{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PL2JM6X2KTARESPIDNHL3ZM4CB","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":"cf308e6082f53c61e4a73c9e30499ecfcf643f9134108cc2d574177d46e926fd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-07-14T10:35:08Z","title_canon_sha256":"3d6b260682577084d4189322d17c331614fdc6f377f878fb314b3ba42946a529"},"schema_version":"1.0","source":{"id":"2407.10146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.10146","created_at":"2026-07-05T08:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"2407.10146v1","created_at":"2026-07-05T08:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.10146","created_at":"2026-07-05T08:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"PL2JM6X2KTAR","created_at":"2026-07-05T08:43:39Z"},{"alias_kind":"pith_short_16","alias_value":"PL2JM6X2KTARESPI","created_at":"2026-07-05T08:43:39Z"},{"alias_kind":"pith_short_8","alias_value":"PL2JM6X2","created_at":"2026-07-05T08:43:39Z"}],"graph_snapshots":[{"event_id":"sha256:e48efbbf1eb1a3f2c281bbd2d3dda419854bee3fc3cb219a07e22f0641c01544","target":"graph","created_at":"2026-07-05T08:43:39Z","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/2407.10146/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Ariel Kulik, Ilan Doron-Arad, Pasin Manurangsi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-07-14T10:35:08Z","title":"Fine Grained Lower Bounds for Multidimensional Knapsack"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.10146","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:d237be23c5cee3fec591c685a657959f4f14fe688adbf10cb7afb9e673a740e4","target":"record","created_at":"2026-07-05T08:43:39Z","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":"cf308e6082f53c61e4a73c9e30499ecfcf643f9134108cc2d574177d46e926fd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-07-14T10:35:08Z","title_canon_sha256":"3d6b260682577084d4189322d17c331614fdc6f377f878fb314b3ba42946a529"},"schema_version":"1.0","source":{"id":"2407.10146","kind":"arxiv","version":1}},"canonical_sha256":"7af4967afa54c11249e81b4ebde59c1057eb1b6da6a4f6bc0320cc3f5dfe0025","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7af4967afa54c11249e81b4ebde59c1057eb1b6da6a4f6bc0320cc3f5dfe0025","first_computed_at":"2026-07-05T08:43:39.758041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:43:39.758041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"usrMcSv2brIGEOMHfClwVgR8d/hk6XvgSSs5wKhp8856jqgRHFmBFvXsVg04a0vnMITFf85DDuy1eeOt6oUhDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:43:39.758499Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.10146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d237be23c5cee3fec591c685a657959f4f14fe688adbf10cb7afb9e673a740e4","sha256:e48efbbf1eb1a3f2c281bbd2d3dda419854bee3fc3cb219a07e22f0641c01544"],"state_sha256":"1195367189bdb14b9c25dcd2a6f7fd5d12d3111fa03bf37e365e2f8121e2ccdd"}