{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WSBWPGLTFP7RRRZYE5QDQJ7GOR","short_pith_number":"pith:WSBWPGLT","canonical_record":{"source":{"id":"2502.07923","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-02-11T19:54:11Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7f6942cafaa89b59cc5d401945e20b516bb012a15aa05155bfd75c6ab342d017","abstract_canon_sha256":"bc8e71a412b345a6169504acf3894dfd147d4cf5ccd7a8fb85956a234019e64a"},"schema_version":"1.0"},"canonical_sha256":"b4836799732bff18c73827603827e6744b441338e77916b04621b5bf5c28908e","source":{"kind":"arxiv","id":"2502.07923","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07923","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07923v2","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07923","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"WSBWPGLTFP7R","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"pith_short_16","alias_value":"WSBWPGLTFP7RRRZY","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"pith_short_8","alias_value":"WSBWPGLT","created_at":"2026-07-05T11:10:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WSBWPGLTFP7RRRZYE5QDQJ7GOR","target":"record","payload":{"canonical_record":{"source":{"id":"2502.07923","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-02-11T19:54:11Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7f6942cafaa89b59cc5d401945e20b516bb012a15aa05155bfd75c6ab342d017","abstract_canon_sha256":"bc8e71a412b345a6169504acf3894dfd147d4cf5ccd7a8fb85956a234019e64a"},"schema_version":"1.0"},"canonical_sha256":"b4836799732bff18c73827603827e6744b441338e77916b04621b5bf5c28908e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:35.093608Z","signature_b64":"Qjz71YW/BBasxGGc3ax6U9Xt2YfCvyalmJsndKMRxUKn0GKMU8zRtEBo8RgDLOnHhEeC0qBMKzf5/QZdY+wECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4836799732bff18c73827603827e6744b441338e77916b04621b5bf5c28908e","last_reissued_at":"2026-07-05T11:10:35.092951Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:35.092951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.07923","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":"2026-07-05T11:10:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7Qksjl6WEIXTRTbJWz+iJPPQAou8eN6dOoaeLNupzfqXg9L20sM8kQj/Y5S2JxsoSbGFNSHOckenHbmlMT8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:11:04.401649Z"},"content_sha256":"1ed333060a7fd1678fdf7d523e19a2e962eb8de4fbf366ae3d7e8d91183aff98","schema_version":"1.0","event_id":"sha256:1ed333060a7fd1678fdf7d523e19a2e962eb8de4fbf366ae3d7e8d91183aff98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WSBWPGLTFP7RRRZYE5QDQJ7GOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Alexander Beznosikov, Alexander Gasnikov, Andrei Semenov, Mark Ikonnikov, Nikita Kornilov, Philip Zmushko","submitted_at":"2025-02-11T19:54:11Z","abstract_excerpt":"In recent years, non-convex optimization problems are more often described by generalized $(L_0, L_1)$-smoothness assumption rather than standard one. Meanwhile, severely corrupted data used in these problems has increased the demand for methods capable of handling heavy-tailed noises, i.e., noises with bounded $\\kappa$-th moment. Motivated by these real-world trends and challenges, we explore sign-based methods in this setup and demonstrate their effectiveness in comparison with other popular solutions like clipping or normalization.\n  In theory, we prove the first-known high probability conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07923","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.07923/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":"2026-07-05T11:10:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"meeFbNWA/kB1TeZ6lAASmMFTRNfLUSWFdHwjG3uT9uIPHOIb9XC5jWwTx9j6RGcKitv8FDmqp3wXfUgzNH02Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:11:04.402151Z"},"content_sha256":"f1381773f56c7f9b4c86bd69a4a27ea0f260f9dc749a49d06ddd7c3226217b24","schema_version":"1.0","event_id":"sha256:f1381773f56c7f9b4c86bd69a4a27ea0f260f9dc749a49d06ddd7c3226217b24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WSBWPGLTFP7RRRZYE5QDQJ7GOR/bundle.json","state_url":"https://pith.science/pith/WSBWPGLTFP7RRRZYE5