{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NCDJSOBUMEHEEI6Y536UN23RYE","short_pith_number":"pith:NCDJSOBU","canonical_record":{"source":{"id":"2505.21394","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-27T16:23:23Z","cross_cats_sorted":[],"title_canon_sha256":"9c96e6d739a4231d52281dbe3cf5453ae4ce91405f197b66efdeb3627e6b9b44","abstract_canon_sha256":"f6837c40d2b729c7f399ce457edc8820db026144846caae6d7ec47d9598fcd83"},"schema_version":"1.0"},"canonical_sha256":"6886993834610e4223d8eefd46eb71c10cdf7c768004d241aa44f0e988b664a4","source":{"kind":"arxiv","id":"2505.21394","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21394","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21394v1","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21394","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"NCDJSOBUMEHE","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"NCDJSOBUMEHEEI6Y","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"NCDJSOBU","created_at":"2026-07-05T11:10:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NCDJSOBUMEHEEI6Y536UN23RYE","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21394","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-27T16:23:23Z","cross_cats_sorted":[],"title_canon_sha256":"9c96e6d739a4231d52281dbe3cf5453ae4ce91405f197b66efdeb3627e6b9b44","abstract_canon_sha256":"f6837c40d2b729c7f399ce457edc8820db026144846caae6d7ec47d9598fcd83"},"schema_version":"1.0"},"canonical_sha256":"6886993834610e4223d8eefd46eb71c10cdf7c768004d241aa44f0e988b664a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:41.348788Z","signature_b64":"cLck2DeDuxog4bzFjqBaO/3/Q0pJsKuRM7Ds2EvC9dj99hT+QQt1CM/cFicDaOZD8nJ9QH8f/SxhODnMt/UEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6886993834610e4223d8eefd46eb71c10cdf7c768004d241aa44f0e988b664a4","last_reissued_at":"2026-07-05T11:10:41.348269Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:41.348269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21394","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":"2026-07-05T11:10:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YHNGD3DDtt4w9cgCd+2gMB4Oh2e2PVXK+usu+6DGrezf/WE9eBDZLXlgo7zvRlpe+WavFQTp0iJ27ECQAUFjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:37:26.963004Z"},"content_sha256":"47b4f0c0f6b2f0ec23e117679509ed08d487cdb3db1db821cffc7f28cad8378f","schema_version":"1.0","event_id":"sha256:47b4f0c0f6b2f0ec23e117679509ed08d487cdb3db1db821cffc7f28cad8378f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NCDJSOBUMEHEEI6Y536UN23RYE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dual Averaging Converges for Nonconvex Smooth Stochastic Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"El Mehdi Saad, Francesco Orabona, Tuo Liu, Wojciech Kot{\\l}owski","submitted_at":"2025-05-27T16:23:23Z","abstract_excerpt":"Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these algorithms have been deeply studied, and we know that they are essentially equivalent in terms of theoretical guarantees. On the other hand, in the non-convex setting, the situation is drastically different: While we know that SGD can minimize the gradient of non-convex smooth functions, no finite-time complexity guarantee for Stochastic Dual Averaging (SDA) wa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21394","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/2505.21394/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":"2026-07-05T11:10:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dcREFzF0KYQVpzvzcRzL1MS+lxFTZrFrsAQeLkN6J4h8L1y0TWTpZJHoxBjqyPizDCOyyWf6pQ755lrY8VHxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:37:26.964127Z"},"content_sha256":"c5ddffbee84400b69993459900afc93b17d71235de150aa19f2b57160a8a2bd3","schema_version":"1.0","event_id":"sha256:c5ddffbee84400b69993459900afc93b17d71235de150aa19f2b57160a8a2bd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NCDJSOBUMEHEEI6Y536UN23RYE/bundle.json","state_url":"https://pith.science/pith/NCDJSOBUMEHEEI6Y536UN23RYE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NCDJSOBUMEHEEI6Y536UN23RYE/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":"2026-08-07T12:37:26Z","links":{"resolver":"https://pith.science/pith/NCDJSOBUMEHEEI6Y536UN23RYE","bundle":"https://pith.science/pith/NCDJSOBUMEHEEI6Y536UN23RYE/bundle.json","state":"https://pith.science/pith/NCDJSOBUMEHEEI6Y536UN23RYE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NCDJSOBUMEHEEI6Y536UN23RYE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NCDJSOBUMEHEEI6Y536UN23RYE","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":"f6837c40d2b729c7f399ce457edc8820db026144846caae6d7ec47d9598fcd83","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-27T16:23:23Z","title_canon_sha256":"9c96e6d739a4231d52281dbe3cf5453ae4ce91405f197b66efdeb3627e6b9b44"},"schema_version":"1.0","source":{"id":"2505.21394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21394","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21394v1","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21394","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"NCDJSOBUMEHE","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"NCDJSOBUMEHEEI6Y","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"NCDJSOBU","created_at":"2026-07-05T11:10:41Z"}],"graph_snapshots":[{"event_id":"sha256:c5ddffbee84400b69993459900afc93b17d71235de150aa19f2b57160a8a2bd3","target":"graph","created_at":"2026-07-05T11:10:41Z","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/2505.21394/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these algorithms have been deeply studied, and we know that they are essentially equivalent in terms of theoretical guarantees. On the other hand, in the non-convex setting, the situation is drastically different: While we know that SGD can minimize the gradient of non-convex smooth functions, no finite-time complexity guarantee for Stochastic Dual Averaging (SDA) wa","authors_text":"El Mehdi Saad, Francesco Orabona, Tuo Liu, Wojciech Kot{\\l}owski","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-27T16:23:23Z","title":"Dual Averaging Converges for Nonconvex Smooth Stochastic Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21394","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":"sha256:47b4f0c0f6b2f0ec23e117679509ed08d487cdb3db1db821cffc7f28cad8378f","target":"record","created_at":"2026-07-05T11:10:41Z","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":"f6837c40d2b729c7f399ce457edc8820db026144846caae6d7ec47d9598fcd83","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-27T16:23:23Z","title_canon_sha256":"9c96e6d739a4231d52281dbe3cf5453ae4ce91405f197b66efdeb3627e6b9b44"},"schema_version":"1.0","source":{"id":"2505.21394","kind":"arxiv","version":1}},"canonical_sha256":"6886993834610e4223d8eefd46eb71c10cdf7c768004d241aa44f0e988b664a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6886993834610e4223d8eefd46eb71c10cdf7c768004d241aa44f0e988b664a4","first_computed_at":"2026-07-05T11:10:41.348269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:41.348269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cLck2DeDuxog4bzFjqBaO/3/Q0pJsKuRM7Ds2EvC9dj99hT+QQt1CM/cFicDaOZD8nJ9QH8f/SxhODnMt/UEBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:41.348788Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47b4f0c0f6b2f0ec23e117679509ed08d487cdb3db1db821cffc7f28cad8378f","sha256:c5ddffbee84400b69993459900afc93b17d71235de150aa19f2b57160a8a2bd3"],"state_sha256":"a803dae82414abc398bb0d0d769ba1bbd165dc30cf3fc23269ac5e0ac24d71bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7NRLNlcbaAfmJ6fKI3sRUN7/JWcO0YtG3NW4L4JvQeGynFkvJix3hH+wwuEvq/jqNdHsCIYN39bFVUp2cNpAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T12:37:26.973080Z","bundle_sha256":"f4445a9c9cd21f58225e0ef9785cfc7fafba0c09f3c1484c93af72d14c8b5033"}}