{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:W2JUHGLHMQOG2NSVMH7RWZFAQD","short_pith_number":"pith:W2JUHGLH","canonical_record":{"source":{"id":"1705.00822","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-02T06:58:30Z","cross_cats_sorted":[],"title_canon_sha256":"06a05e9e2ec43ecf184669d90cce7045eefa5c190b94fa7390745afd3192ea50","abstract_canon_sha256":"88f145d2c0c56d3a861afbddcceb77fe64683a71064715953b8ed728d72794ac"},"schema_version":"1.0"},"canonical_sha256":"b693439967641c6d365561ff1b64a080dc3cb8f5259161dc42f5271cfdd060e4","source":{"kind":"arxiv","id":"1705.00822","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00822","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00822v5","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00822","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"W2JUHGLHMQOG","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"pith_short_16","alias_value":"W2JUHGLHMQOG2NSV","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"pith_short_8","alias_value":"W2JUHGLH","created_at":"2026-07-05T04:08:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:W2JUHGLHMQOG2NSVMH7RWZFAQD","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00822","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-02T06:58:30Z","cross_cats_sorted":[],"title_canon_sha256":"06a05e9e2ec43ecf184669d90cce7045eefa5c190b94fa7390745afd3192ea50","abstract_canon_sha256":"88f145d2c0c56d3a861afbddcceb77fe64683a71064715953b8ed728d72794ac"},"schema_version":"1.0"},"canonical_sha256":"b693439967641c6d365561ff1b64a080dc3cb8f5259161dc42f5271cfdd060e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:08:22.516556Z","signature_b64":"+jsWESiqFIt2C6jCN1mtXr+xiq0050zE1U9cCArbWwEo/fsD2kxMjq5tVW/aGtLmDy1oq+/lHjRiIx0N7+wvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b693439967641c6d365561ff1b64a080dc3cb8f5259161dc42f5271cfdd060e4","last_reissued_at":"2026-07-05T04:08:22.516068Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:08:22.516068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00822","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d5UIsp276hXao6ux4CyBoGBBAAuIEUYdU/BTxwNaf5B6kD1Ajz0zFPtrDjvSDDdFFHHg6tkQ9ycif9FXJe5WDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:04:53.277018Z"},"content_sha256":"80e561f20fabd04009ce0fae39027c1c00aab315787dae1b8fd1f0152dac8a0f","schema_version":"1.0","event_id":"sha256:80e561f20fabd04009ce0fae39027c1c00aab315787dae1b8fd1f0152dac8a0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:W2JUHGLHMQOG2NSVMH7RWZFAQD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sample average approximation with heavier tails I: non-asymptotic bounds with weak assumptions and stochastic constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Philip Thompson, Roberto I. Oliveira","submitted_at":"2017-05-02T06:58:30Z","abstract_excerpt":"We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are \"sub-Gaussian\"~even when the randomness of the problem is fairly heavy tailed. Additionally, we obtain good (often optimal) dependence on the sample size and geometrical parameters of the problem. Finally, we allow for random constraints on the SAA and unbounded feasible sets, which also do not seem to have been considered before in the non-asymptotic literature. Our proofs combine different ideas of po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00822","kind":"arxiv","version":5},"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/1705.00822/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"To4OKDoCkmQ4NYzOL0i2mI/THuvP3L9kAtr8IkARlJ//UM+OWtVCD8F4ic8IjkgKmc1THxLm8u+EyX9Nzqx5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:04:53.277857Z"},"content_sha256":"dd9f46c59abd16fc3631a5e89c1bccbac733c631b54c788b0992a463487f8b87","schema_version":"1.0","event_id":"sha256:dd9f46c59abd16fc3631a5e89c1bccbac733c631b54c788b0992a463487f8b87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2JUHGLHMQOG2NSVMH7RWZFAQD/bundle.json","state_url":"https://pith.science/pith/W2JUHGLHMQOG2NSVMH7RWZFAQD