{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XQPIQ7RSEZK3F4S6DDU5QA6VHS","short_pith_number":"pith:XQPIQ7RS","canonical_record":{"source":{"id":"1507.01995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-08T00:02:08Z","cross_cats_sorted":[],"title_canon_sha256":"4c1fc3572d199a467b4f79cbc7995d77b2dbdc6e93839bf22b9ea1c475846722","abstract_canon_sha256":"9ebcaf4979d2ed84ea43769a82be8c7defa3e52d3126ca17b26eee5ca49018ab"},"schema_version":"1.0"},"canonical_sha256":"bc1e887e322655b2f25e18e9d803d53c91e28087c3cd6a1bb599bd62c677a7d6","source":{"kind":"arxiv","id":"1507.01995","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01995","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01995v2","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01995","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"XQPIQ7RSEZK3","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XQPIQ7RSEZK3F4S6","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XQPIQ7RS","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XQPIQ7RSEZK3F4S6DDU5QA6VHS","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-08T00:02:08Z","cross_cats_sorted":[],"title_canon_sha256":"4c1fc3572d199a467b4f79cbc7995d77b2dbdc6e93839bf22b9ea1c475846722","abstract_canon_sha256":"9ebcaf4979d2ed84ea43769a82be8c7defa3e52d3126ca17b26eee5ca49018ab"},"schema_version":"1.0"},"canonical_sha256":"bc1e887e322655b2f25e18e9d803d53c91e28087c3cd6a1bb599bd62c677a7d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:53.754739Z","signature_b64":"gMddPBAA27YkYzF21hKNPDvu7wabhHJ11CHF07ecbfeqsJny/gWyeVTcTIQvL4H9zqfWU3aRWoVnQ+kltbZcAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc1e887e322655b2f25e18e9d803d53c91e28087c3cd6a1bb599bd62c677a7d6","last_reissued_at":"2026-05-18T01:19:53.754276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:53.754276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01995","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":"2026-05-18T01:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FX5fOWps0/0FIA931LWCRvU+mC9AKukSu0hbu5kortvaiouO+LdPNMgppO35Tt8B+shSJFuUFOzbwPhvjZrMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:10:45.918395Z"},"content_sha256":"27ac52463b3b155c2bdbe89751b13d66002d325c411d5b223b843a3ab81d1a12","schema_version":"1.0","event_id":"sha256:27ac52463b3b155c2bdbe89751b13d66002d325c411d5b223b843a3ab81d1a12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XQPIQ7RSEZK3F4S6DDU5QA6VHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-sided linear chance constraints and extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel Bienstock, Juan Pablo Vielma, Miles Lubin","submitted_at":"2015-07-08T00:02:08Z","abstract_excerpt":"We examine the convexity and tractability of the two-sided linear chance constraint model under Gaussian uncertainty. We show that these constraints can be applied directly to model a larger class of nonlinear chance constraints as well as provide a reasonable approximation for a challenging class of quadratic chance constraints of direct interest for applications in power systems. With a view towards practical computations, we develop a second-order cone outer approximation of the two-sided chance constraint with provably small approximation error."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01995","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":"2026-05-18T01:19:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Qt7JCG1RsYvYzDPcHKok4QPNX+XteOKpmiMl8qvSmNChYY8U0KObydToifHoWBbwHBumEXNsXnhpjKdOYeJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:10:45.918750Z"},"content_sha256":"0a7cfb7325b78e9e76f8ce0b8b397798688f2c3ae0203b765f23c3cbefc5c412","schema_version":"1.0","event_id":"sha256:0a7cfb7325b78e9e76f8ce0b8b397798688f2c3ae0203b765f23c3cbefc5c412"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XQPIQ7RSEZK3F4S6DDU5QA6VHS/bundle.json","state_url":"https://pith.science/pith/XQPIQ7RSEZK3F4S6DDU5QA6VHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XQPIQ7RSEZK3F4S6DDU5QA6VHS/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":"2026-06-11T14:10:45Z","links":{"resolver":"https://pith.science/pith/XQPIQ7RSEZK3F4S6DDU5QA6VHS","bundle":"https://pith.science/pith/XQPIQ7RSEZK3F4S6DDU5QA6VHS/bundle.json","state":"https://pith.science/pith/XQPIQ7RSEZK3F4S6DDU5QA6VHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XQPIQ7RSEZK3F4S6DDU5QA6VHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XQPIQ7RSEZK3F4S6DDU5QA6VHS","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":"9ebcaf4979d2ed84ea43769a82be8c7defa3e52d3126ca17b26eee5ca49018ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-08T00:02:08Z","title_canon_sha256":"4c1fc3572d199a467b4f79cbc7995d77b2dbdc6e93839bf22b9ea1c475846722"},"schema_version":"1.0","source":{"id":"1507.01995","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01995","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01995v2","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01995","created_at":"2026-05-18T01:19:53Z"},{"alias_kind":"pith_short_12","alias_value":"XQPIQ7RSEZK3","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XQPIQ7RSEZK3F4S6","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XQPIQ7RS","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:0a7cfb7325b78e9e76f8ce0b8b397798688f2c3ae0203b765f23c3cbefc5c412","target":"graph","created_at":"2026-05-18T01:19:53Z","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":"We examine the convexity and tractability of the two-sided linear chance constraint model under Gaussian uncertainty. We show that these constraints can be applied directly to model a larger class of nonlinear chance constraints as well as provide a reasonable approximation for a challenging class of quadratic chance constraints of direct interest for applications in power systems. With a view towards practical computations, we develop a second-order cone outer approximation of the two-sided chance constraint with provably small approximation error.","authors_text":"Daniel Bienstock, Juan Pablo Vielma, Miles Lubin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-08T00:02:08Z","title":"Two-sided linear chance constraints and extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01995","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":"sha256:27ac52463b3b155c2bdbe89751b13d66002d325c411d5b223b843a3ab81d1a12","target":"record","created_at":"2026-05-18T01:19:53Z","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":"9ebcaf4979d2ed84ea43769a82be8c7defa3e52d3126ca17b26eee5ca49018ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-08T00:02:08Z","title_canon_sha256":"4c1fc3572d199a467b4f79cbc7995d77b2dbdc6e93839bf22b9ea1c475846722"},"schema_version":"1.0","source":{"id":"1507.01995","kind":"arxiv","version":2}},"canonical_sha256":"bc1e887e322655b2f25e18e9d803d53c91e28087c3cd6a1bb599bd62c677a7d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc1e887e322655b2f25e18e9d803d53c91e28087c3cd6a1bb599bd62c677a7d6","first_computed_at":"2026-05-18T01:19:53.754276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:53.754276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gMddPBAA27YkYzF21hKNPDvu7wabhHJ11CHF07ecbfeqsJny/gWyeVTcTIQvL4H9zqfWU3aRWoVnQ+kltbZcAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:53.754739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01995","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27ac52463b3b155c2bdbe89751b13d66002d325c411d5b223b843a3ab81d1a12","sha256:0a7cfb7325b78e9e76f8ce0b8b397798688f2c3ae0203b765f23c3cbefc5c412"],"state_sha256":"8860b7d8d051c658b7e42976bb162a925b3052987ac69cdc6ab9d46f32bdbef5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G7+isFx0SvC19AbQPvxm9Tw1OXL1/Ku+dfdUYxDRwk4XGZbYhrjTEjkLe8loTjBU6S8uz3sAQJZ45RxgR5fjBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:10:45.920835Z","bundle_sha256":"c7d8ca8db7a73848c1fe40797cda17d338f5ad094292dc4be2ff30438ad1edde"}}