{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:W2O55AEOCXBFBSGKKCXFXYVRWG","short_pith_number":"pith:W2O55AEO","canonical_record":{"source":{"id":"1710.10187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-27T15:03:11Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"616b8db255f4baecec2275b0219a3c5f7e4cb028c77e9c50167b2ed01a77823e","abstract_canon_sha256":"563678ee555e675ff2a4d25f274e3fb9c9deadc70f90c5c4efd11af7639e4489"},"schema_version":"1.0"},"canonical_sha256":"b69dde808e15c250c8ca50ae5be2b1b1adebb9b4ad4e8dc94574e95ce0cbe258","source":{"kind":"arxiv","id":"1710.10187","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10187","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10187v1","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10187","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"pith_short_12","alias_value":"W2O55AEOCXBF","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"W2O55AEOCXBFBSGK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"W2O55AEO","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:W2O55AEOCXBFBSGKKCXFXYVRWG","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-27T15:03:11Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"616b8db255f4baecec2275b0219a3c5f7e4cb028c77e9c50167b2ed01a77823e","abstract_canon_sha256":"563678ee555e675ff2a4d25f274e3fb9c9deadc70f90c5c4efd11af7639e4489"},"schema_version":"1.0"},"canonical_sha256":"b69dde808e15c250c8ca50ae5be2b1b1adebb9b4ad4e8dc94574e95ce0cbe258","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:54.570142Z","signature_b64":"jH4Zg8l4VlTuSfgfubhTARoRyWk6A3GTARFkWwhpmFFiIiygAZ6052v/kBTQhu2F5bRvS+JRKSpwhnXByUdBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b69dde808e15c250c8ca50ae5be2b1b1adebb9b4ad4e8dc94574e95ce0cbe258","last_reissued_at":"2026-05-18T00:31:54.569712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:54.569712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10187","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":"2026-05-18T00:31:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X39dsrjFx9c9Pj1G+uFUQlWyNaTyFbi1bxuQCVRDNUK5mP36CDIgXAsyxDSDHFY8wW1UwCrvrxsGbeYMQwX6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:20:14.718856Z"},"content_sha256":"5ada161dba9b2ee6f051aeba2d516935b6401d88808ea969429c53875aaa86f1","schema_version":"1.0","event_id":"sha256:5ada161dba9b2ee6f051aeba2d516935b6401d88808ea969429c53875aaa86f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:W2O55AEOCXBFBSGKKCXFXYVRWG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general representation of delta-normal sets to sublevels of convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OC","authors_text":"Abderrahim Hantoute, Anton Svensson","submitted_at":"2017-10-27T15:03:11Z","abstract_excerpt":"The (delta-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either epsilon-subdifferentials at the nominal point or exact subdifferentials at nearby points. Our tools include (epsilon-) calculus rules for sup/max functions. The framework of this work is that of a locally convex space, however, formulas using exact subdifferentials require some restriction either on the space (e.g. Banach), or on the function (e.g. epi-pointed)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10187","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":"2026-05-18T00:31:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2K+DTykthG+ZulqvfMJbQQBMhYqxhGNbG0DcyqE5kjOs5powDtOb+JpVCEhDkGc3cfBo3BmX0enXugJZjf7yDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:20:14.719576Z"},"content_sha256":"5f4f77fda9560f510f7c7e06fa2db9169c2309f569c60850b6589e874bf3d927","schema_version":"1.0","event_id":"sha256:5f4f77fda9560f510f7c7e06fa2db9169c2309f569c60850b6589e874bf3d927"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2O55AEOCXBFBSGKKCXFXYVRWG/bundle.json","state_url":"https://pith.science/pith/W2O55AEOCXBFBSGKKCXFXYVRWG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2O55AEOCXBFBSGKKCXFXYVRWG/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":"2026-06-09T19:20:14Z","links":{"resolver":"https://pith.science/pith/W2O55AEOCXBFBSGKKCXFXYVRWG","bundle":"https://pith.science/pith/W2O55AEOCXBFBSGKKCXFXYVRWG/bundle.json","state":"https://pith.science/pith/W2O55AEOCXBFBSGKKCXFXYVRWG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2O55AEOCXBFBSGKKCXFXYVRWG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:W2O55AEOCXBFBSGKKCXFXYVRWG","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":"563678ee555e675ff2a4d25f274e3fb9c9deadc70f90c5c4efd11af7639e4489","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-27T15:03:11Z","title_canon_sha256":"616b8db255f4baecec2275b0219a3c5f7e4cb028c77e9c50167b2ed01a77823e"},"schema_version":"1.0","source":{"id":"1710.10187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10187","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10187v1","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10187","created_at":"2026-05-18T00:31:54Z"},{"alias_kind":"pith_short_12","alias_value":"W2O55AEOCXBF","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"W2O55AEOCXBFBSGK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"W2O55AEO","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:5f4f77fda9560f510f7c7e06fa2db9169c2309f569c60850b6589e874bf3d927","target":"graph","created_at":"2026-05-18T00:31:54Z","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":"The (delta-) normal cone to an arbitrary intersection of sublevel sets of proper, lower semicontinuous, and convex functions is characterized, using either epsilon-subdifferentials at the nominal point or exact subdifferentials at nearby points. Our tools include (epsilon-) calculus rules for sup/max functions. The framework of this work is that of a locally convex space, however, formulas using exact subdifferentials require some restriction either on the space (e.g. Banach), or on the function (e.g. epi-pointed).","authors_text":"Abderrahim Hantoute, Anton Svensson","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-27T15:03:11Z","title":"A general representation of delta-normal sets to sublevels of convex functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10187","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":"sha256:5ada161dba9b2ee6f051aeba2d516935b6401d88808ea969429c53875aaa86f1","target":"record","created_at":"2026-05-18T00:31:54Z","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":"563678ee555e675ff2a4d25f274e3fb9c9deadc70f90c5c4efd11af7639e4489","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-27T15:03:11Z","title_canon_sha256":"616b8db255f4baecec2275b0219a3c5f7e4cb028c77e9c50167b2ed01a77823e"},"schema_version":"1.0","source":{"id":"1710.10187","kind":"arxiv","version":1}},"canonical_sha256":"b69dde808e15c250c8ca50ae5be2b1b1adebb9b4ad4e8dc94574e95ce0cbe258","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b69dde808e15c250c8ca50ae5be2b1b1adebb9b4ad4e8dc94574e95ce0cbe258","first_computed_at":"2026-05-18T00:31:54.569712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:54.569712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jH4Zg8l4VlTuSfgfubhTARoRyWk6A3GTARFkWwhpmFFiIiygAZ6052v/kBTQhu2F5bRvS+JRKSpwhnXByUdBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:54.570142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ada161dba9b2ee6f051aeba2d516935b6401d88808ea969429c53875aaa86f1","sha256:5f4f77fda9560f510f7c7e06fa2db9169c2309f569c60850b6589e874bf3d927"],"state_sha256":"38fd402833b180ffc38d1eb07284d948e0f055e5137e0513c739db0fb0834f97"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zzdE0oagIh6E2rEOPrRLJyGVw57rcr7wPDN+aw7s2C7AFY+Rpk3BBn3Q1cz3QTSYC4VG+fFtfpruxazRSXKDAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:20:14.723578Z","bundle_sha256":"19637854dbffb84d5a421974c9fc74ce988e4f9e51aab56ab6dd41851f59baa9"}}