{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UMWDXLMRT3KNC5FBDUO7MTD7MM","short_pith_number":"pith:UMWDXLMR","canonical_record":{"source":{"id":"1112.1436","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-06T22:08:55Z","cross_cats_sorted":[],"title_canon_sha256":"b32a25c9f8eac2c848dfdcef06a8694e6f7cd568c149128bebe9c794caa25458","abstract_canon_sha256":"114eb77e959a10b9cb1a8783e6a7be5363c40dfc6d4df61aa75be59913121230"},"schema_version":"1.0"},"canonical_sha256":"a32c3bad919ed4d174a11d1df64c7f6338635aa61a23942068a33a8b584068ef","source":{"kind":"arxiv","id":"1112.1436","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1436","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1436v6","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1436","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"UMWDXLMRT3KN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UMWDXLMRT3KNC5FB","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UMWDXLMR","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UMWDXLMRT3KNC5FBDUO7MTD7MM","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1436","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-06T22:08:55Z","cross_cats_sorted":[],"title_canon_sha256":"b32a25c9f8eac2c848dfdcef06a8694e6f7cd568c149128bebe9c794caa25458","abstract_canon_sha256":"114eb77e959a10b9cb1a8783e6a7be5363c40dfc6d4df61aa75be59913121230"},"schema_version":"1.0"},"canonical_sha256":"a32c3bad919ed4d174a11d1df64c7f6338635aa61a23942068a33a8b584068ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:24.013550Z","signature_b64":"uFssUkGgJjSbwl4IYLTKFCOW7VuBhkYqTfiK+MQdpp3803FeFxAjjqL1l2FuHlWIkfPLG39KlRg0hh9/o0zbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a32c3bad919ed4d174a11d1df64c7f6338635aa61a23942068a33a8b584068ef","last_reissued_at":"2026-05-18T00:50:24.012951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:24.012951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1436","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9JdZPFzof/Vzq7czqbicge8dg7LwHXJfbPPzRkfRDX+zJIKmoghmPNHmM2Y6iwNY2zr0lgia/OPNtaEvSstaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:57:22.411933Z"},"content_sha256":"e6ed917a697a6fa7954c33039ca4ee23666f5d02db3c48371b3606e7185f88a1","schema_version":"1.0","event_id":"sha256:e6ed917a697a6fa7954c33039ca4ee23666f5d02db3c48371b3606e7185f88a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UMWDXLMRT3KNC5FBDUO7MTD7MM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bad semidefinite programs: they all look the same","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gabor Pataki","submitted_at":"2011-12-06T22:08:55Z","abstract_excerpt":"Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We call a conic linear system $Ax <= b$ {\\em badly behaved} if the value of $\\sup { < c, x > | A x <= b }$ is finite but the dual program has no solution with the same value for {\\em some} $c.$ We describe simple and intuitive geometric characterizations of badly behaved conic linear systems. Our main motivation is the striking similarity of badly behaved semidef"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1436","kind":"arxiv","version":6},"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":"2026-05-18T00:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p02pJMmw3CSUU1yV49Zn0w/GaeHF7gyzwzOzCR0AkzVAk9/232vhx3K544m/XnkVzDoBDMb9v9ELZXSZ3ZsxCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:57:22.412626Z"},"content_sha256":"7e4e994459ca4cf3740cdf2ed0f2bc2a0b25dd172950e452ab33167b602ddd99","schema_version":"1.0","event_id":"sha256:7e4e994459ca4cf3740cdf2ed0f2bc2a0b25dd172950e452ab33167b602ddd99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMWDXLMRT3KNC5FBDUO7MTD7MM/bundle.json","state_url":"https://pith.science/pith/UMWDXLMRT3KNC5FBDUO7MTD7MM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMWDXLMRT3KNC5FBDUO7MTD7MM/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":"2026-06-05T01:57:22Z","links":{"resolver":"https://pith.science/pith/UMWDXLMRT3KNC5FBDUO7MTD7MM","bundle":"https://pith.science/pith/UMWDXLMRT3KNC5FBDUO7MTD7MM/bundle.json","state":"https://pith.science/pith/UMWDXLMRT3KNC5FBDUO7MTD7MM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMWDXLMRT3KNC5FBDUO7MTD7MM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UMWDXLMRT3KNC5FBDUO7MTD7MM","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":"114eb77e959a10b9cb1a8783e6a7be5363c40dfc6d4df61aa75be59913121230","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-06T22:08:55Z","title_canon_sha256":"b32a25c9f8eac2c848dfdcef06a8694e6f7cd568c149128bebe9c794caa25458"},"schema_version":"1.0","source":{"id":"1112.1436","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1436","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1436v6","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1436","created_at":"2026-05-18T00:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"UMWDXLMRT3KN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UMWDXLMRT3KNC5FB","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UMWDXLMR","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:7e4e994459ca4cf3740cdf2ed0f2bc2a0b25dd172950e452ab33167b602ddd99","target":"graph","created_at":"2026-05-18T00:50:24Z","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":"Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We call a conic linear system $Ax <= b$ {\\em badly behaved} if the value of $\\sup { < c, x > | A x <= b }$ is finite but the dual program has no solution with the same value for {\\em some} $c.$ We describe simple and intuitive geometric characterizations of badly behaved conic linear systems. Our main motivation is the striking similarity of badly behaved semidef","authors_text":"Gabor Pataki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-06T22:08:55Z","title":"Bad semidefinite programs: they all look the same"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1436","kind":"arxiv","version":6},"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:e6ed917a697a6fa7954c33039ca4ee23666f5d02db3c48371b3606e7185f88a1","target":"record","created_at":"2026-05-18T00:50:24Z","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":"114eb77e959a10b9cb1a8783e6a7be5363c40dfc6d4df61aa75be59913121230","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-06T22:08:55Z","title_canon_sha256":"b32a25c9f8eac2c848dfdcef06a8694e6f7cd568c149128bebe9c794caa25458"},"schema_version":"1.0","source":{"id":"1112.1436","kind":"arxiv","version":6}},"canonical_sha256":"a32c3bad919ed4d174a11d1df64c7f6338635aa61a23942068a33a8b584068ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a32c3bad919ed4d174a11d1df64c7f6338635aa61a23942068a33a8b584068ef","first_computed_at":"2026-05-18T00:50:24.012951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:24.012951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uFssUkGgJjSbwl4IYLTKFCOW7VuBhkYqTfiK+MQdpp3803FeFxAjjqL1l2FuHlWIkfPLG39KlRg0hh9/o0zbCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:24.013550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1436","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6ed917a697a6fa7954c33039ca4ee23666f5d02db3c48371b3606e7185f88a1","sha256:7e4e994459ca4cf3740cdf2ed0f2bc2a0b25dd172950e452ab33167b602ddd99"],"state_sha256":"7afa1bb2cfbccbd400b9540f57033a1297a8b377c6fae1eb7ab0980de224669d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vMM5T8OPI9z2Dl1+glw9kom6XxhvP2w8pMNztujuOVPLZLFp2DBxjXs67MFx2c3O/Oe0ASgampjX8WS/Xs8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:57:22.415931Z","bundle_sha256":"cc857d7b2a4444337e3d57a980f0d8cb9756743b6a49448264a139a17dd833d7"}}