{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YZWRBWKWWTHSLMDCEWI7UT4ORV","short_pith_number":"pith:YZWRBWKW","canonical_record":{"source":{"id":"1212.4507","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-12-18T21:06:10Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"b6470250bc93114b5c5e8858ac130b247e0adf70ee466da7de75f5d617595e0d","abstract_canon_sha256":"4abcf68dea8bf20ef9de8406e6abcd642ae2694e006c5d6f6bb6dd8c20932e11"},"schema_version":"1.0"},"canonical_sha256":"c66d10d956b4cf25b0622591fa4f8e8d70a5d4ea2a2f1f1fa6217b9781acad3c","source":{"kind":"arxiv","id":"1212.4507","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4507","created_at":"2026-05-18T03:38:03Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4507v2","created_at":"2026-05-18T03:38:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4507","created_at":"2026-05-18T03:38:03Z"},{"alias_kind":"pith_short_12","alias_value":"YZWRBWKWWTHS","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YZWRBWKWWTHSLMDC","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YZWRBWKW","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YZWRBWKWWTHSLMDCEWI7UT4ORV","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4507","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-12-18T21:06:10Z","cross_cats_sorted":["cs.LG","cs.NA"],"title_canon_sha256":"b6470250bc93114b5c5e8858ac130b247e0adf70ee466da7de75f5d617595e0d","abstract_canon_sha256":"4abcf68dea8bf20ef9de8406e6abcd642ae2694e006c5d6f6bb6dd8c20932e11"},"schema_version":"1.0"},"canonical_sha256":"c66d10d956b4cf25b0622591fa4f8e8d70a5d4ea2a2f1f1fa6217b9781acad3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:03.298246Z","signature_b64":"GKyWNeogkbv5eZMZAv1Zl8oNmikRqNwT876OM2Z9AGIxGgMypVh8XhBZB6lgl2qTSs+H2BVMCrNuBYyNr5XfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c66d10d956b4cf25b0622591fa4f8e8d70a5d4ea2a2f1f1fa6217b9781acad3c","last_reissued_at":"2026-05-18T03:38:03.297610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:03.297610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4507","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":"2026-05-18T03:38:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"03JFMugzpSN6mF+NFVkDaz8ZEZwl+9RZQdXbCukigu0lxY4vkthVs2mrv+j06gInLmJjh4Giquhk19EBj037CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:26:12.461596Z"},"content_sha256":"54ace9ccf23859d23fe32526b99e5d1046495895295c086cc0ef19de2e72fc69","schema_version":"1.0","event_id":"sha256:54ace9ccf23859d23fe32526b99e5d1046495895295c086cc0ef19de2e72fc69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YZWRBWKWWTHSLMDCEWI7UT4ORV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA"],"primary_cat":"stat.ML","authors_text":"David Barber, Joe Staines","submitted_at":"2012-12-18T21:06:10Z","abstract_excerpt":"We discuss a general technique that can be used to form a differentiable bound on the optima of non-differentiable or discrete objective functions. We form a unified description of these methods and consider under which circumstances the bound is concave. In particular we consider two concrete applications of the method, namely sparse learning and support vector classification."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4507","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":"2026-05-18T03:38:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tcQ6oXf3o0DquU6ZhsNpbC99PEq1LPJ4o9cPWgrbEjAIqNpdPFg3u9op6zlDu8uSpFk8HPfBF/oRKS0Ce47ZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:26:12.462343Z"},"content_sha256":"0ac7e7dcc127e2eb6991e124003f148bca0b03d07822e357975ff73e61136422","schema_version":"1.0","event_id":"sha256:0ac7e7dcc127e2eb6991e124003f148bca0b03d07822e357975ff73e61136422"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZWRBWKWWTHSLMDCEWI7UT4ORV/bundle.json","state_url":"https://pith.science/pith/YZWRBWKWWTHSLMDCEWI7UT4ORV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZWRBWKWWTHSLMDCEWI7UT4ORV/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":"2026-05-26T13:26:12Z","links":{"resolver":"https://pith.science/pith/YZWRBWKWWTHSLMDCEWI7UT4ORV","bundle":"https://pith.science/pith/YZWRBWKWWTHSLMDCEWI7UT4ORV/bundle.json","state":"https://pith.science/pith/YZWRBWKWWTHSLMDCEWI7UT4ORV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZWRBWKWWTHSLMDCEWI7UT4ORV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YZWRBWKWWTHSLMDCEWI7UT4ORV","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":"4abcf68dea8bf20ef9de8406e6abcd642ae2694e006c5d6f6bb6dd8c20932e11","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-12-18T21:06:10Z","title_canon_sha256":"b6470250bc93114b5c5e8858ac130b247e0adf70ee466da7de75f5d617595e0d"},"schema_version":"1.0","source":{"id":"1212.4507","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4507","created_at":"2026-05-18T03:38:03Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4507v2","created_at":"2026-05-18T03:38:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4507","created_at":"2026-05-18T03:38:03Z"},{"alias_kind":"pith_short_12","alias_value":"YZWRBWKWWTHS","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YZWRBWKWWTHSLMDC","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YZWRBWKW","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:0ac7e7dcc127e2eb6991e124003f148bca0b03d07822e357975ff73e61136422","target":"graph","created_at":"2026-05-18T03:38:03Z","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 discuss a general technique that can be used to form a differentiable bound on the optima of non-differentiable or discrete objective functions. We form a unified description of these methods and consider under which circumstances the bound is concave. In particular we consider two concrete applications of the method, namely sparse learning and support vector classification.","authors_text":"David Barber, Joe Staines","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-12-18T21:06:10Z","title":"Variational Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4507","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":"sha256:54ace9ccf23859d23fe32526b99e5d1046495895295c086cc0ef19de2e72fc69","target":"record","created_at":"2026-05-18T03:38:03Z","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":"4abcf68dea8bf20ef9de8406e6abcd642ae2694e006c5d6f6bb6dd8c20932e11","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2012-12-18T21:06:10Z","title_canon_sha256":"b6470250bc93114b5c5e8858ac130b247e0adf70ee466da7de75f5d617595e0d"},"schema_version":"1.0","source":{"id":"1212.4507","kind":"arxiv","version":2}},"canonical_sha256":"c66d10d956b4cf25b0622591fa4f8e8d70a5d4ea2a2f1f1fa6217b9781acad3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c66d10d956b4cf25b0622591fa4f8e8d70a5d4ea2a2f1f1fa6217b9781acad3c","first_computed_at":"2026-05-18T03:38:03.297610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:03.297610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GKyWNeogkbv5eZMZAv1Zl8oNmikRqNwT876OM2Z9AGIxGgMypVh8XhBZB6lgl2qTSs+H2BVMCrNuBYyNr5XfCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:03.298246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4507","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54ace9ccf23859d23fe32526b99e5d1046495895295c086cc0ef19de2e72fc69","sha256:0ac7e7dcc127e2eb6991e124003f148bca0b03d07822e357975ff73e61136422"],"state_sha256":"da5308eb90fd89cd5687643593181ae70f17fd877f6e2849645a28a0d3c8ac9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GY9t6aG9reOzIn72gxS5vQ4w4S6/syDR4E6Td/4ZmdpaAHHGiaB7o/gzCarO6aXQiYpll5+zuYODxv6XkuWqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:26:12.466350Z","bundle_sha256":"f3cfcae9e8f09e7e381f0e5cca829d3dcab34b6ecd9427fe776a4a09e53be10c"}}