{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:B3UJFLBD7XNORSLYOKS57KPRKW","short_pith_number":"pith:B3UJFLBD","canonical_record":{"source":{"id":"2608.06182","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-08-06T15:42:40Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a1574b6569d6c976377ecd880067b8a06b1b17d46b0d1b59450e59a1c4e96bed","abstract_canon_sha256":"e735a009f22b48262f2fd7230b116c06c31edcc3988e91c6e41d25248caceb11"},"schema_version":"1.0"},"canonical_sha256":"0ee892ac23fddae8c97872a5dfa9f155a5c3d927e26a98d1c928042ad8fe5303","source":{"kind":"arxiv","id":"2608.06182","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06182","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06182v1","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06182","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"B3UJFLBD7XNO","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"pith_short_16","alias_value":"B3UJFLBD7XNORSLY","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"pith_short_8","alias_value":"B3UJFLBD","created_at":"2026-08-07T01:40:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:B3UJFLBD7XNORSLYOKS57KPRKW","target":"record","payload":{"canonical_record":{"source":{"id":"2608.06182","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-08-06T15:42:40Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a1574b6569d6c976377ecd880067b8a06b1b17d46b0d1b59450e59a1c4e96bed","abstract_canon_sha256":"e735a009f22b48262f2fd7230b116c06c31edcc3988e91c6e41d25248caceb11"},"schema_version":"1.0"},"canonical_sha256":"0ee892ac23fddae8c97872a5dfa9f155a5c3d927e26a98d1c928042ad8fe5303","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T01:40:53.528873Z","signature_b64":"D7vK9SJiaUYedPo4+MNnXBl9FofD2us/3x9rK93Xl4owtVvFdIkRWhq89GozpXP5QtsoQ3CuiVFnP3pWjiRZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ee892ac23fddae8c97872a5dfa9f155a5c3d927e26a98d1c928042ad8fe5303","last_reissued_at":"2026-08-07T01:40:53.527166Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T01:40:53.527166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.06182","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":"2026-08-07T01:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pAOuO9bp05VX6TLAyh6vbQQQysiJcFvC6C0b9e6vEbV2ADI5rDuV+5ka5k4OJ9lObnpk2cxR7Zppsobn6hzCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:43:57.997546Z"},"content_sha256":"f359ffd442a467fe4afa8b8113923ba9052a44aab2004120e598a09376144299","schema_version":"1.0","event_id":"sha256:f359ffd442a467fe4afa8b8113923ba9052a44aab2004120e598a09376144299"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:B3UJFLBD7XNORSLYOKS57KPRKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Nicolas Loizou, TaeHo Yoon","submitted_at":"2026-08-06T15:42:40Z","abstract_excerpt":"We study stochastic extragradient (SEG) methods for solving monotone variational inequality problems (VIPs) over a feasible set. Although extragradient is a foundational algorithm for VIPs and its deterministic convergence theory is well developed, its stochastic counterpart remains less understood. Most existing analyses focus on independent-sample SEG (I-SEG) and assume either that the domain is compact or that the variance of the stochastic operator is uniformly bounded. The behavior of same-sample SEG (S-SEG), a natural variant with materially different properties, has received far less at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06182","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.06182/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-07T01:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rJ0UHBfRsSjOX3pqNI9L/rF3qWBoRIJWUfkbOG5aKwVrwi1iMfjSd3IbBQSmnYnKITFk05LB47e/ZlJPmTq1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:43:57.998085Z"},"content_sha256":"bc6e8871696f466435992b792d7047d99f2724fca4c83bc25a182ca63a4ecea9","schema_version":"1.0","event_id":"sha256:bc6e8871696f466435992b792d7047d99f2724fca4c83bc25a182ca63a4ecea9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3UJFLBD7XNORSLYOKS57KPRKW/bundle.json","state_url":"https://pith