{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RII6RS44O6COXAZHI27NF5VKLC","short_pith_number":"pith:RII6RS44","canonical_record":{"source":{"id":"1011.2249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-10T01:31:44Z","cross_cats_sorted":[],"title_canon_sha256":"7ff652146e3d29f52a1c82b98b3ec697dc8c3ba1acee2b356549311ecb577aed","abstract_canon_sha256":"612ec9e1ad124b1c2c812a3af4e17ec226e1c3297b2637d81f269d0ef5492742"},"schema_version":"1.0"},"canonical_sha256":"8a11e8cb9c7784eb832746bed2f6aa588fbc2d38e2bc1264e15c9fcccd2895db","source":{"kind":"arxiv","id":"1011.2249","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2249","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2249v1","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2249","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"pith_short_12","alias_value":"RII6RS44O6CO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RII6RS44O6COXAZH","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RII6RS44","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RII6RS44O6COXAZHI27NF5VKLC","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-10T01:31:44Z","cross_cats_sorted":[],"title_canon_sha256":"7ff652146e3d29f52a1c82b98b3ec697dc8c3ba1acee2b356549311ecb577aed","abstract_canon_sha256":"612ec9e1ad124b1c2c812a3af4e17ec226e1c3297b2637d81f269d0ef5492742"},"schema_version":"1.0"},"canonical_sha256":"8a11e8cb9c7784eb832746bed2f6aa588fbc2d38e2bc1264e15c9fcccd2895db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:30.754778Z","signature_b64":"NgR/c0hqLPt0usxyVImjRkonqiOSCreXIDS+NEn6BzbgHIO4/a9EejNnbz0qWXLmHiyns4Vq1Qoq1zZ49ue+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a11e8cb9c7784eb832746bed2f6aa588fbc2d38e2bc1264e15c9fcccd2895db","last_reissued_at":"2026-05-18T04:36:30.754244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:30.754244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2249","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":"2026-05-18T04:36:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TscyBgCeMS7Fr0eU7pg/P0At5KXajI5WumXk5mZw+ZAoawTkWVbhdZFdY0MfSxYh0AuKSpbEK2aWKNtlKZV7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:45:39.204846Z"},"content_sha256":"7ac53b836351ce9e80b053cc74cd7d545da133d45ac2f31d95b7754eacb776ed","schema_version":"1.0","event_id":"sha256:7ac53b836351ce9e80b053cc74cd7d545da133d45ac2f31d95b7754eacb776ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RII6RS44O6COXAZHI27NF5VKLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pareto Optimal Solutions for Smoothed Analysts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ankur Moitra, Ryan O'Donnell","submitted_at":"2010-11-10T01:31:44Z","abstract_excerpt":"Consider an optimization problem with $n$ binary variables and $d+1$ linear objective functions. Each valid solution $x \\in \\{0,1\\}^n$ gives rise to an objective vector in $\\R^{d+1}$, and one often wants to enumerate the Pareto optima among them. In the worst case there may be exponentially many Pareto optima; however, it was recently shown that in (a generalization of) the smoothed analysis framework, the expected number is polynomial in $n$. Unfortunately, the bound obtained had a rather bad dependence on $d$; roughly $n^{d^d}$. In this paper we show a significantly improved bound of $n^{2d}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2249","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":"2026-05-18T04:36:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3jCcG2JZHHjZsPNqF2SEFLZyYRpcURzH0y5ozJDDGHWBVibAzzv+vYky2akUM7zPs5RZzOsZs1jCIDuYscd+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:45:39.205192Z"},"content_sha256":"fc68d8a773d6e40045bac233eb261ef04c0e55e088a0e58b36256af54916c9cb","schema_version":"1.0","event_id":"sha256:fc68d8a773d6e40045bac233eb261ef04c0e55e088a0e58b36256af54916c9cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RII6RS44O6COXAZHI27NF5VKLC/bundle.json","state_url":"https://pith.science/pith/RII6RS44O6COXAZHI27NF5VKLