{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QPCVH735LUYW5RZOUTHBSGDU53","short_pith_number":"pith:QPCVH735","canonical_record":{"source":{"id":"1411.0209","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-02T06:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"d5d925c08746aa0d2de1c8b026ba44cc55f87dabb15da71f0707a37865d80776","abstract_canon_sha256":"80052372d60694bf0d1c51fd424a84c415b09ddc66d0e7838713a46b048d85d1"},"schema_version":"1.0"},"canonical_sha256":"83c553ff7d5d316ec72ea4ce191874eef6e4563434f76d0c5614249768adfde7","source":{"kind":"arxiv","id":"1411.0209","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0209","created_at":"2026-05-18T01:23:24Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0209v2","created_at":"2026-05-18T01:23:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0209","created_at":"2026-05-18T01:23:24Z"},{"alias_kind":"pith_short_12","alias_value":"QPCVH735LUYW","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QPCVH735LUYW5RZO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QPCVH735","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QPCVH735LUYW5RZOUTHBSGDU53","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0209","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-02T06:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"d5d925c08746aa0d2de1c8b026ba44cc55f87dabb15da71f0707a37865d80776","abstract_canon_sha256":"80052372d60694bf0d1c51fd424a84c415b09ddc66d0e7838713a46b048d85d1"},"schema_version":"1.0"},"canonical_sha256":"83c553ff7d5d316ec72ea4ce191874eef6e4563434f76d0c5614249768adfde7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:24.680743Z","signature_b64":"vaVYckZYIV6uWwQtobWnxVxbDFilwTJVgN8E5snEgAh+N3LC1/tTZLvkW15n8S9JjC2qdweoRnCWUn87CyGgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83c553ff7d5d316ec72ea4ce191874eef6e4563434f76d0c5614249768adfde7","last_reissued_at":"2026-05-18T01:23:24.680036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:24.680036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0209","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":"2026-05-18T01:23:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iFwRicxtJ+wKi4/q7EiYgFAQnwgCFP7551Eel+OMvhpmGDMt9VdaEv5zHJ6tF2RztMmAHShOzVbWD0BHwKzyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:18:35.898114Z"},"content_sha256":"665f09b148abec21d4a39dd861111f394e4deada14a82309802e16d066bad1d5","schema_version":"1.0","event_id":"sha256:665f09b148abec21d4a39dd861111f394e4deada14a82309802e16d066bad1d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QPCVH735LUYW5RZOUTHBSGDU53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Smoothing, Regularization and Averaging in Stochastic Approximation Methods for Stochastic Variational Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Angelia Nedi\\'c, Farzad Yousefian, Uday V. Shanbhag","submitted_at":"2014-11-02T06:03:20Z","abstract_excerpt":"Traditionally, stochastic approximation schemes for SVIs have relied on strong monotonicity and Lipschitzian properties of the underlying map. In contrast, we consider monotone stochastic variational inequality (SVI) problems where the strong monotonicity and Lipschitzian assumptions on the mappings are weakened. In the first part of the paper, to address such shortcomings, a regularized smoothed SA (RSSA) scheme is developed wherein the stepsize, smoothing, and regularization parameters are diminishing sequences updated after every iteration. Under suitable assumptions on the sequences, we sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0209","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":"2026-05-18T01:23:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wULKNu+3W2eVTXpGOga4aLy6PeBNLRsIyEvwv2/b1O/PqrWwoxVkVRAuVL/uc0YlpxWuqhumyMvJNv4xn2OCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:18:35.898760Z"},"content_sha256":"0ec4042f50b9630bf8ad5d1fddec9c381303aa842af593226dbfab587c8b09e7","schema_version":"1.0","event_id":"sha256:0ec4042f50b9630bf8ad5d1fddec9c381303aa842af593226dbfab587c8b09e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPCVH735LUYW5RZOUTHBSGDU53/bundle.json","state_url":"https://pith.science/pith/QPCVH735