{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QZ3TIE3V2GY7SPH623AIBPHXHZ","short_pith_number":"pith:QZ3TIE3V","canonical_record":{"source":{"id":"2503.02809","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:35:13Z","cross_cats_sorted":[],"title_canon_sha256":"80e65d948b9ee242f310481858c6bfe05d69e7932fa62372b76f97c6e9d39657","abstract_canon_sha256":"3626870d494e681285a61c9fc1a271c742a3cd7cb9f3eb831288097039f086e5"},"schema_version":"1.0"},"canonical_sha256":"8677341375d1b1f93cfed6c080bcf73e502ff3185c520ec28c864c8a507c107a","source":{"kind":"arxiv","id":"2503.02809","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.02809","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"2503.02809v1","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.02809","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"QZ3TIE3V2GY7","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_16","alias_value":"QZ3TIE3V2GY7SPH6","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_8","alias_value":"QZ3TIE3V","created_at":"2026-07-05T10:24:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QZ3TIE3V2GY7SPH623AIBPHXHZ","target":"record","payload":{"canonical_record":{"source":{"id":"2503.02809","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:35:13Z","cross_cats_sorted":[],"title_canon_sha256":"80e65d948b9ee242f310481858c6bfe05d69e7932fa62372b76f97c6e9d39657","abstract_canon_sha256":"3626870d494e681285a61c9fc1a271c742a3cd7cb9f3eb831288097039f086e5"},"schema_version":"1.0"},"canonical_sha256":"8677341375d1b1f93cfed6c080bcf73e502ff3185c520ec28c864c8a507c107a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:24:14.165879Z","signature_b64":"WXSlSGrRLpZHNn8Kp34WZbNuab4tq38RdJyd8MiZEMd33bP/8NKWfYHVGjsGmf2/f9RR0l1W+O/n/RTrW919BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8677341375d1b1f93cfed6c080bcf73e502ff3185c520ec28c864c8a507c107a","last_reissued_at":"2026-07-05T10:24:14.164903Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:24:14.164903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.02809","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":"2026-07-05T10:24:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P7lpfAjMPsFcM00F1T4AoQ5U7OEFXApZzl0VdGsl4XpVmbSCDjY2FWyI1UYjx9UDY2OE+hNCvfhGriJZvc6pBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:45:25.081537Z"},"content_sha256":"c4ae21b70645ac2274c3c384606c3e29406611f0db59f451b629443717c6ba77","schema_version":"1.0","event_id":"sha256:c4ae21b70645ac2274c3c384606c3e29406611f0db59f451b629443717c6ba77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QZ3TIE3V2GY7SPH623AIBPHXHZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Minimalist Example of Edge-of-Stability and Progressive Sharpening","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Liming Liu, Simon Du, Tuo Zhao, Zixuan Zhang","submitted_at":"2025-03-04T17:35:13Z","abstract_excerpt":"Recent advances in deep learning optimization have unveiled two intriguing phenomena under large learning rates: Edge of Stability (EoS) and Progressive Sharpening (PS), challenging classical Gradient Descent (GD) analyses. Current research approaches, using either generalist frameworks or minimalist examples, face significant limitations in explaining these phenomena. This paper advances the minimalist approach by introducing a two-layer network with a two-dimensional input, where one dimension is relevant to the response and the other is irrelevant. Through this model, we rigorously prove th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02809","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/2503.02809/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":"2026-07-05T10:24:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cT6PS8X3wVXzgNtUmHxrWrGzXbVw+ZVnPjSEVGr4fFRkYdVd/HHeywubFp8LlUyXo0V1r19VwMvBALwjV8b8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:45:25.082028Z"},"content_sha256":"39058691c7cb2d13c54a78866b92c5f7ccf36f66b5b302cb9d5d38add2c20470","schema_version":"1.0","event_id":"sha256:39058691c7cb2d13c54a78866b92c5f7ccf36f66b5b302cb9d5d38add2c20470"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZ3TIE3V2GY7SPH623AIBPHXHZ/bundle.json","state_url":