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2JUHGLHMQOG2NSVMH7RWZFAQD/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":"2026-08-15T21:04:53Z","links":{"resolver":"https://pith.science/pith/W2JUHGLHMQOG2NSVMH7RWZFAQD","bundle":"https://pith.science/pith/W2JUHGLHMQOG2NSVMH7RWZFAQD/bundle.json","state":"https://pith.science/pith/W2JUHGLHMQOG2NSVMH7RWZFAQD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2JUHGLHMQOG2NSVMH7RWZFAQD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:W2JUHGLHMQOG2NSVMH7RWZFAQD","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":"88f145d2c0c56d3a861afbddcceb77fe64683a71064715953b8ed728d72794ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-02T06:58:30Z","title_canon_sha256":"06a05e9e2ec43ecf184669d90cce7045eefa5c190b94fa7390745afd3192ea50"},"schema_version":"1.0","source":{"id":"1705.00822","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00822","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00822v5","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00822","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"W2JUHGLHMQOG","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"pith_short_16","alias_value":"W2JUHGLHMQOG2NSV","created_at":"2026-07-05T04:08:22Z"},{"alias_kind":"pith_short_8","alias_value":"W2JUHGLH","created_at":"2026-07-05T04:08:22Z"}],"graph_snapshots":[{"event_id":"sha256:dd9f46c59abd16fc3631a5e89c1bccbac733c631b54c788b0992a463487f8b87","target":"graph","created_at":"2026-07-05T04:08:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1705.00822/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are \"sub-Gaussian\"~even when the randomness of the problem is fairly heavy tailed. Additionally, we obtain good (often optimal) dependence on the sample size and geometrical parameters of the problem. Finally, we allow for random constraints on the SAA and unbounded feasible sets, which also do not seem to have been considered before in the non-asymptotic literature. Our proofs combine different ideas of po","authors_text":"Philip Thompson, Roberto I. Oliveira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-02T06:58:30Z","title":"Sample average approximation with heavier tails I: non-asymptotic bounds with weak assumptions and stochastic constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00822","kind":"arxiv","version":5},"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":"sha256:80e561f20fabd04009ce0fae39027c1c00aab315787dae1b8fd1f0152dac8a0f","target":"record","created_at":"2026-07-05T04:08:22Z","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":"88f145d2c0c56d3a861afbddcceb77fe64683a71064715953b8ed728d72794ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-02T06:58:30Z","title_canon_sha256":"06a05e9e2ec43ecf184669d90cce7045eefa5c190b94fa7390745afd3192ea50"},"schema_version":"1.0","source":{"id":"1705.00822","kind":"arxiv","version":5}},"canonical_sha256":"b693439967641c6d365561ff1b64a080dc3cb8f5259161dc42f5271cfdd060e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b693439967641c6d365561ff1b64a080dc3cb8f5259161dc42f5271cfdd060e4","first_computed_at":"2026-07-05T04:08:22.516068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:08:22.516068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+jsWESiqFIt2C6jCN1mtXr+xiq0050zE1U9cCArbWwEo/fsD2kxMjq5tVW/aGtLmDy1oq+/lHjRiIx0N7+wvDA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:08:22.516556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00822","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80e561f20fabd04009ce0fae39027c1c00aab315787dae1b8fd1f0152dac8a0f","sha256:dd9f46c59abd16fc3631a5e89c1bccbac733c631b54c788b0992a463487f8b87"],"state_sha256":"5c490f094811969ed87e173d9ef052b5ee58d56d6ff9e4f35330d15a29c250ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TMUx2JUrezvIzirRPLEgPH+lANI5/5cNUsEojn1cGJsXS9ZrZWNRHaYc1i/g21RJS0h4eKltmT0o6tjov/RIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T21:04:53.284273Z","bundle_sha256":"621efe7008f5e95aa85a4fd9102dd3262fa0fbd55b2c4d9b520bf9ef48720373"}}