{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PJT7TATLHK2CZ7MEUXSNZ3W6KS","short_pith_number":"pith:PJT7TATL","schema_version":"1.0","canonical_sha256":"7a67f9826b3ab42cfd84a5e4dceede54b32ba269763e82d72ba5138de1a0df68","source":{"kind":"arxiv","id":"1707.07766","version":1},"attestation_state":"computed","paper":{"title":"Second-oder analysis in second-oder cone programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Boris S. Mordukhovich, M. Ebrahim Sarabi, Nguyen T. V. Hang","submitted_at":"2017-07-24T22:47:57Z","abstract_excerpt":"The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone $Q$. From one hand, we prove that the indicator function of $Q$ is always twice epi-differentiable and apply this result to characterizing the uniqueness of Lagrange multipliers at stationary points together with an error bound estimate in the general second-order cone setting involving ${\\cal C}^2$-smooth data. On the other hand, we precisely calculate the graphical derivative of the normal cone mapping to $Q$ under the we"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.07766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-24T22:47:57Z","cross_cats_sorted":[],"title_canon_sha256":"20126a65357337481f9acf2f8d0a9339a5db17e47bb669e20afc7b860f990087","abstract_canon_sha256":"e92f2d13c2248ba0937c0ec295901c5a4b100b7aebd3faf049330d7ebe5dea2c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:30.476348Z","signature_b64":"q3Ln/81ChvGAQqy+ioz1rpLJIqMrsRYecEGMlS6h+276cU+pdBv/+UKLfIuIsjwU3ESj9gshlerG2eFmNHdFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a67f9826b3ab42cfd84a5e4dceede54b32ba269763e82d72ba5138de1a0df68","last_reissued_at":"2026-05-18T00:39:30.475710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:30.475710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second-oder analysis in second-oder cone programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Boris S. Mordukhovich, M. Ebrahim Sarabi, Nguyen T. V. Hang","submitted_at":"2017-07-24T22:47:57Z","abstract_excerpt":"The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone $Q$. From one hand, we prove that the indicator function of $Q$ is always twice epi-differentiable and apply this result to characterizing the uniqueness of Lagrange multipliers at stationary points together with an error bound estimate in the general second-order cone setting involving ${\\cal C}^2$-smooth data. On the other hand, we precisely calculate the graphical derivative of the normal cone mapping to $Q$ under the we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07766","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.07766","created_at":"2026-05-18T00:39:30.475808+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.07766v1","created_at":"2026-05-18T00:39:30.475808+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07766","created_at":"2026-05-18T00:39:30.475808+00:00"},{"alias_kind":"pith_short_12","alias_value":"PJT7TATLHK2C","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PJT7TATLHK2CZ7ME","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PJT7TATL","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PJT7TATLHK2CZ7MEUXSNZ3W6KS","json":"https://pith.science/pith/PJT7TATLHK2CZ7MEUXSNZ3W6KS.json","graph_json":"https://pith.science/api/pith-number/PJT7TATLHK2CZ7MEUXSNZ3W6KS/graph.json","events_json":"https://pith.science/api/pith-number/PJT7TATLHK2CZ7MEUXSNZ3W6KS/events.json","paper":"https://pith.science/paper/PJT7TATL"},"agent_actions":{"view_html":"https://pith.science/pith/PJT7TATLHK2CZ7MEUXSNZ3W6KS","download_json":"https://pith.science/pith/PJT7TATLHK2CZ7MEUXSNZ3W6KS.json","view_paper":"https://pith.science/paper/PJT7TATL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.07766&json=true","fetch_graph":"https://pith.science/api/pith-number/PJT7TATLHK2CZ7MEUXSNZ3W6KS/graph.json","fetch_events":"https://pith.science/api/pith-number/PJT7TATLHK2CZ7MEUXSNZ3W6KS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PJT7TATLHK2CZ7MEUXSNZ3W6KS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PJT7TATLHK2CZ7MEUXSNZ3W6KS/action/storage_attestation","attest_author":"https://pith.science/pith/PJT7TATLHK2CZ7MEUXSNZ3W6KS/action/author_attestation","sign_citation":"https://pith.science/pith/PJT7TATLHK2CZ7MEUXSNZ3W6KS/action/citation_signature","submit_replication":"https://pith.science/pith/PJT7TATLHK2CZ7MEUXSNZ3W6KS/action/replication_record"}},"created_at":"2026-05-18T00:39:30.475808+00:00","updated_at":"2026-05-18T00:39:30.475808+00:00"}