{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:K6XSLILHKG3SJFNHRW2VL5HMTR","short_pith_number":"pith:K6XSLILH","canonical_record":{"source":{"id":"1404.7208","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2014-04-29T01:49:37Z","cross_cats_sorted":[],"title_canon_sha256":"ab735561e1cd6b35940eac7e148e2b65f53ecd549df7a45124938b69cfc7b6f1","abstract_canon_sha256":"c46f1a61335f65c5b2e34ee6dff150318ca1598572f7cf75448287a7a8f1b6f2"},"schema_version":"1.0"},"canonical_sha256":"57af25a16751b72495a78db555f4ec9c454b9fc8386e1e80edbddb998bc0fb0e","source":{"kind":"arxiv","id":"1404.7208","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7208","created_at":"2026-05-18T02:52:25Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7208v2","created_at":"2026-05-18T02:52:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7208","created_at":"2026-05-18T02:52:25Z"},{"alias_kind":"pith_short_12","alias_value":"K6XSLILHKG3S","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K6XSLILHKG3SJFNH","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K6XSLILH","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:K6XSLILHKG3SJFNHRW2VL5HMTR","target":"record","payload":{"canonical_record":{"source":{"id":"1404.7208","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2014-04-29T01:49:37Z","cross_cats_sorted":[],"title_canon_sha256":"ab735561e1cd6b35940eac7e148e2b65f53ecd549df7a45124938b69cfc7b6f1","abstract_canon_sha256":"c46f1a61335f65c5b2e34ee6dff150318ca1598572f7cf75448287a7a8f1b6f2"},"schema_version":"1.0"},"canonical_sha256":"57af25a16751b72495a78db555f4ec9c454b9fc8386e1e80edbddb998bc0fb0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:25.044032Z","signature_b64":"SvR4fzKOj1otClcZxKWTod81qSX7j9tdoK2jUF0KUQiFSSUNk51AnBXWGYPXC8518c04LdbSCyjBU2DBzmLjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57af25a16751b72495a78db555f4ec9c454b9fc8386e1e80edbddb998bc0fb0e","last_reissued_at":"2026-05-18T02:52:25.043439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:25.043439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.7208","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":"2026-05-18T02:52:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVYYVEBALxWw9u19diSHQ21YQXwVXDHg28X+Fwb02xGzPL8IvLRbRrT242Zuch1EQU34sA4XrpzBujuMYxh0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:19:30.971473Z"},"content_sha256":"e50f6fcaabe224c9f37c5000a493778b1d558c22d8c5748348e44bd9ff1d8b01","schema_version":"1.0","event_id":"sha256:e50f6fcaabe224c9f37c5000a493778b1d558c22d8c5748348e44bd9ff1d8b01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:K6XSLILHKG3SJFNHRW2VL5HMTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Validating Sample Average Approximation Solutions with Negatively Dependent Batches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.OT","authors_text":"Cong Han Lim, Jeff Linderoth, Jiajie Chen, Peter Z. G. Qian, Stephen J. Wright","submitted_at":"2014-04-29T01:49:37Z","abstract_excerpt":"Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower bound on the optimal objective value of the true problem which, when coupled with an upper bound, provides confidence intervals for the true optimal objective value and valuable information about the quality of the approximate solutions. Specifically, the lower bound can be estimated by solving multiple SAA problems (each obtained using a particular sampling"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7208","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":"2026-05-18T02:52:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OS78tRGjLfP1e/m5G4AkSG6rMBZqUpUAPvl/tidLKZ4112ySg1jWwo/RAZts7mjfyBV2I/hqhJWMfyejbgakBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:19:30.971822Z"},"content_sha256":"7cea2253d50bc8d9c3c9672a78727bec2bd2dc1e01b56eb09f742db35bd14329","schema_version":"1.0","event_id":"sha256:7cea2253d50bc8d9c3c9672a78727bec2bd2dc1e01b56eb09f742db35bd14329"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6XSLILHKG3SJFNHRW2VL5HMTR/bundle.json