for this problem, where $\\varepsilon$ is the error parameter and $n$ is the encoding size. Despite decades of active research, the best running time of a PTAS has remained $O(n^{\\lceil d/\\varepsilon \\rceil - d})$. Unfortunately, existing"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2407.10146","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-07-14T10:35:08Z","cross_cats_sorted":[],"title_canon_sha256":"3d6b260682577084d4189322d17c331614fdc6f377f878fb314b3ba42946a529","abstract_canon_sha256":"cf308e6082f53c61e4a73c9e30499ecfcf643f9134108cc2d574177d46e926fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:43:39.758499Z","signature_b64":"usrMcSv2brIGEOMHfClwVgR8d/hk6XvgSSs5wKhp8856jqgRHFmBFvXsVg04a0vnMITFf85DDuy1eeOt6oUhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7af4967afa54c11249e81b4ebde59c1057eb1b6da6a4f6bc0320cc3f5dfe0025","last_reissued_at":"2026-07-05T08:43:39.758041Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:43:39.758041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fine Grained Lower Bounds for Multidimensional Knapsack","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ariel Kulik, Ilan Doron-Arad, Pasin Manurangsi","submitted_at":"2024-07-14T10:35:08Z","abstract_excerpt":"We study the $d$-dimensional knapsack problem. We are given a set of items, each with a $d$-dimensional cost vector and a profit, along with a $d$-dimensional budget vector. The goal is to select a set of items that do not exceed the budget in all dimensions and maximize the total profit. A PTAS with running time $n^{\\Theta(d/\\varepsilon)}$ has long been known for this problem, where $\\varepsilon$ is the error parameter and $n$ is the encoding size. Despite decades of active research, the best running time of a PTAS has remained $O(n^{\\lceil d/\\varepsilon \\rceil - d})$. Unfortunately, existing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.10146","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/2407.10146/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2407.10146","created_at":"2026-07-05T08:43:39.758108+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.10146v1","created_at":"2026-07-05T08:43:39.758108+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.10146","created_at":"2026-07-05T08:43:39.758108+00:00"},{"alias_kind":"pith_short_12","alias_value":"PL2JM6X2KTAR","created_at":"2026-07-05T08:43:39.758108+00:00"},{"alias_kind":"pith_short_16","alias_value":"PL2JM6X2KTARESPI","created_at":"2026-07-05T08:43:39.758108+00:00"},{"alias_kind":"pith_short_8","alias_value":"PL2JM6X2","created_at":"2026-07-05T08:43:39.758108+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.13271","citing_title":"One-dimensional vs. Multi-dimensional Pricing in Blockchain Protocols","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PL2JM6X2KTARESPIDNHL3ZM4CB","json":"https://pith.science/pith/PL2JM6X2KTARESPIDNHL3ZM4CB.json","graph_json":"https://pith.science/api/pith-number/PL2JM6X2KTARESPIDNHL3ZM4CB/graph.json","events_json":"https://pith.science/api/pith-number/PL2JM6X2KTARESPIDNHL3ZM4CB/events.json","paper":"https://pith.science/paper/PL2JM6X2"},"agent_actions":{"view_html":"https://pith.science/pith/PL2JM6X2KTARESPIDNHL3ZM4CB","download_json":"https://pith.science/pith/PL2JM6X2KTARESPIDNHL3ZM4CB.json","view_paper":"https://pith.science/paper/PL2JM6X2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.10146&json=true","fetch_graph":"https://pith.science/api/pith-number/PL2JM6X2KTARESPIDNHL3ZM4CB/graph.json","fetch_events":"https://pith.science/api/pith-number/PL2JM6X2KTARESPIDNHL3ZM4CB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PL2JM6X2KTARESPIDNHL3ZM4CB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PL2JM6X2KTARESPIDNHL3ZM4CB/action/storage_attestation","attest_author":"https://pith.science/pith/PL2JM6X2KTARESPIDNHL3ZM4CB/action/author_attestation","sign_citation":"https://pith.science/pith/PL2JM6X2KTARESPIDNHL3ZM4CB/action/citation_signature","submit_replication":"https://pith.science/pith/PL2JM6X2KTARESPIDNHL3ZM4CB/action/replication_record"}},"created_at":"2026-07-05T08:43:39.758108+00:00","updated_at":"2026-07-05T08:43:39.758108+00:00"}