{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SD4TGJNCHFKVTPAV74BXWULN7Z","short_pith_number":"pith:SD4TGJNC","canonical_record":{"source":{"id":"2501.13038","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-22T17:36:20Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"2020ff376d967415c204bfa6c77c90794738b58f416c909a2d77b01e84c6e81d","abstract_canon_sha256":"6de4b9cac23c601200733f40c889e718a021c7713a5c81ec38a9974ddf7aa9ad"},"schema_version":"1.0"},"canonical_sha256":"90f93325a2395559bc15ff037b516dfe60c03c24c01e5c5d6fab97392fd8ebf9","source":{"kind":"arxiv","id":"2501.13038","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13038","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13038v1","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13038","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"SD4TGJNCHFKV","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"pith_short_16","alias_value":"SD4TGJNCHFKVTPAV","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"pith_short_8","alias_value":"SD4TGJNC","created_at":"2026-07-05T10:04:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SD4TGJNCHFKVTPAV74BXWULN7Z","target":"record","payload":{"canonical_record":{"source":{"id":"2501.13038","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-22T17:36:20Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"2020ff376d967415c204bfa6c77c90794738b58f416c909a2d77b01e84c6e81d","abstract_canon_sha256":"6de4b9cac23c601200733f40c889e718a021c7713a5c81ec38a9974ddf7aa9ad"},"schema_version":"1.0"},"canonical_sha256":"90f93325a2395559bc15ff037b516dfe60c03c24c01e5c5d6fab97392fd8ebf9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:04:01.958773Z","signature_b64":"P7Qxb0a0giKVDG59v2wyQJlo0AXqTk5fisD4ugiVKH6EDwiXGdBRfWhUzacNXzg/JXDT7elctvqetp50fyZkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90f93325a2395559bc15ff037b516dfe60c03c24c01e5c5d6fab97392fd8ebf9","last_reissued_at":"2026-07-05T10:04:01.958399Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:04:01.958399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.13038","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":"2026-07-05T10:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6oARf6m9VGcAw9H0VgUqKPpLYxEOXUIhSv6yOKR791yGisCSZCcXtSFxjKO/4dLbquTQraYWxF+JdtQzoyP6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T07:13:37.407313Z"},"content_sha256":"39918820e62a0501cd515ecbb500d9f2cd60a4104eff4fbf3c97488e228a7184","schema_version":"1.0","event_id":"sha256:39918820e62a0501cd515ecbb500d9f2cd60a4104eff4fbf3c97488e228a7184"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SD4TGJNCHFKVTPAV74BXWULN7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterative Optimization of Multidimensional Functions on Turing Machines under Performance Guarantees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.OC","authors_text":"Holger Boche, H. Vincent Poor, Volker Pohl","submitted_at":"2025-01-22T17:36:20Z","abstract_excerpt":"This paper studies the effective convergence of iterative methods for solving convex minimization problems using block Gauss--Seidel algorithms. It investigates whether it is always possible to algorithmically terminate the iteration in such a way that the outcome of the iterative algorithm satisfies any predefined error bound. It is shown that the answer is generally negative. Specifically, it is shown that even if a computable continuous function which is convex in each variable possesses computable minimizers, a block Gauss--Seidel iterative method might not be able to effectively compute a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13038","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/2501.13038/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":"2026-07-05T10:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aw2VFwy+O6K1QVVPBc1RlY2zGWUqrni55bN1f4ZsSg8NPtjs+U3riyG8hZmn1A5LMUnBcWuXzavl+3PK9gG1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T07:13:37.407841Z"},"content_sha256":"d07fc7e7820ce487725d35863c47ae2c1c142091c84946321212ba389440c365","schema_version":"1.0","event_id":"sha256:d07fc7e7820ce487725d35863c47ae2c1c142091c84946321212ba389440c365"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SD4TGJNCHFKVTPAV74BXWULN7Z/bundle.json","state_url":"