{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:URDMRKNKVJLOWGUYTHZSUXTTXC","short_pith_number":"pith:URDMRKNK","canonical_record":{"source":{"id":"1501.04191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-17T11:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"b7e09a0387fb06d7991c3e27dc49aed78b765066c4c808f34ce99af3fa1811ce","abstract_canon_sha256":"ab6c814b5986b43fa43099d6959c90480352fd71dc9d4ea8dd3c40c773cc5d12"},"schema_version":"1.0"},"canonical_sha256":"a446c8a9aaaa56eb1a9899f32a5e73b88b896b9a96735b49425e8095ea377a6b","source":{"kind":"arxiv","id":"1501.04191","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04191","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04191v2","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04191","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"URDMRKNKVJLO","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"URDMRKNKVJLOWGUY","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"URDMRKNK","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:URDMRKNKVJLOWGUYTHZSUXTTXC","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-17T11:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"b7e09a0387fb06d7991c3e27dc49aed78b765066c4c808f34ce99af3fa1811ce","abstract_canon_sha256":"ab6c814b5986b43fa43099d6959c90480352fd71dc9d4ea8dd3c40c773cc5d12"},"schema_version":"1.0"},"canonical_sha256":"a446c8a9aaaa56eb1a9899f32a5e73b88b896b9a96735b49425e8095ea377a6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:40.618273Z","signature_b64":"flS2FI/As9mel38KsxRkgGsoh/KKGG7D6A6zNpZAcwguRwThlRTiKGLNQJ/Xiow9Zch8iplqLlAa7gGjeja9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a446c8a9aaaa56eb1a9899f32a5e73b88b896b9a96735b49425e8095ea377a6b","last_reissued_at":"2026-05-18T00:22:40.617760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:40.617760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04191","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2e4AY9gboUYKURZrIB5jywkLvpMgHM/NKxsRKlosB01J+gs4AkBuhnzyzV4HcsFom3+r2Tp5WtBQAdERzLxtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:26:44.567634Z"},"content_sha256":"53e56d62ffffc67110439fec2cb41116910dfeeab125ad5543ef48e1530e1fb9","schema_version":"1.0","event_id":"sha256:53e56d62ffffc67110439fec2cb41116910dfeeab125ad5543ef48e1530e1fb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:URDMRKNKVJLOWGUYTHZSUXTTXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of collections of sets and convergence of inexact alternating projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexander Y. Kruger, Nguyen H. Thao","submitted_at":"2015-01-17T11:38:02Z","abstract_excerpt":"We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two settings of inexact alternating projections are considered and the corresponding convergence estimates are established and discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04191","kind":"arxiv","version":2},"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":"2026-05-18T00:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bDcFJZ2tdzd5MPC4LnvhQLcpA6f+Q3idKbwmXtMqKsQcmOW5ajvs91yIPONMD8Csc3IZ48hZ9unVO7nnby4GCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:26:44.567967Z"},"content_sha256":"ea001ea553c5b240e6e5b4bc4cbee278479af6c0799ec89de029c069e981aa8d","schema_version":"1.0","event_id":"sha256:ea001ea553c5b240e6e5b4bc4cbee278479af6c0799ec89de029c069e981aa8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/URDMRKNKVJLOWGUYTHZSUXTTXC/bundle.json","state_url":"https://pith.science/pith/URDMRKNKVJLOWGUYTHZSUXTTXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/URDMRKNKVJLOWGUYTHZSUXTTXC/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":"2026-06-27T18:26:44Z","links":{"resolver":"https://pith.science/pith/URDMRKNKVJLOWGUYTHZSUXTTXC","bundle":"https://pith.science/pith/URDMRKNKVJLOWGUYTHZSUXTTXC/bundle.json","state":"https://pith.science/pith/URDMRKNKVJLOWGUYTHZSUXTTXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/URDMRKNKVJLOWGUYTHZSUXTTXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:URDMRKNKVJLOWGUYTHZSUXTTXC","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":"ab6c814b5986b43fa43099d6959c90480352fd71dc9d4ea8dd3c40c773cc5d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-17T11:38:02Z","title_canon_sha256":"b7e09a0387fb06d7991c3e27dc49aed78b765066c4c808f34ce99af3fa1811ce"},"schema_version":"1.0","source":{"id":"1501.04191","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04191","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04191v2","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04191","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"URDMRKNKVJLO","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"URDMRKNKVJLOWGUY","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"URDMRKNK","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:ea001ea553c5b240e6e5b4bc4cbee278479af6c0799ec89de029c069e981aa8d","target":"graph","created_at":"2026-05-18T00:22:40Z","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":"We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two settings of inexact alternating projections are considered and the corresponding convergence estimates are established and discussed.","authors_text":"Alexander Y. Kruger, Nguyen H. Thao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-17T11:38:02Z","title":"Regularity of collections of sets and convergence of inexact alternating projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04191","kind":"arxiv","version":2},"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":"sha256:53e56d62ffffc67110439fec2cb41116910dfeeab125ad5543ef48e1530e1fb9","target":"record","created_at":"2026-05-18T00:22:40Z","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":"ab6c814b5986b43fa43099d6959c90480352fd71dc9d4ea8dd3c40c773cc5d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-17T11:38:02Z","title_canon_sha256":"b7e09a0387fb06d7991c3e27dc49aed78b765066c4c808f34ce99af3fa1811ce"},"schema_version":"1.0","source":{"id":"1501.04191","kind":"arxiv","version":2}},"canonical_sha256":"a446c8a9aaaa56eb1a9899f32a5e73b88b896b9a96735b49425e8095ea377a6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a446c8a9aaaa56eb1a9899f32a5e73b88b896b9a96735b49425e8095ea377a6b","first_computed_at":"2026-05-18T00:22:40.617760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:40.617760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"flS2FI/As9mel38KsxRkgGsoh/KKGG7D6A6zNpZAcwguRwThlRTiKGLNQJ/Xiow9Zch8iplqLlAa7gGjeja9CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:40.618273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04191","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53e56d62ffffc67110439fec2cb41116910dfeeab125ad5543ef48e1530e1fb9","sha256:ea001ea553c5b240e6e5b4bc4cbee278479af6c0799ec89de029c069e981aa8d"],"state_sha256":"8e1213a9087f9963d3f39e3b107cdb7adfe1ba25ef998f2de941bf4f86d302e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Rw8qeiQ3IQdmLMZhlajr0FSXDmsVWbU9dfkh0dDyghjXJCdYrtzgQqcAaFLkxqLEjMBNBi509Pn8Up7+PhxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T18:26:44.569806Z","bundle_sha256":"b2903766ffafc72f4e53bae577854979b9ba103b453aae790c8da0c3706a541f"}}