{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DB4CIPYGWDCRMQ5VUMYG25QU7T","short_pith_number":"pith:DB4CIPYG","canonical_record":{"source":{"id":"1802.07843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-21T23:14:45Z","cross_cats_sorted":[],"title_canon_sha256":"2202f36b92e34b4be63afabee27508091f19ded48161e63d023b55d908a53669","abstract_canon_sha256":"da5bff3d9b272b0efe1820cc25549dbd6b0b9722d5cd30f49c5000f811a022c3"},"schema_version":"1.0"},"canonical_sha256":"1878243f06b0c51643b5a3306d7614fcc65db36ea8f1f0331c3c7fa4803aa403","source":{"kind":"arxiv","id":"1802.07843","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07843","created_at":"2026-05-18T00:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07843v1","created_at":"2026-05-18T00:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07843","created_at":"2026-05-18T00:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"DB4CIPYGWDCR","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DB4CIPYGWDCRMQ5V","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DB4CIPYG","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DB4CIPYGWDCRMQ5VUMYG25QU7T","target":"record","payload":{"canonical_record":{"source":{"id":"1802.07843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-21T23:14:45Z","cross_cats_sorted":[],"title_canon_sha256":"2202f36b92e34b4be63afabee27508091f19ded48161e63d023b55d908a53669","abstract_canon_sha256":"da5bff3d9b272b0efe1820cc25549dbd6b0b9722d5cd30f49c5000f811a022c3"},"schema_version":"1.0"},"canonical_sha256":"1878243f06b0c51643b5a3306d7614fcc65db36ea8f1f0331c3c7fa4803aa403","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:48.759395Z","signature_b64":"qqjSurTHaEX0+tTdFRDffHnEd5JXndbnHQldmt5222O+5RLyVXcuhmlXOeOzbisUyJ/ej/vD2WlPp804YJHRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1878243f06b0c51643b5a3306d7614fcc65db36ea8f1f0331c3c7fa4803aa403","last_reissued_at":"2026-05-18T00:22:48.758914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:48.758914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.07843","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":"2026-05-18T00:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fV1OLJFGl6Wdp7T65ivyRRgOwtPd1KB5xEpVFX6DKWRpNnNBoV9Fw2Bzi/IKFy7h5pulgtUlNwbGd5uDjWECDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:28:31.511464Z"},"content_sha256":"b3def9648be010e10667608fb38691f24edeccdb3cbc5d14c7abd2df652e3ca8","schema_version":"1.0","event_id":"sha256:b3def9648be010e10667608fb38691f24edeccdb3cbc5d14c7abd2df652e3ca8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DB4CIPYGWDCRMQ5VUMYG25QU7T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Concise Complexity Analyses for Trust-Region Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel P. Robinson, Frank E. Curtis, Zachary Lubberts","submitted_at":"2018-02-21T23:14:45Z","abstract_excerpt":"Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain control over the choice of trust region radius after any successful iteration. The analyses highlight the essential algorithm components required to obtain certain complexity bounds. In addition, a new update strategy for the trust region radius is proposed that offers a second-order complexity bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07843","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":""},"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":"2026-05-18T00:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sgzSnN6tKOdvmpT7bYecKkpQb/hbCMdnowII/tbY3tV9UjuXj0Cg3Mvd+zYr4pbBqC2XkVGAlhh7IpMdVLjPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:28:31.511802Z"},"content_sha256":"f59f0193c067b55d22d7860636bed1909fcbdb0827e033c6619a76a7003380e0","schema_version":"1.0","event_id":"sha256:f59f0193c067b55d22d7860636bed1909fcbdb0827e033c6619a76a7003380e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DB4CIPYGWDCRMQ5VUMYG25QU7T/bundle.json","state_url":"https://pith.science/pith/DB4CIPYGWDCRMQ5VUMYG25QU7T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DB4CIPYGWDCRMQ5VUMYG25QU7T/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":"2026-06-01T23:28:31Z","links":{"resolver":"https://pith.science/pith/DB4CIPYGWDCRMQ5VUMYG25QU7T","bundle":"https://pith.science/pith/DB4CIPYGWDCRMQ5VUMYG25QU7T/bundle.json","state":"https://pith.science/pith/DB4CIPYGWDCRMQ5VUMYG25QU7T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DB4CIPYGWDCRMQ5VUMYG25QU7T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DB4CIPYGWDCRMQ5VUMYG25QU7T","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":"da5bff3d9b272b0efe1820cc25549dbd6b0b9722d5cd30f49c5000f811a022c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-21T23:14:45Z","title_canon_sha256":"2202f36b92e34b4be63afabee27508091f19ded48161e63d023b55d908a53669"},"schema_version":"1.0","source":{"id":"1802.07843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07843","created_at":"2026-05-18T00:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07843v1","created_at":"2026-05-18T00:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07843","created_at":"2026-05-18T00:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"DB4CIPYGWDCR","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DB4CIPYGWDCRMQ5V","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DB4CIPYG","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:f59f0193c067b55d22d7860636bed1909fcbdb0827e033c6619a76a7003380e0","target":"graph","created_at":"2026-05-18T00:22:48Z","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"},"paper":{"abstract_excerpt":"Concise complexity analyses are presented for simple trust region algorithms for solving unconstrained optimization problems. In contrast to a traditional trust region algorithm, the algorithms considered in this paper require certain control over the choice of trust region radius after any successful iteration. The analyses highlight the essential algorithm components required to obtain certain complexity bounds. In addition, a new update strategy for the trust region radius is proposed that offers a second-order complexity bound.","authors_text":"Daniel P. Robinson, Frank E. Curtis, Zachary Lubberts","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-21T23:14:45Z","title":"Concise Complexity Analyses for Trust-Region Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07843","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:b3def9648be010e10667608fb38691f24edeccdb3cbc5d14c7abd2df652e3ca8","target":"record","created_at":"2026-05-18T00:22:48Z","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":"da5bff3d9b272b0efe1820cc25549dbd6b0b9722d5cd30f49c5000f811a022c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-21T23:14:45Z","title_canon_sha256":"2202f36b92e34b4be63afabee27508091f19ded48161e63d023b55d908a53669"},"schema_version":"1.0","source":{"id":"1802.07843","kind":"arxiv","version":1}},"canonical_sha256":"1878243f06b0c51643b5a3306d7614fcc65db36ea8f1f0331c3c7fa4803aa403","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1878243f06b0c51643b5a3306d7614fcc65db36ea8f1f0331c3c7fa4803aa403","first_computed_at":"2026-05-18T00:22:48.758914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:48.758914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qqjSurTHaEX0+tTdFRDffHnEd5JXndbnHQldmt5222O+5RLyVXcuhmlXOeOzbisUyJ/ej/vD2WlPp804YJHRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:48.759395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3def9648be010e10667608fb38691f24edeccdb3cbc5d14c7abd2df652e3ca8","sha256:f59f0193c067b55d22d7860636bed1909fcbdb0827e033c6619a76a7003380e0"],"state_sha256":"65bc0e1526ce427764bde4c2b3f46bf39bbc61e4a9479bce1e80cad005b92422"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"le5WPj58mB0RrKWqx390hWvjlGknc1BISAUUtBoxegzS9vQ4UHF2mU3hi7XeXQO3WzbG4zuNqSrezcGC5R4qCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:28:31.513772Z","bundle_sha256":"fc182b9ed05e602c05d2d8e1446fcfd6cbcdc2087df66024734d6a426cb91fa1"}}