","state_url":"https://pith.science/pith/K6XSLILHKG3SJFNHRW2VL5HMTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6XSLILHKG3SJFNHRW2VL5HMTR/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":"2026-05-26T20:19:30Z","links":{"resolver":"https://pith.science/pith/K6XSLILHKG3SJFNHRW2VL5HMTR","bundle":"https://pith.science/pith/K6XSLILHKG3SJFNHRW2VL5HMTR/bundle.json","state":"https://pith.science/pith/K6XSLILHKG3SJFNHRW2VL5HMTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6XSLILHKG3SJFNHRW2VL5HMTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:K6XSLILHKG3SJFNHRW2VL5HMTR","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":"c46f1a61335f65c5b2e34ee6dff150318ca1598572f7cf75448287a7a8f1b6f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2014-04-29T01:49:37Z","title_canon_sha256":"ab735561e1cd6b35940eac7e148e2b65f53ecd549df7a45124938b69cfc7b6f1"},"schema_version":"1.0","source":{"id":"1404.7208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7208","created_at":"2026-05-18T02:52:25Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7208v2","created_at":"2026-05-18T02:52:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7208","created_at":"2026-05-18T02:52:25Z"},{"alias_kind":"pith_short_12","alias_value":"K6XSLILHKG3S","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"K6XSLILHKG3SJFNH","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"K6XSLILH","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:7cea2253d50bc8d9c3c9672a78727bec2bd2dc1e01b56eb09f742db35bd14329","target":"graph","created_at":"2026-05-18T02:52:25Z","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":"Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower bound on the optimal objective value of the true problem which, when coupled with an upper bound, provides confidence intervals for the true optimal objective value and valuable information about the quality of the approximate solutions. Specifically, the lower bound can be estimated by solving multiple SAA problems (each obtained using a particular sampling","authors_text":"Cong Han Lim, Jeff Linderoth, Jiajie Chen, Peter Z. G. Qian, Stephen J. Wright","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2014-04-29T01:49:37Z","title":"Validating Sample Average Approximation Solutions with Negatively Dependent Batches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7208","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:e50f6fcaabe224c9f37c5000a493778b1d558c22d8c5748348e44bd9ff1d8b01","target":"record","created_at":"2026-05-18T02:52:25Z","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":"c46f1a61335f65c5b2e34ee6dff150318ca1598572f7cf75448287a7a8f1b6f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.OT","submitted_at":"2014-04-29T01:49:37Z","title_canon_sha256":"ab735561e1cd6b35940eac7e148e2b65f53ecd549df7a45124938b69cfc7b6f1"},"schema_version":"1.0","source":{"id":"1404.7208","kind":"arxiv","version":2}},"canonical_sha256":"57af25a16751b72495a78db555f4ec9c454b9fc8386e1e80edbddb998bc0fb0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57af25a16751b72495a78db555f4ec9c454b9fc8386e1e80edbddb998bc0fb0e","first_computed_at":"2026-05-18T02:52:25.043439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:25.043439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SvR4fzKOj1otClcZxKWTod81qSX7j9tdoK2jUF0KUQiFSSUNk51AnBXWGYPXC8518c04LdbSCyjBU2DBzmLjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:25.044032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e50f6fcaabe224c9f37c5000a493778b1d558c22d8c5748348e44bd9ff1d8b01","sha256:7cea2253d50bc8d9c3c9672a78727bec2bd2dc1e01b56eb09f742db35bd14329"],"state_sha256":"ddbc4b3a8ee68be1c5c0e556727b91c5d096db18e0f5cf5c9bf701ba248cb7e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+czAvF0zokATFGt97bBqA9PKZtDQEKzP+708oZlJOxGeU+jZRtQPnXyuLLPnN4w/xKWm/CMlWGphuG+rQn8eAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:19:30.974080Z","bundle_sha256":"285da1682055e02a802f658f55d06984b9883937a291533e6a7abe495b77d809"}}