{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EBKFLAUJXCET35PCFIO7QWTTMQ","short_pith_number":"pith:EBKFLAUJ","canonical_record":{"source":{"id":"1410.7187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-27T11:20:16Z","cross_cats_sorted":[],"title_canon_sha256":"90e4515972d342d03cadd91fbbff551e39c4ea5f0bde3b645c591cc943f8032a","abstract_canon_sha256":"78c41a95b37c15e378281ce8d308eb6106e582f704b7ce08a7316eb4458fb708"},"schema_version":"1.0"},"canonical_sha256":"2054558289b8893df5e22a1df85a73643bca88254fc25224b6b17ca750f40c72","source":{"kind":"arxiv","id":"1410.7187","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7187","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7187v1","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7187","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"EBKFLAUJXCET","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EBKFLAUJXCET35PC","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EBKFLAUJ","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EBKFLAUJXCET35PCFIO7QWTTMQ","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-27T11:20:16Z","cross_cats_sorted":[],"title_canon_sha256":"90e4515972d342d03cadd91fbbff551e39c4ea5f0bde3b645c591cc943f8032a","abstract_canon_sha256":"78c41a95b37c15e378281ce8d308eb6106e582f704b7ce08a7316eb4458fb708"},"schema_version":"1.0"},"canonical_sha256":"2054558289b8893df5e22a1df85a73643bca88254fc25224b6b17ca750f40c72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:17.864700Z","signature_b64":"POPl+z59z9EjC4jKyQ68KX30zkHVzLM2RzWq2TPGfXu+UHn+87A2bteXX6GQgvsHhsOjvyHQe1++rEi2CBonCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2054558289b8893df5e22a1df85a73643bca88254fc25224b6b17ca750f40c72","last_reissued_at":"2026-05-18T02:39:17.864272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:17.864272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7187","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":"2026-05-18T02:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"agolN0406+MKAWaTqI1oPrDivkt6WzqYMfM207mnI6gvLU/obt4D3v8r5tz2iSUoOc/VopPtmzYmJaAMPSMvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:03:55.497926Z"},"content_sha256":"ad67c7d2833543cccf6ee654d66723fac86b18868623cdb70c79424b8edb9fe0","schema_version":"1.0","event_id":"sha256:ad67c7d2833543cccf6ee654d66723fac86b18868623cdb70c79424b8edb9fe0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EBKFLAUJXCET35PCFIO7QWTTMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tractable approximations of sets defined with quantifiers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean B. Lasserre","submitted_at":"2014-10-27T11:20:16Z","abstract_excerpt":"Given a compact basic semi-algebraic set $K\\subset R^n\\times R^m$, a simple set $B$ (box or ellipsoid), and some semi-algebraic function $f$, we consider sets defined with quantifiers, of the form $R_f:=\\{x\\in B: \\mbox{$f(x,y)\\leq 0$ for all $y$ such that $(x,y)\\in K$}\\}$ and $D_f:=\\{x\\in B: \\mbox{$f(x,y)\\geq 0$ for some $y$ such that $(x,y)\\in K$}\\}$. The former set $R_f$ is particularly useful to qualify \"robust\" decisions $x$ versus noise parameter $y$ (e.g. in robust optimization on some set $\\mathbf{\\Omega}\\subset B$) whereas the latter set $D_f$ is useful (e.g. in optimization) when one "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7187","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":"2026-05-18T02:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bsTYikVWTwBgW72px4L34Dm9R3TYwX+aOkujE6Gw17N/LP/EHLZOsVv+X/tq0cD41hwA8FHDkDnlK1ktV9AfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:03:55.498629Z"},"content_sha256":"9726a7bcd80cd640a26facba3339920de594f25429dec04be6c01bc7ec420a69","schema_version":"1.0","event_id":"sha256:9726a7bcd80cd640a26facba3339920de594f25429dec04be6c01bc7ec420a69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EBKFLAUJXCET35PCFIO7QWTTMQ/bundle.json","state_url":"https://pith.science/pith/EBKFLAUJXCET