{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ESY6GGZ42JK3I4XCAGAS7UN2XL","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":"772a8d271f892192258f1c57c08ef2c258a5aca4ea8708b1b4893b771ad06507","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-23T17:56:05Z","title_canon_sha256":"93fe9a891afaafec8e798266a27ad701fbd4ad4cd6f32b9cdf68427f893be6a3"},"schema_version":"1.0","source":{"id":"2607.21579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21579","created_at":"2026-07-24T01:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21579v1","created_at":"2026-07-24T01:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21579","created_at":"2026-07-24T01:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"ESY6GGZ42JK3","created_at":"2026-07-24T01:24:41Z"},{"alias_kind":"pith_short_16","alias_value":"ESY6GGZ42JK3I4XC","created_at":"2026-07-24T01:24:41Z"},{"alias_kind":"pith_short_8","alias_value":"ESY6GGZ4","created_at":"2026-07-24T01:24:41Z"}],"graph_snapshots":[{"event_id":"sha256:b92f174476dbc7426314f8a0830f919522ec02bc7f7cba5414ce5083a1231a81","target":"graph","created_at":"2026-07-24T01:24:41Z","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/2607.21579/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Barzilai--Borwein (BB) method has shown strong practical performance in continuous optimization, yet its convergence dynamics remains poorly understood. In particular, a central unresolved question is whether BB converges superlinearly for almost every strictly convex quadratic problem and initialization. We provide a negative answer to this question. Specifically, for every finite dimension $n\\geq4$, we construct a nonempty open, hence positive-Lebesgue-measure, family of strictly convex quadratic problems and initial points for which the long Barzilai--Borwein method (BB1) converges but cann","authors_text":"Dawei Li, Mingyi Hong, Xiaotian Jiang","cross_cats":["cs.AI","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-23T17:56:05Z","title":"Barzilai-Borwein Fails Superlinear Convergence on an Open Set of Quadratics for Every Dimension $n\\geq 4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21579","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":"sha256:573f60d225b1f65515da9b8cbc535fe844245165c4077321d0a6a5e38e38c0db","target":"record","created_at":"2026-07-24T01:24:41Z","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":"772a8d271f892192258f1c57c08ef2c258a5aca4ea8708b1b4893b771ad06507","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-23T17:56:05Z","title_canon_sha256":"93fe9a891afaafec8e798266a27ad701fbd4ad4cd6f32b9cdf68427f893be6a3"},"schema_version":"1.0","source":{"id":"2607.21579","kind":"arxiv","version":1}},"canonical_sha256":"24b1e31b3cd255b472e201812fd1babac1532bfcbeb2ad7590933ce7de5b4d43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24b1e31b3cd255b472e201812fd1babac1532bfcbeb2ad7590933ce7de5b4d43","first_computed_at":"2026-07-24T01:24:41.139622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-24T01:24:41.139622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fGrmRuHSsOreZBI/t/my/cfLaODM87NXtll3V1AgmbsXnlvyZOe0OrW8+EuuFoZPhEq6S7a4ugtCa6Lqz5avBA==","signature_status":"signed_v1","signed_at":"2026-07-24T01:24:41.140503Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.21579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:573f60d225b1f65515da9b8cbc535fe844245165c4077321d0a6a5e38e38c0db","sha256:b92f174476dbc7426314f8a0830f919522ec02bc7f7cba5414ce5083a1231a81"],"state_sha256":"08110cb2148f824de59bed2933555c4bbd20624f2b3d2ae84a33d1fc6cda47cb"}