{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FLJGA2LLT5YSRLISYWVHAIXIQG","short_pith_number":"pith:FLJGA2LL","canonical_record":{"source":{"id":"1907.02375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-04T12:45:31Z","cross_cats_sorted":[],"title_canon_sha256":"bdac8e1223b537d44333df617de244d7bcb20c124a92225d54a23f66daa9472b","abstract_canon_sha256":"8c7a21069a98a5140bf119bb5c3e81d1a6d57d469888f562c0438ff3641ba628"},"schema_version":"1.0"},"canonical_sha256":"2ad260696b9f7128ad12c5aa7022e881b7517c86a77533740f337bed7ee82366","source":{"kind":"arxiv","id":"1907.02375","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02375","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02375v1","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02375","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"FLJGA2LLT5YS","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FLJGA2LLT5YSRLIS","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FLJGA2LL","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FLJGA2LLT5YSRLISYWVHAIXIQG","target":"record","payload":{"canonical_record":{"source":{"id":"1907.02375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-04T12:45:31Z","cross_cats_sorted":[],"title_canon_sha256":"bdac8e1223b537d44333df617de244d7bcb20c124a92225d54a23f66daa9472b","abstract_canon_sha256":"8c7a21069a98a5140bf119bb5c3e81d1a6d57d469888f562c0438ff3641ba628"},"schema_version":"1.0"},"canonical_sha256":"2ad260696b9f7128ad12c5aa7022e881b7517c86a77533740f337bed7ee82366","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:28.774671Z","signature_b64":"zu1fOcwupZh4/qde/IKrbcz1ARnm43Yo0Twm+kICWtcoRStgSD/zAeLMREYVIdg9u5VYanP0RjDg66+ABY4qBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ad260696b9f7128ad12c5aa7022e881b7517c86a77533740f337bed7ee82366","last_reissued_at":"2026-05-17T23:41:28.774003Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:28.774003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.02375","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":"2026-05-17T23:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6kXa53o7fFtuehUhB+dZXl7ZaiRld3Ul02MK+4IedejgxSypBbc1K3kglhEcCkXk7p5yKnO2iHzJcBKW9O+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:56:49.611159Z"},"content_sha256":"9e920c7fe4031270ddbd5ee2a7a5fc5f75d39da638ca1cfce7e46bb8b72e54b7","schema_version":"1.0","event_id":"sha256:9e920c7fe4031270ddbd5ee2a7a5fc5f75d39da638ca1cfce7e46bb8b72e54b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FLJGA2LLT5YSRLISYWVHAIXIQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lipschitz modulus of linear and convex systems with the Hausdorff metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gerald Beer, Juan Parra, Marco A. L\\'opez, Mar\\'ia J. C\\'anovas","submitted_at":"2019-07-04T12:45:31Z","abstract_excerpt":"This paper analyzes the Lipschitz behavior of the feasible set in two parametric settings, associated with linear and convex systems in R^n. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified with the corresponding sets of coefficient vectors, which are assumed to be closed subsets of R^(n+1). In this framework, where the Hausdorff distance is used to measure the size of perturbations, an explicit formula for computing the Lipschitz modulus of the feasible set mapping is provided. As direct antecedent, we appeal to its counterpart in the paramet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02375","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":"2026-05-17T23:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c9mb7Ti3TXpqETJFX0vRL1N4Kc/4BlHRLwnI4l4y6YZZv3MqiWE6+pZOmCMNyCwY7ifR5QZLfWFtACc2X/MWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:56:49.611517Z"},"content_sha256":"3bf4a157de5734b3f4cf437bf7aff248ddd9b80342b62cf638c9abc3bbe53523","schema_version":"1.0","event_id":"sha256:3bf4a157de5734b3f4cf437bf7aff248ddd9b80342b62cf638c9abc3bbe53523"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FLJGA2LLT5YSRLISYWVHAIXIQG/bundle.json","state_url":"https://pith.science/pith/FLJGA2LLT5YSRLISYWVHAIXIQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FLJGA2LLT5YSRLISYWVHAIXIQG/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":"2026-06-25T11:56:49Z","links":{"resolver":"https://pith.science/pith/FLJGA2LLT5YSRLISYWVHAIXIQG","bundle":"https://pith.science/pith/FLJGA2LLT5YSRLISYWVHAIXIQG/bundle.json","state":"https://pith.science/pith/FLJGA2LLT5YSRLISYWVHAIXIQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FLJGA2LLT5YSRLISYWVHAIXIQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FLJGA2LLT5YSRLISYWVHAIXIQG","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":"8c7a21069a98a5140bf119bb5c3e81d1a6d57d469888f562c0438ff3641ba628","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-04T12:45:31Z","title_canon_sha256":"bdac8e1223b537d44333df617de244d7bcb20c124a92225d54a23f66daa9472b"},"schema_version":"1.0","source":{"id":"1907.02375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02375","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02375v1","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02375","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"FLJGA2LLT5YS","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FLJGA2LLT5YSRLIS","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FLJGA2LL","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:3bf4a157de5734b3f4cf437bf7aff248ddd9b80342b62cf638c9abc3bbe53523","target":"graph","created_at":"2026-05-17T23:41:28Z","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":"This paper analyzes the Lipschitz behavior of the feasible set in two parametric settings, associated with linear and convex systems in R^n. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified with the corresponding sets of coefficient vectors, which are assumed to be closed subsets of R^(n+1). In this framework, where the Hausdorff distance is used to measure the size of perturbations, an explicit formula for computing the Lipschitz modulus of the feasible set mapping is provided. As direct antecedent, we appeal to its counterpart in the paramet","authors_text":"Gerald Beer, Juan Parra, Marco A. L\\'opez, Mar\\'ia J. C\\'anovas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-04T12:45:31Z","title":"Lipschitz modulus of linear and convex systems with the Hausdorff metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02375","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":"sha256:9e920c7fe4031270ddbd5ee2a7a5fc5f75d39da638ca1cfce7e46bb8b72e54b7","target":"record","created_at":"2026-05-17T23:41:28Z","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":"8c7a21069a98a5140bf119bb5c3e81d1a6d57d469888f562c0438ff3641ba628","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-04T12:45:31Z","title_canon_sha256":"bdac8e1223b537d44333df617de244d7bcb20c124a92225d54a23f66daa9472b"},"schema_version":"1.0","source":{"id":"1907.02375","kind":"arxiv","version":1}},"canonical_sha256":"2ad260696b9f7128ad12c5aa7022e881b7517c86a77533740f337bed7ee82366","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ad260696b9f7128ad12c5aa7022e881b7517c86a77533740f337bed7ee82366","first_computed_at":"2026-05-17T23:41:28.774003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:28.774003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zu1fOcwupZh4/qde/IKrbcz1ARnm43Yo0Twm+kICWtcoRStgSD/zAeLMREYVIdg9u5VYanP0RjDg66+ABY4qBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:28.774671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e920c7fe4031270ddbd5ee2a7a5fc5f75d39da638ca1cfce7e46bb8b72e54b7","sha256:3bf4a157de5734b3f4cf437bf7aff248ddd9b80342b62cf638c9abc3bbe53523"],"state_sha256":"f21c2f9c338db2a0a60b79f4ebb38e558a2fbee6fbfacc10716e1603b097a2b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UYaCZngReP8Rs+9UrZuFJ/aAGHwAyQBHc0QM9WYlIC1qA2ewBXuFpmCXqmvpErQTegl4VS1aQj+f9fvRPHLRDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:56:49.613443Z","bundle_sha256":"587688e4138d57a81051b8a13d8dc0c41469b8b449042f106cd0e1e893ff9ad2"}}