.science/pith/B3UJFLBD7XNORSLYOKS57KPRKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3UJFLBD7XNORSLYOKS57KPRKW/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":"2026-08-08T11:43:58Z","links":{"resolver":"https://pith.science/pith/B3UJFLBD7XNORSLYOKS57KPRKW","bundle":"https://pith.science/pith/B3UJFLBD7XNORSLYOKS57KPRKW/bundle.json","state":"https://pith.science/pith/B3UJFLBD7XNORSLYOKS57KPRKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3UJFLBD7XNORSLYOKS57KPRKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:B3UJFLBD7XNORSLYOKS57KPRKW","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":"e735a009f22b48262f2fd7230b116c06c31edcc3988e91c6e41d25248caceb11","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-08-06T15:42:40Z","title_canon_sha256":"a1574b6569d6c976377ecd880067b8a06b1b17d46b0d1b59450e59a1c4e96bed"},"schema_version":"1.0","source":{"id":"2608.06182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06182","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06182v1","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06182","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"B3UJFLBD7XNO","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"pith_short_16","alias_value":"B3UJFLBD7XNORSLY","created_at":"2026-08-07T01:40:53Z"},{"alias_kind":"pith_short_8","alias_value":"B3UJFLBD","created_at":"2026-08-07T01:40:53Z"}],"graph_snapshots":[{"event_id":"sha256:bc6e8871696f466435992b792d7047d99f2724fca4c83bc25a182ca63a4ecea9","target":"graph","created_at":"2026-08-07T01:40:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.06182/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study stochastic extragradient (SEG) methods for solving monotone variational inequality problems (VIPs) over a feasible set. Although extragradient is a foundational algorithm for VIPs and its deterministic convergence theory is well developed, its stochastic counterpart remains less understood. Most existing analyses focus on independent-sample SEG (I-SEG) and assume either that the domain is compact or that the variance of the stochastic operator is uniformly bounded. The behavior of same-sample SEG (S-SEG), a natural variant with materially different properties, has received far less at","authors_text":"Nicolas Loizou, TaeHo Yoon","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-08-06T15:42:40Z","title":"On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06182","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:f359ffd442a467fe4afa8b8113923ba9052a44aab2004120e598a09376144299","target":"record","created_at":"2026-08-07T01:40:53Z","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":"e735a009f22b48262f2fd7230b116c06c31edcc3988e91c6e41d25248caceb11","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-08-06T15:42:40Z","title_canon_sha256":"a1574b6569d6c976377ecd880067b8a06b1b17d46b0d1b59450e59a1c4e96bed"},"schema_version":"1.0","source":{"id":"2608.06182","kind":"arxiv","version":1}},"canonical_sha256":"0ee892ac23fddae8c97872a5dfa9f155a5c3d927e26a98d1c928042ad8fe5303","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ee892ac23fddae8c97872a5dfa9f155a5c3d927e26a98d1c928042ad8fe5303","first_computed_at":"2026-08-07T01:40:53.527166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T01:40:53.527166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D7vK9SJiaUYedPo4+MNnXBl9FofD2us/3x9rK93Xl4owtVvFdIkRWhq89GozpXP5QtsoQ3CuiVFnP3pWjiRZCQ==","signature_status":"signed_v1","signed_at":"2026-08-07T01:40:53.528873Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f359ffd442a467fe4afa8b8113923ba9052a44aab2004120e598a09376144299","sha256:bc6e8871696f466435992b792d7047d99f2724fca4c83bc25a182ca63a4ecea9"],"state_sha256":"14073b86e54c88ddc67710509b466dd885ebe9b761c47fafdd9dd96e263ef822"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aLPZL/6268UpnJ5Qq+GCenyiyCuT2oJCHooLsb70wPb2nqUkU9g16JH8AEbbCaHJfzFVs5t5N4Z6wZRa6R0wCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T11:43:58.002258Z","bundle_sha256":"1739a82da4301a853c41eb37e2c1546a2bf16510fd1b11a209bb2a59c46a5f08"}}