{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5ECSZ7SV67JBCX4OEP3QTHBU76","short_pith_number":"pith:5ECSZ7SV","canonical_record":{"source":{"id":"1602.05837","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-18T15:24:22Z","cross_cats_sorted":["cs.CC","cs.CG"],"title_canon_sha256":"b12277d89368a3e716e9973cccdbbdedcf267f5b4992dffcd95122495b6f0fa9","abstract_canon_sha256":"fc405fe39f580e357a5b4126730f81976fba3b1a6b264b70bc42f9960510ac1c"},"schema_version":"1.0"},"canonical_sha256":"e9052cfe55f7d2115f8e23f7099c34ff8bd84a1eec537f64a68162dd86568509","source":{"kind":"arxiv","id":"1602.05837","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05837","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05837v2","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05837","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"pith_short_12","alias_value":"5ECSZ7SV67JB","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5ECSZ7SV67JBCX4O","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5ECSZ7SV","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5ECSZ7SV67JBCX4OEP3QTHBU76","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05837","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-18T15:24:22Z","cross_cats_sorted":["cs.CC","cs.CG"],"title_canon_sha256":"b12277d89368a3e716e9973cccdbbdedcf267f5b4992dffcd95122495b6f0fa9","abstract_canon_sha256":"fc405fe39f580e357a5b4126730f81976fba3b1a6b264b70bc42f9960510ac1c"},"schema_version":"1.0"},"canonical_sha256":"e9052cfe55f7d2115f8e23f7099c34ff8bd84a1eec537f64a68162dd86568509","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:40.249822Z","signature_b64":"xjSDk2AX8Qk3cC1mC5EmtxF/fetBO5x1PtEw8nES01/lR2NPjacPY9Dme3wt3iybJv4ZbOhoKZdYJvU1MYGbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9052cfe55f7d2115f8e23f7099c34ff8bd84a1eec537f64a68162dd86568509","last_reissued_at":"2026-05-18T01:19:40.249183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:40.249183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05837","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Dui3WlfmEnRfzbHJWxn3KH+rhL7MnnnilohuHEKmusfag9ozjXHtK3Z10LcyZFO8mv+rd75U3+0UnvdDsw8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:43:49.848827Z"},"content_sha256":"d5570e45a794213b29f762140d38db398feb476a7b23ecba140f2084fa8e20f2","schema_version":"1.0","event_id":"sha256:d5570e45a794213b29f762140d38db398feb476a7b23ecba140f2084fa8e20f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5ECSZ7SV67JBCX4OEP3QTHBU76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight Hardness Results for Maximum Weight Rectangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CG"],"primary_cat":"cs.DS","authors_text":"Arturs Backurs, Christos Tzamos, Nishanth Dikkala","submitted_at":"2016-02-18T15:24:22Z","abstract_excerpt":"Given $n$ weighted points (positive or negative) in $d$ dimensions, what is the axis-aligned box which maximizes the total weight of the points it contains?\n  The best known algorithm for this problem is based on a reduction to a related problem, the Weighted Depth problem [T. M. Chan, FOCS'13], and runs in time $O(n^d)$. It was conjectured [Barbay et al., CCCG'13] that this runtime is tight up to subpolynomial factors. We answer this conjecture affirmatively by providing a matching conditional lower bound. We also provide conditional lower bounds for the special case when points are arranged "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05837","kind":"arxiv","version":2},"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":"2026-05-18T01:19:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2uuHtt9mSGZy6RmiYexd/Ns9JEOWBB3K53KROrtQIKfyfl/PCGxm2JdihvzHCYpUFe+8RERTOqBffiv+KfHNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:43:49.849542Z"},"content_sha256":"16abea18c90dac738a9909e62006fd16c788ce9b72bf140aad32c119d20622c4","schema_version":"1.0","event_id":"sha256:16abea18c90dac738a9909e62006fd16c788ce9b72bf140aad32c119d20622c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ECSZ7SV67JBCX4OEP3QTHBU76/bundle.json","state_url":"https://pith.science/pith/5ECSZ7SV67JBCX4OEP3QTHBU76