"https://pith.science/pith/QZ3TIE3V2GY7SPH623AIBPHXHZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZ3TIE3V2GY7SPH623AIBPHXHZ/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":"2026-08-10T23:45:25Z","links":{"resolver":"https://pith.science/pith/QZ3TIE3V2GY7SPH623AIBPHXHZ","bundle":"https://pith.science/pith/QZ3TIE3V2GY7SPH623AIBPHXHZ/bundle.json","state":"https://pith.science/pith/QZ3TIE3V2GY7SPH623AIBPHXHZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZ3TIE3V2GY7SPH623AIBPHXHZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QZ3TIE3V2GY7SPH623AIBPHXHZ","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":"3626870d494e681285a61c9fc1a271c742a3cd7cb9f3eb831288097039f086e5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:35:13Z","title_canon_sha256":"80e65d948b9ee242f310481858c6bfe05d69e7932fa62372b76f97c6e9d39657"},"schema_version":"1.0","source":{"id":"2503.02809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.02809","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"2503.02809v1","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.02809","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"QZ3TIE3V2GY7","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_16","alias_value":"QZ3TIE3V2GY7SPH6","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_8","alias_value":"QZ3TIE3V","created_at":"2026-07-05T10:24:14Z"}],"graph_snapshots":[{"event_id":"sha256:39058691c7cb2d13c54a78866b92c5f7ccf36f66b5b302cb9d5d38add2c20470","target":"graph","created_at":"2026-07-05T10:24:14Z","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/2503.02809/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent advances in deep learning optimization have unveiled two intriguing phenomena under large learning rates: Edge of Stability (EoS) and Progressive Sharpening (PS), challenging classical Gradient Descent (GD) analyses. Current research approaches, using either generalist frameworks or minimalist examples, face significant limitations in explaining these phenomena. This paper advances the minimalist approach by introducing a two-layer network with a two-dimensional input, where one dimension is relevant to the response and the other is irrelevant. Through this model, we rigorously prove th","authors_text":"Liming Liu, Simon Du, Tuo Zhao, Zixuan Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:35:13Z","title":"A Minimalist Example of Edge-of-Stability and Progressive Sharpening"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02809","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:c4ae21b70645ac2274c3c384606c3e29406611f0db59f451b629443717c6ba77","target":"record","created_at":"2026-07-05T10:24:14Z","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":"3626870d494e681285a61c9fc1a271c742a3cd7cb9f3eb831288097039f086e5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:35:13Z","title_canon_sha256":"80e65d948b9ee242f310481858c6bfe05d69e7932fa62372b76f97c6e9d39657"},"schema_version":"1.0","source":{"id":"2503.02809","kind":"arxiv","version":1}},"canonical_sha256":"8677341375d1b1f93cfed6c080bcf73e502ff3185c520ec28c864c8a507c107a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8677341375d1b1f93cfed6c080bcf73e502ff3185c520ec28c864c8a507c107a","first_computed_at":"2026-07-05T10:24:14.164903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:24:14.164903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WXSlSGrRLpZHNn8Kp34WZbNuab4tq38RdJyd8MiZEMd33bP/8NKWfYHVGjsGmf2/f9RR0l1W+O/n/RTrW919BA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:24:14.165879Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.02809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4ae21b70645ac2274c3c384606c3e29406611f0db59f451b629443717c6ba77","sha256:39058691c7cb2d13c54a78866b92c5f7ccf36f66b5b302cb9d5d38add2c20470"],"state_sha256":"4e9796f6e09e867ae893babea08ce7df65d97a9f824810f47db1009c8bbddfa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PvfpNiXf6tXT9wzS1aQ+382Gc1RGQS07wW97Kq61Q6xOASX/9u5aRGMaJQVg3IElANNUhawvuKzFJK9SVy3oAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T23:45:25.085504Z","bundle_sha256":"098c7134cc386ff37fdc6b78a3952c7456aca6c720d38f5e3d90502d237f33d3"}}