{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:P64LSTQD5GRW6FSBZBI6SNLXMI","merge_version":"pith-open-graph-merge-v1","event_count":5,"valid_event_count":5,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"86358fed8f0b2c5b763c46a67567acd2db7861d37ea499e960bd86a0f3814076","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T15:50:40Z","title_canon_sha256":"5aa39333e0097b93ef5577f5d61f8beb309f0718bb37441e8ea24c6114e3911a"},"schema_version":"1.0","source":{"id":"2605.22644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22644","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22644v1","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22644","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"P64LSTQD5GRW","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"pith_short_16","alias_value":"P64LSTQD5GRW6FSB","created_at":"2026-05-22T02:04:47Z"},{"alias_kind":"pith_short_8","alias_value":"P64LSTQD","created_at":"2026-05-22T02:04:47Z"}],"graph_snapshots":[{"event_id":"sha256:48d38dca88793d03e3d0ce638b9111a0cb819463557ad30b6181e17b7033eea9","target":"graph","created_at":"2026-05-22T02:04:47Z","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/2605.22644/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Stochastic Gradient Descent (SGD) is commonly modeled as a Langevin process, assuming that minibatch noise acts as Brownian motion. However, this approximation relies on a continuous-time limit and a sqrt(eta) noise scaling that does not match the discrete SGD update at finite learning rate. In this work, we propose an alternative formulation of SGD as deterministic dynamics in a fluctuating loss landscape induced by minibatch sampling. Starting directly from the discrete update, we derive a master equation for the parameter distribution and obtain a discrete Fokker--Planck equation that diffe","authors_text":"Aleksandr Beznosikov, Aleksandr Kovalenko, Aleksandr Shestakov, Andrew Semenov, Andrey Leonidov, Andrey Veprikov, Anna Radovskaya, Egor Lopatin, Igor Ignashin, Stanislav Potapov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T15:50:40Z","title":"Why SGD is not Brownian Motion: A New Perspective on Stochastic Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22644","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:fe796f1e00f070f18bd74b3f40f98517928581d251121e93caaaa4200703be30","target":"record","created_at":"2026-05-22T02:04:47Z","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":"86358fed8f0b2c5b763c46a67567acd2db7861d37ea499e960bd86a0f3814076","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-21T15:50:40Z","title_canon_sha256":"5aa39333e0097b93ef5577f5d61f8beb309f0718bb37441e8ea24c6114e3911a"},"schema_version":"1.0","source":{"id":"2605.22644","kind":"arxiv","version":1}},"canonical_sha256":"7fb8b94e03e9a36f1641c851e93577622c50e8e817600ac9f0b0511b955db2a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fb8b94e03e9a36f1641c851e93577622c50e8e817600ac9f0b0511b955db2a1","first_computed_at":"2026-05-22T02:04:47.754035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T02:04:47.754035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cVao27D8qov53dxfL6iLwJgcdMkl4pjsV5Q+JvK1DiCN2kZF4ymssvUVtiPYg+yypP79LafNmMwbjCpJdXVZDw==","signature_status":"signed_v1","signed_at":"2026-05-22T02:04:47.754876Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22644","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:99cf121c9faff334d406a1bf442a9b11398c4ae2eb4a04562f5965e5daacd8bf","sha256:e0ae48472c5ecd3851d9540e849009d7dc8dd346d00327ad747573c92143994c","sha256:ee9a93891f92257553472a6d27f6f7a1e5a9617b3ad69f120f4e8cf248b0c146"]}],"invalid_events":[],"applied_event_ids":["sha256:fe796f1e00f070f18bd74b3f40f98517928581d251121e93caaaa4200703be30","sha256:48d38dca88793d03e3d0ce638b9111a0cb819463557ad30b6181e17b7033eea9"],"state_sha256":"7eb186424788180eb80c810c17c505ac02ebd8a21307cedd10423b8b12f2b691"}