LUYW5RZOUTHBSGDU53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPCVH735LUYW5RZOUTHBSGDU53/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":"2026-06-12T05:18:35Z","links":{"resolver":"https://pith.science/pith/QPCVH735LUYW5RZOUTHBSGDU53","bundle":"https://pith.science/pith/QPCVH735LUYW5RZOUTHBSGDU53/bundle.json","state":"https://pith.science/pith/QPCVH735LUYW5RZOUTHBSGDU53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPCVH735LUYW5RZOUTHBSGDU53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QPCVH735LUYW5RZOUTHBSGDU53","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":"80052372d60694bf0d1c51fd424a84c415b09ddc66d0e7838713a46b048d85d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-02T06:03:20Z","title_canon_sha256":"d5d925c08746aa0d2de1c8b026ba44cc55f87dabb15da71f0707a37865d80776"},"schema_version":"1.0","source":{"id":"1411.0209","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0209","created_at":"2026-05-18T01:23:24Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0209v2","created_at":"2026-05-18T01:23:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0209","created_at":"2026-05-18T01:23:24Z"},{"alias_kind":"pith_short_12","alias_value":"QPCVH735LUYW","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QPCVH735LUYW5RZO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QPCVH735","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:0ec4042f50b9630bf8ad5d1fddec9c381303aa842af593226dbfab587c8b09e7","target":"graph","created_at":"2026-05-18T01:23:24Z","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":"Traditionally, stochastic approximation schemes for SVIs have relied on strong monotonicity and Lipschitzian properties of the underlying map. In contrast, we consider monotone stochastic variational inequality (SVI) problems where the strong monotonicity and Lipschitzian assumptions on the mappings are weakened. In the first part of the paper, to address such shortcomings, a regularized smoothed SA (RSSA) scheme is developed wherein the stepsize, smoothing, and regularization parameters are diminishing sequences updated after every iteration. Under suitable assumptions on the sequences, we sh","authors_text":"Angelia Nedi\\'c, Farzad Yousefian, Uday V. Shanbhag","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-02T06:03:20Z","title":"On Smoothing, Regularization and Averaging in Stochastic Approximation Methods for Stochastic Variational Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0209","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":"sha256:665f09b148abec21d4a39dd861111f394e4deada14a82309802e16d066bad1d5","target":"record","created_at":"2026-05-18T01:23:24Z","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":"80052372d60694bf0d1c51fd424a84c415b09ddc66d0e7838713a46b048d85d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-11-02T06:03:20Z","title_canon_sha256":"d5d925c08746aa0d2de1c8b026ba44cc55f87dabb15da71f0707a37865d80776"},"schema_version":"1.0","source":{"id":"1411.0209","kind":"arxiv","version":2}},"canonical_sha256":"83c553ff7d5d316ec72ea4ce191874eef6e4563434f76d0c5614249768adfde7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83c553ff7d5d316ec72ea4ce191874eef6e4563434f76d0c5614249768adfde7","first_computed_at":"2026-05-18T01:23:24.680036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:24.680036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vaVYckZYIV6uWwQtobWnxVxbDFilwTJVgN8E5snEgAh+N3LC1/tTZLvkW15n8S9JjC2qdweoRnCWUn87CyGgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:24.680743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0209","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:665f09b148abec21d4a39dd861111f394e4deada14a82309802e16d066bad1d5","sha256:0ec4042f50b9630bf8ad5d1fddec9c381303aa842af593226dbfab587c8b09e7"],"state_sha256":"1ce99edfaef46b28727834ea2a70733a344a7648ce3bab44f2d14088f2949ee5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Ym+sD54wHEQN99DyRe+rzU5SUMC8YROXGaE7/TIcEbjlehM2N26aCqmN/jCUg3/ZVBiEl5LHEWw95nlZPuaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:18:35.902252Z","bundle_sha256":"459a8ad5b737aea862723a1516f40770d02133846e9bcd86398858afdefc27e9"}}