{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Y5BQRUWF4KCXENAWUJEESXYN72","short_pith_number":"pith:Y5BQRUWF","canonical_record":{"source":{"id":"1803.07683","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T22:54:29Z","cross_cats_sorted":["cs.CC","math.AG","math.NA"],"title_canon_sha256":"4f62447af100c1d42e1f602fefc0fd3ca40977dab85a294613736ae2a926fd7b","abstract_canon_sha256":"b35a64808118d7360084d665449ddfd155999beea9d765a387430d9e4a285983"},"schema_version":"1.0"},"canonical_sha256":"c74308d2c5e285723416a248495f0dfea9637fd253da8dd06f88c32aff328b9e","source":{"kind":"arxiv","id":"1803.07683","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07683","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07683v2","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07683","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"Y5BQRUWF4KCX","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Y5BQRUWF4KCXENAW","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Y5BQRUWF","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Y5BQRUWF4KCXENAWUJEESXYN72","target":"record","payload":{"canonical_record":{"source":{"id":"1803.07683","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T22:54:29Z","cross_cats_sorted":["cs.CC","math.AG","math.NA"],"title_canon_sha256":"4f62447af100c1d42e1f602fefc0fd3ca40977dab85a294613736ae2a926fd7b","abstract_canon_sha256":"b35a64808118d7360084d665449ddfd155999beea9d765a387430d9e4a285983"},"schema_version":"1.0"},"canonical_sha256":"c74308d2c5e285723416a248495f0dfea9637fd253da8dd06f88c32aff328b9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:31.348439Z","signature_b64":"30ZyoXIuIO2K7m+Cvg6laey5wDSnsGRgYgzqzeIruQddbPddXlKndpISOReq/K407HgirPiWPOnQ2nk1/ywSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c74308d2c5e285723416a248495f0dfea9637fd253da8dd06f88c32aff328b9e","last_reissued_at":"2026-05-17T23:47:31.347908Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:31.347908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.07683","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":"2026-05-17T23:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"znXdRex916I3agGXIc2mm76MbHUk0J9UHUYtcZq35nYjl42pqfHvD76HX12obj32TJyzR7okARpPENL4kGOBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:58:35.215682Z"},"content_sha256":"f26720f0be3660b87f2f73342baeb9b676c574e1449dadbedf5b5a6f92835d7d","schema_version":"1.0","event_id":"sha256:f26720f0be3660b87f2f73342baeb9b676c574e1449dadbedf5b5a6f92835d7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Y5BQRUWF4KCXENAWUJEESXYN72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Complexity of Testing Attainment of the Optimal Value in Nonlinear Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AG","math.NA"],"primary_cat":"math.OC","authors_text":"Amir Ali Ahmadi, Jeffrey Zhang","submitted_at":"2018-03-20T22:54:29Z","abstract_excerpt":"We prove that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can test whether the optimal value of a nonlinear optimization problem where the objective and constraints are given by low-degree polynomials is attained. If the degrees of these polynomials are fixed, our results along with previously-known \"Frank-Wolfe type\" theorems imply that exactly one of two cases can occur: either the optimal value is attained on every instance, or it is strongly NP-hard to distinguish attainment from non-attainment. We also show that testing for some well-known "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07683","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":"2026-05-17T23:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1w1JTAc7zNAi7T/zRAPjDKu8f07ie8a4XwjXSVqW6LlWqbyissje/PdJ96fc3vz4pOdx7CsvDStDeiuPnewlDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:58:35.216038Z"},"content_sha256":"27f6428b2c44c341e19982edd03145eeed9c4f24cd78ce9025158b990572f2e0","schema_version":"1.0","event_id":"sha256:27f6428b2c44c341e19982edd03145eeed9c4f24cd78ce9025158b990572f2e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5BQRUWF4KCXENAWUJEESXYN72/bundle.json","state_url":"https://pith.science/pith/Y5BQRUWF4KCXENAWUJEESXYN72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5BQRUWF4KCXENAWUJEESXYN72/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":"2026-06-27T14:58:35Z","links":{"resolver":"https://pith.science/pith/Y5BQRUWF4KCXENAWUJEESXYN72","bundle":"https://pith.science/pith/Y5BQRUWF4KCXENAWUJEESXYN72/bundle.json","state":"https://pith.science/pith/Y5BQRUWF4KCXENAWUJEESXYN72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5BQRUWF4KCXENAWUJEESXYN72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Y5BQRUWF4KCXENAWUJEESXYN72","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":"b35a64808118d7360084d665449ddfd155999beea9d765a387430d9e4a285983","cross_cats_sorted":["cs.CC","math.AG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T22:54:29Z","title_canon_sha256":"4f62447af100c1d42e1f602fefc0fd3ca40977dab85a294613736ae2a926fd7b"},"schema_version":"1.0","source":{"id":"1803.07683","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07683","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07683v2","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07683","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"Y5BQRUWF4KCX","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Y5BQRUWF4KCXENAW","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Y5BQRUWF","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:27f6428b2c44c341e19982edd03145eeed9c4f24cd78ce9025158b990572f2e0","target":"graph","created_at":"2026-05-17T23:47:31Z","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 prove that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can test whether the optimal value of a nonlinear optimization problem where the objective and constraints are given by low-degree polynomials is attained. If the degrees of these polynomials are fixed, our results along with previously-known \"Frank-Wolfe type\" theorems imply that exactly one of two cases can occur: either the optimal value is attained on every instance, or it is strongly NP-hard to distinguish attainment from non-attainment. We also show that testing for some well-known ","authors_text":"Amir Ali Ahmadi, Jeffrey Zhang","cross_cats":["cs.CC","math.AG","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T22:54:29Z","title":"On the Complexity of Testing Attainment of the Optimal Value in Nonlinear Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07683","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:f26720f0be3660b87f2f73342baeb9b676c574e1449dadbedf5b5a6f92835d7d","target":"record","created_at":"2026-05-17T23:47:31Z","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":"b35a64808118d7360084d665449ddfd155999beea9d765a387430d9e4a285983","cross_cats_sorted":["cs.CC","math.AG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-20T22:54:29Z","title_canon_sha256":"4f62447af100c1d42e1f602fefc0fd3ca40977dab85a294613736ae2a926fd7b"},"schema_version":"1.0","source":{"id":"1803.07683","kind":"arxiv","version":2}},"canonical_sha256":"c74308d2c5e285723416a248495f0dfea9637fd253da8dd06f88c32aff328b9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c74308d2c5e285723416a248495f0dfea9637fd253da8dd06f88c32aff328b9e","first_computed_at":"2026-05-17T23:47:31.347908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:31.347908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"30ZyoXIuIO2K7m+Cvg6laey5wDSnsGRgYgzqzeIruQddbPddXlKndpISOReq/K407HgirPiWPOnQ2nk1/ywSCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:31.348439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07683","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f26720f0be3660b87f2f73342baeb9b676c574e1449dadbedf5b5a6f92835d7d","sha256:27f6428b2c44c341e19982edd03145eeed9c4f24cd78ce9025158b990572f2e0"],"state_sha256":"00df0816991020eeda91069ce93e0d817113c4f5da2a83bf60772124aa1c3d6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ri3JIBIO0rY627qAymD7ronhZMUtcjefZptGu1+in2+CYC8h5AO6ntnfXDiwhSJwUnrwhUOv9ZJsqjaX8WIaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:58:35.217927Z","bundle_sha256":"3825661542f12eafee4ba6ac3e227062ea918160a2c35a7fbbe92c14f1df12bf"}}