{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LRDHJNICB54ZNW2P36NXLEMET5","short_pith_number":"pith:LRDHJNIC","schema_version":"1.0","canonical_sha256":"5c4674b5020f7996db4fdf9b7591849f451d0d61ed9e3f9f982d7a62a5421a6b","source":{"kind":"arxiv","id":"2607.19647","version":1},"attestation_state":"computed","paper":{"title":"On the Universality of Simple Trust-Region Algorithms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Clemens Sirotenko","submitted_at":"2026-07-22T01:06:15Z","abstract_excerpt":"We establish universal complexity guarantees for quadratic trust-region methods and identify a common mechanism underlying their universal behavior under convexity, based on a function-gap model-decrease estimate that appears to be new in the trust-region literature. First, we prove that the basic trust-region method with inexact subproblem solves is universal under convexity. Under a $\\nu$-H\\\"older-continuous Hessian, it attains the global complexity bound $\\mathcal{O}(\\varepsilon^{-1/(1+\\nu)})$ for computing an $\\varepsilon$-approximate minimizer, without knowledge of $\\nu\\in[0,1]$ or the co"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.19647","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-22T01:06:15Z","cross_cats_sorted":[],"title_canon_sha256":"a95528a0be053dff9ab5c9bee0dea54c5d3dc94277ee22668a0bad6d1f388fff","abstract_canon_sha256":"3900640c955d831b9d2d220dcd2b541dcb62b44752254cec77254bf0abee92f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-23T00:24:01.693425Z","signature_b64":"cZTbdd0TShhxW4Ffu9EXtZaZ4eExf4GTuqwGkQoosIJfGZC2oIoo6QVIC1f2zfOL09kICQf0WR2AnCFyuZlnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c4674b5020f7996db4fdf9b7591849f451d0d61ed9e3f9f982d7a62a5421a6b","last_reissued_at":"2026-07-23T00:24:01.692513Z","signature_status":"signed_v1","first_computed_at":"2026-07-23T00:24:01.692513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Universality of Simple Trust-Region Algorithms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Clemens Sirotenko","submitted_at":"2026-07-22T01:06:15Z","abstract_excerpt":"We establish universal complexity guarantees for quadratic trust-region methods and identify a common mechanism underlying their universal behavior under convexity, based on a function-gap model-decrease estimate that appears to be new in the trust-region literature. First, we prove that the basic trust-region method with inexact subproblem solves is universal under convexity. Under a $\\nu$-H\\\"older-continuous Hessian, it attains the global complexity bound $\\mathcal{O}(\\varepsilon^{-1/(1+\\nu)})$ for computing an $\\varepsilon$-approximate minimizer, without knowledge of $\\nu\\in[0,1]$ or the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19647","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/2607.19647/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.19647","created_at":"2026-07-23T00:24:01.692970+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.19647v1","created_at":"2026-07-23T00:24:01.692970+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19647","created_at":"2026-07-23T00:24:01.692970+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRDHJNICB54Z","created_at":"2026-07-23T00:24:01.692970+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRDHJNICB54ZNW2P","created_at":"2026-07-23T00:24:01.692970+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRDHJNIC","created_at":"2026-07-23T00:24:01.692970+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LRDHJNICB54ZNW2P36NXLEMET5","json":"https://pith.science/pith/LRDHJNICB54ZNW2P36NXLEMET5.json","graph_json":"https://pith.science/api/pith-number/LRDHJNICB54ZNW2P36NXLEMET5/graph.json","events_json":"https://pith.science/api/pith-number/LRDHJNICB54ZNW2P36NXLEMET5/events.json","paper":"https://pith.science/paper/LRDHJNIC"},"agent_actions":{"view_html":"https://pith.science/pith/LRDHJNICB54ZNW2P36NXLEMET5","download_json":"https://pith.science/pith/LRDHJNICB54ZNW2P36NXLEMET5.json","view_paper":"https://pith.science/paper/LRDHJNIC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.19647&json=true","fetch_graph":"https://pith.science/api/pith-number/LRDHJNICB54ZNW2P36NXLEMET5/graph.json","fetch_events":"https://pith.science/api/pith-number/LRDHJNICB54ZNW2P36NXLEMET5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRDHJNICB54ZNW2P36NXLEMET5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRDHJNICB54ZNW2P36NXLEMET5/action/storage_attestation","attest_author":"https://pith.science/pith/LRDHJNICB54ZNW2P36NXLEMET5/action/author_attestation","sign_citation":"https://pith.science/pith/LRDHJNICB54ZNW2P36NXLEMET5/action/citation_signature","submit_replication":"https://pith.science/pith/LRDHJNICB54ZNW2P36NXLEMET5/action/replication_record"}},"created_at":"2026-07-23T00:24:01.692970+00:00","updated_at":"2026-07-23T00:24:01.692970+00:00"}