{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IFWQKZQK64MLDVQE3ARFXHPWWQ","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":"d7b722979913df499b45453b5374ba7d753aa5a97460b5c5c0d3d6767228525c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-13T22:06:50Z","title_canon_sha256":"c0103300bde6bd59e7889744d0df411da80d89caa37cf2f990b0984230f8f0f7"},"schema_version":"1.0","source":{"id":"2605.14151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.14151","created_at":"2026-05-17T23:39:11Z"},{"alias_kind":"arxiv_version","alias_value":"2605.14151v1","created_at":"2026-05-17T23:39:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14151","created_at":"2026-05-17T23:39:11Z"},{"alias_kind":"pith_short_12","alias_value":"IFWQKZQK64ML","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"IFWQKZQK64MLDVQE","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"IFWQKZQK","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:8ed83547179df78d34f7ccb32ae2af7123f7fe589db2a2b4642982c62e2fdcb2","target":"graph","created_at":"2026-05-17T23:39:11Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We identify a gap parameter -- an analogue of a spectral gap for random walks -- that controls the rate at which the iterates approach the global minimum value. Finally, we argue that the same analysis yields a blind-spot robustness property: sufficiently narrow, deep dips of the loss function have limited influence on the algorithm's trajectory."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The convergence analysis rests on the existence and positivity of the gap parameter defined from the geometric distribution of restricted minima across random k-dimensional subspaces; the abstract provides no explicit construction, bound, or verification procedure for this quantity on arbitrary continuous functions."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A stochastic global optimizer samples random k-dimensional subspaces, solves the restricted problem on each, and moves to the improved point, with rate controlled by a gap parameter on the distribution of restricted minima."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Random walks on Grassmannians converge to global minima of continuous functions at a rate set by a geometric gap parameter."}],"snapshot_sha256":"840268697d2a67ba14d3f35bd924de5f570f0e60ed7ab68c4bd91567121219dd"},"formal_canon":{"evidence_count":1,"snapshot_sha256":"9a99ff3b68afa39a4c063c4452c9565be8bf309044da66dd2cd202f3b4f987ef"},"paper":{"abstract_excerpt":"We introduce a stochastic global optimization method based on random walks on Grassmannian manifolds. To minimize a continuous objective $\\ell:\\mathbb{R}^d\\rightarrow\\mathbb{R}$, the method repeatedly samples random $k$-dimensional linear subspaces (with $k\\ll d$), solves the resulting low-dimensional restrictions of these problems to these subspaces using an arbitrary black-box optimizer, and updates the iterate (which monotonically improves upon the previous iterate). Unlike classical optimization analyses that rely on convexity, smoothness, Lipschitz bounds, or Polyak-Lojasiewicz-type condi","authors_text":"Kartik Gupta, Pradeep Ravikumar, Ramarathnam Venkatesan, Stephen D. Miller","cross_cats":[],"headline":"Random walks on Grassmannians converge to global minima of continuous functions at a rate set by a geometric gap parameter.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-13T22:06:50Z","title":"Stochastic global optimization of continuous functions via random walks on Grassmannians"},"references":{"count":24,"internal_anchors":1,"resolved_work":24,"sample":[{"cited_arxiv_id":"","doi":"10.1080/10586458.2009.10129052","is_internal_anchor":false,"ref_index":1,"title":"Ballinger, B., Blekherman, G., Cohn, H., Giansiracusa, N., Kelly, E., & Schürmann, A. (2009). Experimental Study of Energy-Minimizing Point Configurations on Spheres. Experimental Mathematics, 18(3), ","work_id":"04ffccf2-3cc9-4716-b2db-cde09d87eecb","year":2009},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Point configurations minimizing harmonic energy on spheres","work_id":"f4f62a8c-cd8c-424a-a138-ecc1dfc31033","year":2021},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"B. Bekka, P. de la Harpe, and A. Valette. Kazhdan's Property (T) . New Mathematical Monographs. Cambridge University Press, 2008","work_id":"4a0d1141-a5c6-4ee6-aa99-ffc0e1775f43","year":2008},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Thomas Bendokat, Ralf Zimmermann, and P.-A. Absil. A Grassmann manifold handbook: basic geometry and computational aspects. Advances in Computational Mathematics , 50(1), January 2024","work_id":"d2329719-4b7a-414b-be59-b21cef6b14f8","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Moser, Alina Oprea, Battista Biggio, Marcello Pelillo, and Fabio Roli","work_id":"ed33d0c1-4453-4efb-8be7-be6a2f23906c","year":2023}],"snapshot_sha256":"2c15d2e59f863b31a95f5c3095109ed658d612b396985e58d799f8bf9d39092a"},"source":{"id":"2605.14151","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T02:02:11.639255Z","id":"b06bf1d4-917d-4925-bee9-5e8a14fd18c6","model_set":{"reader":"grok-4.3"},"one_line_summary":"A stochastic global optimizer samples random k-dimensional subspaces, solves the restricted problem on each, and moves to the improved point, with rate controlled by a gap parameter on the distribution of restricted minima.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Random walks on Grassmannians converge to global minima of continuous functions at a rate set by a geometric gap parameter.","strongest_claim":"We identify a gap parameter -- an analogue of a spectral gap for random walks -- that controls the rate at which the iterates approach the global minimum value. Finally, we argue that the same analysis yields a blind-spot robustness property: sufficiently narrow, deep dips of the loss function have limited influence on the algorithm's trajectory.","weakest_assumption":"The convergence analysis rests on the existence and positivity of the gap parameter defined from the geometric distribution of restricted minima across random k-dimensional subspaces; the abstract provides no explicit construction, bound, or verification procedure for this quantity on arbitrary continuous functions."}},"verdict_id":"b06bf1d4-917d-4925-bee9-5e8a14fd18c6"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ec411b83ee96d73641cf2668b9f27e95b9a3d6a95cbe46acced87818b993c07c","target":"record","created_at":"2026-05-17T23:39:11Z","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":"d7b722979913df499b45453b5374ba7d753aa5a97460b5c5c0d3d6767228525c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-13T22:06:50Z","title_canon_sha256":"c0103300bde6bd59e7889744d0df411da80d89caa37cf2f990b0984230f8f0f7"},"schema_version":"1.0","source":{"id":"2605.14151","kind":"arxiv","version":1}},"canonical_sha256":"416d05660af718b1d604d8225b9df6b4232408790ee326942ec2974b2cdc90be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"416d05660af718b1d604d8225b9df6b4232408790ee326942ec2974b2cdc90be","first_computed_at":"2026-05-17T23:39:11.581846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:11.581846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wt/uyUQ2uK9P7kOm5/8+ogqFZ/zWEWyspWHKV9LxZFqjQyYRmObk8HGG2RM0D7A3k4WNiebWwG0rB1OwW00xDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:11.582280Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.14151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec411b83ee96d73641cf2668b9f27e95b9a3d6a95cbe46acced87818b993c07c","sha256:8ed83547179df78d34f7ccb32ae2af7123f7fe589db2a2b4642982c62e2fdcb2"],"state_sha256":"bf6f45954f04c968d6a48c87a28de4d1149682f2ce87b341ac2341f6c45546df"}