{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FODOHLFFE56F7R3AFQ2YMV5CJH","short_pith_number":"pith:FODOHLFF","canonical_record":{"source":{"id":"1412.8063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-27T15:39:30Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.PR"],"title_canon_sha256":"662653442a956640d0ef83508bd667fba144e180fc866c0274cd54d6d19766fa","abstract_canon_sha256":"ad15d56bdd53236853c4efae6292beb6e45a6e85d3700169a3d9cea63184b46e"},"schema_version":"1.0"},"canonical_sha256":"2b86e3aca5277c5fc7602c358657a249ef6257836d14951a3d9f8dc42da19d48","source":{"kind":"arxiv","id":"1412.8063","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8063","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8063v2","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8063","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"FODOHLFFE56F","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FODOHLFFE56F7R3A","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FODOHLFF","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FODOHLFFE56F7R3AFQ2YMV5CJH","target":"record","payload":{"canonical_record":{"source":{"id":"1412.8063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-27T15:39:30Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.PR"],"title_canon_sha256":"662653442a956640d0ef83508bd667fba144e180fc866c0274cd54d6d19766fa","abstract_canon_sha256":"ad15d56bdd53236853c4efae6292beb6e45a6e85d3700169a3d9cea63184b46e"},"schema_version":"1.0"},"canonical_sha256":"2b86e3aca5277c5fc7602c358657a249ef6257836d14951a3d9f8dc42da19d48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:58.700103Z","signature_b64":"BysYjGHktLnyxB6V+XkqUx5WPHS9gLIXSo2uEzjtGq58VX0kX3SGeUIuuAd+aJpQG7Gr4X36PFRf/vO57RnIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b86e3aca5277c5fc7602c358657a249ef6257836d14951a3d9f8dc42da19d48","last_reissued_at":"2026-05-18T02:00:58.699565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:58.699565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.8063","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":"2026-05-18T02:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"agR/QMvr9vsMUsL0VlMHKtq4TSN1CqKV4ChDwF/19SXgnxLKJgeiUSb+zd+n6FpG0iV9CgdHSxZpZ/5qlxb1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T02:08:11.687950Z"},"content_sha256":"1203e0dce06ff0ca986d6df70f4ded11aad5b6a8212e0a2aca8120a7fa4eed0f","schema_version":"1.0","event_id":"sha256:1203e0dce06ff0ca986d6df70f4ded11aad5b6a8212e0a2aca8120a7fa4eed0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FODOHLFFE56F7R3AFQ2YMV5CJH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coordinate Descent with Arbitrary Sampling II: Expected Separable Overapproximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","math.PR"],"primary_cat":"math.OC","authors_text":"Peter Richt\\'arik, Zheng Qu","submitted_at":"2014-12-27T15:39:30Z","abstract_excerpt":"The design and complexity analysis of randomized coordinate descent methods, and in particular of variants which update a random subset (sampling) of coordinates in each iteration, depends on the notion of expected separable overapproximation (ESO). This refers to an inequality involving the objective function and the sampling, capturing in a compact way certain smoothness properties of the function in a random subspace spanned by the sampled coordinates. ESO inequalities were previously established for special classes of samplings only, almost invariably for uniform samplings. In this paper w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8063","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":"2026-05-18T02:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Gy1MF0+6jnpkyCGGHneWnueXumi3z77w6Bejvm16AASFj0qJxP8rfTtXqU4yTo6VZkXzmD1X6Rp7IvgKcGDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T02:08:11.688613Z"},"content_sha256":"ac8e3667e9cb03e8b6355e2f1bfdb5c75f91a2248caabffbad190fbc9a1fb44f","schema_version":"1.0","event_id":"sha256:ac8e3667e9cb03e8b6355e2f1bfdb5c75f91a2248caabffbad190fbc9a1fb44f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FODOHLFFE56F7R3AFQ2YMV5CJH/bundle.json","state_url":"https://pith.science/pith/FODOHLFFE56F7R3AFQ2YMV5CJH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FODOHLFFE56F7R3AFQ2YMV5CJH/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":"2026-05-24T02:08:11Z","links":{"resolver":"https://pith.science/pith/FODOHLFFE56F7R3AFQ2YMV5CJH","bundle":"https://pith.science/pith/FODOHLFFE56F7R3AFQ2YMV5CJH/bundle.json","state":"https://pith.science/pith/FODOHLFFE56F7R3AFQ2YMV5CJH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FODOHLFFE56F7R3AFQ2YMV5CJH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FODOHLFFE56F7R3AFQ2YMV5CJH","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":"ad15d56bdd53236853c4efae6292beb6e45a6e85d3700169a3d9cea63184b46e","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-27T15:39:30Z","title_canon_sha256":"662653442a956640d0ef83508bd667fba144e180fc866c0274cd54d6d19766fa"},"schema_version":"1.0","source":{"id":"1412.8063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8063","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8063v2","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8063","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"FODOHLFFE56F","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FODOHLFFE56F7R3A","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FODOHLFF","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:ac8e3667e9cb03e8b6355e2f1bfdb5c75f91a2248caabffbad190fbc9a1fb44f","target":"graph","created_at":"2026-05-18T02:00:58Z","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 design and complexity analysis of randomized coordinate descent methods, and in particular of variants which update a random subset (sampling) of coordinates in each iteration, depends on the notion of expected separable overapproximation (ESO). This refers to an inequality involving the objective function and the sampling, capturing in a compact way certain smoothness properties of the function in a random subspace spanned by the sampled coordinates. ESO inequalities were previously established for special classes of samplings only, almost invariably for uniform samplings. In this paper w","authors_text":"Peter Richt\\'arik, Zheng Qu","cross_cats":["cs.LG","cs.NA","math.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-27T15:39:30Z","title":"Coordinate Descent with Arbitrary Sampling II: Expected Separable Overapproximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8063","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":"sha256:1203e0dce06ff0ca986d6df70f4ded11aad5b6a8212e0a2aca8120a7fa4eed0f","target":"record","created_at":"2026-05-18T02:00:58Z","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":"ad15d56bdd53236853c4efae6292beb6e45a6e85d3700169a3d9cea63184b46e","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-27T15:39:30Z","title_canon_sha256":"662653442a956640d0ef83508bd667fba144e180fc866c0274cd54d6d19766fa"},"schema_version":"1.0","source":{"id":"1412.8063","kind":"arxiv","version":2}},"canonical_sha256":"2b86e3aca5277c5fc7602c358657a249ef6257836d14951a3d9f8dc42da19d48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b86e3aca5277c5fc7602c358657a249ef6257836d14951a3d9f8dc42da19d48","first_computed_at":"2026-05-18T02:00:58.699565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:58.699565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BysYjGHktLnyxB6V+XkqUx5WPHS9gLIXSo2uEzjtGq58VX0kX3SGeUIuuAd+aJpQG7Gr4X36PFRf/vO57RnIAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:58.700103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.8063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1203e0dce06ff0ca986d6df70f4ded11aad5b6a8212e0a2aca8120a7fa4eed0f","sha256:ac8e3667e9cb03e8b6355e2f1bfdb5c75f91a2248caabffbad190fbc9a1fb44f"],"state_sha256":"cff99612a763bed9dd2fbf1ef2471753479e441bea973c3b99cdeae68a3dfef9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"myqdyaEQvVjLGCRybUcAnc3+6fiN+484DT+1V5+ScR0sfbnqY1JeskW/QDzwWVJQSse9GuVS/6ENswfKzzDEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T02:08:11.691588Z","bundle_sha256":"a058ee2ab5987dbea668f93fab62ce461efc28b453780b4ca7a3d86d76d25e38"}}