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ECSZ7SV67JBCX4OEP3QTHBU76/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":"2026-05-30T08:43:49Z","links":{"resolver":"https://pith.science/pith/5ECSZ7SV67JBCX4OEP3QTHBU76","bundle":"https://pith.science/pith/5ECSZ7SV67JBCX4OEP3QTHBU76/bundle.json","state":"https://pith.science/pith/5ECSZ7SV67JBCX4OEP3QTHBU76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ECSZ7SV67JBCX4OEP3QTHBU76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5ECSZ7SV67JBCX4OEP3QTHBU76","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":"fc405fe39f580e357a5b4126730f81976fba3b1a6b264b70bc42f9960510ac1c","cross_cats_sorted":["cs.CC","cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-18T15:24:22Z","title_canon_sha256":"b12277d89368a3e716e9973cccdbbdedcf267f5b4992dffcd95122495b6f0fa9"},"schema_version":"1.0","source":{"id":"1602.05837","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05837","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05837v2","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05837","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"pith_short_12","alias_value":"5ECSZ7SV67JB","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5ECSZ7SV67JBCX4O","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5ECSZ7SV","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:16abea18c90dac738a9909e62006fd16c788ce9b72bf140aad32c119d20622c4","target":"graph","created_at":"2026-05-18T01:19:40Z","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":"Given $n$ weighted points (positive or negative) in $d$ dimensions, what is the axis-aligned box which maximizes the total weight of the points it contains?\n  The best known algorithm for this problem is based on a reduction to a related problem, the Weighted Depth problem [T. M. Chan, FOCS'13], and runs in time $O(n^d)$. It was conjectured [Barbay et al., CCCG'13] that this runtime is tight up to subpolynomial factors. We answer this conjecture affirmatively by providing a matching conditional lower bound. We also provide conditional lower bounds for the special case when points are arranged ","authors_text":"Arturs Backurs, Christos Tzamos, Nishanth Dikkala","cross_cats":["cs.CC","cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-18T15:24:22Z","title":"Tight Hardness Results for Maximum Weight Rectangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05837","kind":"arxiv","version":2},"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:d5570e45a794213b29f762140d38db398feb476a7b23ecba140f2084fa8e20f2","target":"record","created_at":"2026-05-18T01:19:40Z","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":"fc405fe39f580e357a5b4126730f81976fba3b1a6b264b70bc42f9960510ac1c","cross_cats_sorted":["cs.CC","cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-18T15:24:22Z","title_canon_sha256":"b12277d89368a3e716e9973cccdbbdedcf267f5b4992dffcd95122495b6f0fa9"},"schema_version":"1.0","source":{"id":"1602.05837","kind":"arxiv","version":2}},"canonical_sha256":"e9052cfe55f7d2115f8e23f7099c34ff8bd84a1eec537f64a68162dd86568509","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9052cfe55f7d2115f8e23f7099c34ff8bd84a1eec537f64a68162dd86568509","first_computed_at":"2026-05-18T01:19:40.249183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:40.249183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xjSDk2AX8Qk3cC1mC5EmtxF/fetBO5x1PtEw8nES01/lR2NPjacPY9Dme3wt3iybJv4ZbOhoKZdYJvU1MYGbBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:40.249822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05837","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5570e45a794213b29f762140d38db398feb476a7b23ecba140f2084fa8e20f2","sha256:16abea18c90dac738a9909e62006fd16c788ce9b72bf140aad32c119d20622c4"],"state_sha256":"41c12f0e64bdb17d21c432989c08aa8d6103be4fb55b01808b850bc08bdf0448"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h2KbzOUeX6TYJuSBtyt+1HTYs0kmcci2qXPw3PU7HngkNgz6MSxX0CCzvYG1VJmAgh4l8y4c/FXbK3sNtGgEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:43:49.853577Z","bundle_sha256":"299bbe78986d7bdbb759d1ba0af483d25e7ce799b6a9291e96605f809359f970"}}