35PCFIO7QWTTMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EBKFLAUJXCET35PCFIO7QWTTMQ/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":"2026-06-08T19:03:55Z","links":{"resolver":"https://pith.science/pith/EBKFLAUJXCET35PCFIO7QWTTMQ","bundle":"https://pith.science/pith/EBKFLAUJXCET35PCFIO7QWTTMQ/bundle.json","state":"https://pith.science/pith/EBKFLAUJXCET35PCFIO7QWTTMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EBKFLAUJXCET35PCFIO7QWTTMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EBKFLAUJXCET35PCFIO7QWTTMQ","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":"78c41a95b37c15e378281ce8d308eb6106e582f704b7ce08a7316eb4458fb708","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-27T11:20:16Z","title_canon_sha256":"90e4515972d342d03cadd91fbbff551e39c4ea5f0bde3b645c591cc943f8032a"},"schema_version":"1.0","source":{"id":"1410.7187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7187","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7187v1","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7187","created_at":"2026-05-18T02:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"EBKFLAUJXCET","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EBKFLAUJXCET35PC","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EBKFLAUJ","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:9726a7bcd80cd640a26facba3339920de594f25429dec04be6c01bc7ec420a69","target":"graph","created_at":"2026-05-18T02:39:17Z","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 a compact basic semi-algebraic set $K\\subset R^n\\times R^m$, a simple set $B$ (box or ellipsoid), and some semi-algebraic function $f$, we consider sets defined with quantifiers, of the form $R_f:=\\{x\\in B: \\mbox{$f(x,y)\\leq 0$ for all $y$ such that $(x,y)\\in K$}\\}$ and $D_f:=\\{x\\in B: \\mbox{$f(x,y)\\geq 0$ for some $y$ such that $(x,y)\\in K$}\\}$. The former set $R_f$ is particularly useful to qualify \"robust\" decisions $x$ versus noise parameter $y$ (e.g. in robust optimization on some set $\\mathbf{\\Omega}\\subset B$) whereas the latter set $D_f$ is useful (e.g. in optimization) when one ","authors_text":"Jean B. Lasserre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-27T11:20:16Z","title":"Tractable approximations of sets defined with quantifiers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7187","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:ad67c7d2833543cccf6ee654d66723fac86b18868623cdb70c79424b8edb9fe0","target":"record","created_at":"2026-05-18T02:39:17Z","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":"78c41a95b37c15e378281ce8d308eb6106e582f704b7ce08a7316eb4458fb708","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-27T11:20:16Z","title_canon_sha256":"90e4515972d342d03cadd91fbbff551e39c4ea5f0bde3b645c591cc943f8032a"},"schema_version":"1.0","source":{"id":"1410.7187","kind":"arxiv","version":1}},"canonical_sha256":"2054558289b8893df5e22a1df85a73643bca88254fc25224b6b17ca750f40c72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2054558289b8893df5e22a1df85a73643bca88254fc25224b6b17ca750f40c72","first_computed_at":"2026-05-18T02:39:17.864272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:17.864272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"POPl+z59z9EjC4jKyQ68KX30zkHVzLM2RzWq2TPGfXu+UHn+87A2bteXX6GQgvsHhsOjvyHQe1++rEi2CBonCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:17.864700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad67c7d2833543cccf6ee654d66723fac86b18868623cdb70c79424b8edb9fe0","sha256:9726a7bcd80cd640a26facba3339920de594f25429dec04be6c01bc7ec420a69"],"state_sha256":"61eb961507756929901a4cbc962cf28564c2a7de10a28655637a0d296793637f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FmbcIKoONFDwV4UgYM0mRTyilpmtARFuEoPqvYdMU0B2rvE4FR8dsQ96I1DWw0fz0+qZCjeTkQNWuxUwfQFqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:03:55.502308Z","bundle_sha256":"1d78ed7a348248f8a959428cd9946b099f41f23cd0d8aade488e3b4b92ac0c70"}}