https://pith.science/pith/SD4TGJNCHFKVTPAV74BXWULN7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SD4TGJNCHFKVTPAV74BXWULN7Z/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":"2026-08-20T07:13:37Z","links":{"resolver":"https://pith.science/pith/SD4TGJNCHFKVTPAV74BXWULN7Z","bundle":"https://pith.science/pith/SD4TGJNCHFKVTPAV74BXWULN7Z/bundle.json","state":"https://pith.science/pith/SD4TGJNCHFKVTPAV74BXWULN7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SD4TGJNCHFKVTPAV74BXWULN7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SD4TGJNCHFKVTPAV74BXWULN7Z","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":"6de4b9cac23c601200733f40c889e718a021c7713a5c81ec38a9974ddf7aa9ad","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-22T17:36:20Z","title_canon_sha256":"2020ff376d967415c204bfa6c77c90794738b58f416c909a2d77b01e84c6e81d"},"schema_version":"1.0","source":{"id":"2501.13038","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13038","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13038v1","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13038","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"SD4TGJNCHFKV","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"pith_short_16","alias_value":"SD4TGJNCHFKVTPAV","created_at":"2026-07-05T10:04:01Z"},{"alias_kind":"pith_short_8","alias_value":"SD4TGJNC","created_at":"2026-07-05T10:04:01Z"}],"graph_snapshots":[{"event_id":"sha256:d07fc7e7820ce487725d35863c47ae2c1c142091c84946321212ba389440c365","target":"graph","created_at":"2026-07-05T10:04:01Z","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/2501.13038/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the effective convergence of iterative methods for solving convex minimization problems using block Gauss--Seidel algorithms. It investigates whether it is always possible to algorithmically terminate the iteration in such a way that the outcome of the iterative algorithm satisfies any predefined error bound. It is shown that the answer is generally negative. Specifically, it is shown that even if a computable continuous function which is convex in each variable possesses computable minimizers, a block Gauss--Seidel iterative method might not be able to effectively compute a","authors_text":"Holger Boche, H. Vincent Poor, Volker Pohl","cross_cats":["cs.CC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-22T17:36:20Z","title":"Iterative Optimization of Multidimensional Functions on Turing Machines under Performance Guarantees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13038","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":"sha256:39918820e62a0501cd515ecbb500d9f2cd60a4104eff4fbf3c97488e228a7184","target":"record","created_at":"2026-07-05T10:04:01Z","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":"6de4b9cac23c601200733f40c889e718a021c7713a5c81ec38a9974ddf7aa9ad","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-22T17:36:20Z","title_canon_sha256":"2020ff376d967415c204bfa6c77c90794738b58f416c909a2d77b01e84c6e81d"},"schema_version":"1.0","source":{"id":"2501.13038","kind":"arxiv","version":1}},"canonical_sha256":"90f93325a2395559bc15ff037b516dfe60c03c24c01e5c5d6fab97392fd8ebf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90f93325a2395559bc15ff037b516dfe60c03c24c01e5c5d6fab97392fd8ebf9","first_computed_at":"2026-07-05T10:04:01.958399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:04:01.958399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P7Qxb0a0giKVDG59v2wyQJlo0AXqTk5fisD4ugiVKH6EDwiXGdBRfWhUzacNXzg/JXDT7elctvqetp50fyZkDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:04:01.958773Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13038","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39918820e62a0501cd515ecbb500d9f2cd60a4104eff4fbf3c97488e228a7184","sha256:d07fc7e7820ce487725d35863c47ae2c1c142091c84946321212ba389440c365"],"state_sha256":"81d2605aeb1c6adbaa968a0bfce01b3ec81cd95fe1bdbd44be871aa42a510b9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NF5nX11ZvD+kJzU3xW0vuX92dC9h6+rf/wJ6owY2c5Ckd8v3Sra+448u/MHIK0aZPp8lTJKXX3Mpw8bf0l+SBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T07:13:37.412227Z","bundle_sha256":"aff3a420f8c5da2213e9e414d863943bf07e6e69c8652dc7830ca067ae5e6031"}}