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RII6RS44O6COXAZHI27NF5VKLC/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":"2026-06-07T14:45:39Z","links":{"resolver":"https://pith.science/pith/RII6RS44O6COXAZHI27NF5VKLC","bundle":"https://pith.science/pith/RII6RS44O6COXAZHI27NF5VKLC/bundle.json","state":"https://pith.science/pith/RII6RS44O6COXAZHI27NF5VKLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RII6RS44O6COXAZHI27NF5VKLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RII6RS44O6COXAZHI27NF5VKLC","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":"612ec9e1ad124b1c2c812a3af4e17ec226e1c3297b2637d81f269d0ef5492742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-10T01:31:44Z","title_canon_sha256":"7ff652146e3d29f52a1c82b98b3ec697dc8c3ba1acee2b356549311ecb577aed"},"schema_version":"1.0","source":{"id":"1011.2249","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2249","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2249v1","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2249","created_at":"2026-05-18T04:36:30Z"},{"alias_kind":"pith_short_12","alias_value":"RII6RS44O6CO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RII6RS44O6COXAZH","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RII6RS44","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:fc68d8a773d6e40045bac233eb261ef04c0e55e088a0e58b36256af54916c9cb","target":"graph","created_at":"2026-05-18T04:36:30Z","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":"Consider an optimization problem with $n$ binary variables and $d+1$ linear objective functions. Each valid solution $x \\in \\{0,1\\}^n$ gives rise to an objective vector in $\\R^{d+1}$, and one often wants to enumerate the Pareto optima among them. In the worst case there may be exponentially many Pareto optima; however, it was recently shown that in (a generalization of) the smoothed analysis framework, the expected number is polynomial in $n$. Unfortunately, the bound obtained had a rather bad dependence on $d$; roughly $n^{d^d}$. In this paper we show a significantly improved bound of $n^{2d}","authors_text":"Ankur Moitra, Ryan O'Donnell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-10T01:31:44Z","title":"Pareto Optimal Solutions for Smoothed Analysts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2249","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":"sha256:7ac53b836351ce9e80b053cc74cd7d545da133d45ac2f31d95b7754eacb776ed","target":"record","created_at":"2026-05-18T04:36:30Z","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":"612ec9e1ad124b1c2c812a3af4e17ec226e1c3297b2637d81f269d0ef5492742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-11-10T01:31:44Z","title_canon_sha256":"7ff652146e3d29f52a1c82b98b3ec697dc8c3ba1acee2b356549311ecb577aed"},"schema_version":"1.0","source":{"id":"1011.2249","kind":"arxiv","version":1}},"canonical_sha256":"8a11e8cb9c7784eb832746bed2f6aa588fbc2d38e2bc1264e15c9fcccd2895db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a11e8cb9c7784eb832746bed2f6aa588fbc2d38e2bc1264e15c9fcccd2895db","first_computed_at":"2026-05-18T04:36:30.754244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:30.754244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NgR/c0hqLPt0usxyVImjRkonqiOSCreXIDS+NEn6BzbgHIO4/a9EejNnbz0qWXLmHiyns4Vq1Qoq1zZ49ue+Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:30.754778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2249","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ac53b836351ce9e80b053cc74cd7d545da133d45ac2f31d95b7754eacb776ed","sha256:fc68d8a773d6e40045bac233eb261ef04c0e55e088a0e58b36256af54916c9cb"],"state_sha256":"56c6f637b57fcfd446284c45e47c1dd37ae05dbe234f01e60e49832fba6067fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rLo+KcCYvbfqLyiv+WT1eWWxVSIxWmqSBRxC+ZA1jcmE/38GxGIDFR1tQ788nMJcG+n/9VAThEazAwYPL3p+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:45:39.207044Z","bundle_sha256":"38dfa0447adab27039bcc32e9847fde0baaadc2baf5f023ab7ceb46c3a33bd09"}}