QDQJ7GOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WSBWPGLTFP7RRRZYE5QDQJ7GOR/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":"2026-08-08T23:11:04Z","links":{"resolver":"https://pith.science/pith/WSBWPGLTFP7RRRZYE5QDQJ7GOR","bundle":"https://pith.science/pith/WSBWPGLTFP7RRRZYE5QDQJ7GOR/bundle.json","state":"https://pith.science/pith/WSBWPGLTFP7RRRZYE5QDQJ7GOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WSBWPGLTFP7RRRZYE5QDQJ7GOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WSBWPGLTFP7RRRZYE5QDQJ7GOR","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":"bc8e71a412b345a6169504acf3894dfd147d4cf5ccd7a8fb85956a234019e64a","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-02-11T19:54:11Z","title_canon_sha256":"7f6942cafaa89b59cc5d401945e20b516bb012a15aa05155bfd75c6ab342d017"},"schema_version":"1.0","source":{"id":"2502.07923","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07923","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07923v2","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07923","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"WSBWPGLTFP7R","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"pith_short_16","alias_value":"WSBWPGLTFP7RRRZY","created_at":"2026-07-05T11:10:35Z"},{"alias_kind":"pith_short_8","alias_value":"WSBWPGLT","created_at":"2026-07-05T11:10:35Z"}],"graph_snapshots":[{"event_id":"sha256:f1381773f56c7f9b4c86bd69a4a27ea0f260f9dc749a49d06ddd7c3226217b24","target":"graph","created_at":"2026-07-05T11:10:35Z","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/2502.07923/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In recent years, non-convex optimization problems are more often described by generalized $(L_0, L_1)$-smoothness assumption rather than standard one. Meanwhile, severely corrupted data used in these problems has increased the demand for methods capable of handling heavy-tailed noises, i.e., noises with bounded $\\kappa$-th moment. Motivated by these real-world trends and challenges, we explore sign-based methods in this setup and demonstrate their effectiveness in comparison with other popular solutions like clipping or normalization.\n  In theory, we prove the first-known high probability conv","authors_text":"Alexander Beznosikov, Alexander Gasnikov, Andrei Semenov, Mark Ikonnikov, Nikita Kornilov, Philip Zmushko","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-02-11T19:54:11Z","title":"Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07923","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":"sha256:1ed333060a7fd1678fdf7d523e19a2e962eb8de4fbf366ae3d7e8d91183aff98","target":"record","created_at":"2026-07-05T11:10:35Z","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":"bc8e71a412b345a6169504acf3894dfd147d4cf5ccd7a8fb85956a234019e64a","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-02-11T19:54:11Z","title_canon_sha256":"7f6942cafaa89b59cc5d401945e20b516bb012a15aa05155bfd75c6ab342d017"},"schema_version":"1.0","source":{"id":"2502.07923","kind":"arxiv","version":2}},"canonical_sha256":"b4836799732bff18c73827603827e6744b441338e77916b04621b5bf5c28908e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4836799732bff18c73827603827e6744b441338e77916b04621b5bf5c28908e","first_computed_at":"2026-07-05T11:10:35.092951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:35.092951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qjz71YW/BBasxGGc3ax6U9Xt2YfCvyalmJsndKMRxUKn0GKMU8zRtEBo8RgDLOnHhEeC0qBMKzf5/QZdY+wECA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:35.093608Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.07923","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ed333060a7fd1678fdf7d523e19a2e962eb8de4fbf366ae3d7e8d91183aff98","sha256:f1381773f56c7f9b4c86bd69a4a27ea0f260f9dc749a49d06ddd7c3226217b24"],"state_sha256":"f038ffbdb2bb92ad67ace706583a2619ed62563eb1eab5816d77238025212578"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lpFY2hIHsbzE7HlkTELDYyPzbx4JjpLV75xx/K3NXyiGKORSjottT7QiEC6m8giXbqxfj8LMQgzbe4Wlr5OpAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T23:11:04.406888Z","bundle_sha256":"d3120022e6d1349bac2a12aff3573704d34050ce0602ef38c5d41bab64e030d4"}}