{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GJDW3P7S4DMP3USAMC55TROGZS","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":"10c160ccb5214ba590224ce5fa560213bb98f5fc3b4aedf59cea679f76afe683","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-07-10T08:20:20Z","title_canon_sha256":"badf273e26de778e16ec95add186b390d410fe5ca6c50dd3106da50295f914fc"},"schema_version":"1.0","source":{"id":"1307.2712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2712","created_at":"2026-05-18T03:18:50Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2712v1","created_at":"2026-05-18T03:18:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2712","created_at":"2026-05-18T03:18:50Z"},{"alias_kind":"pith_short_12","alias_value":"GJDW3P7S4DMP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GJDW3P7S4DMP3USA","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GJDW3P7S","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:ef5babd12c36fed8fc19571c153565eff26b0abfe113867de44501c2ed09d058","target":"graph","created_at":"2026-05-18T03:18:50Z","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":"Suppose that $A$ and $B$ are closed subsets of a Euclidean space such that $A\\cap B\\neq\\varnothing$, and we aim to find a point in this intersection with the help of the sequences $(a_n)_\\nnn$ and $(b_n)_\\nnn$ generated by the \\emph{method of alternating projections}. It is well known that if $A$ and $B$ are convex, then $(a_n)_\\nnn$ and $(b_n)_\\nnn$ converge to some point in $A\\cap B$. The situation in the nonconvex case is much more delicate. In 1990, Combettes and Trussell presented a dichotomy result that guarantees either convergence to a point in the intersection or a nondegenerate compa","authors_text":"Dominikus Noll, Heinz H. Bauschke","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-07-10T08:20:20Z","title":"On cluster points of alternating projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2712","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":"sha256:5c4f574ce605865438505ae37ec54bd666a72b11db850e9fb299bbc476553025","target":"record","created_at":"2026-05-18T03:18:50Z","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":"10c160ccb5214ba590224ce5fa560213bb98f5fc3b4aedf59cea679f76afe683","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-07-10T08:20:20Z","title_canon_sha256":"badf273e26de778e16ec95add186b390d410fe5ca6c50dd3106da50295f914fc"},"schema_version":"1.0","source":{"id":"1307.2712","kind":"arxiv","version":1}},"canonical_sha256":"32476dbff2e0d8fdd24060bbd9c5c6cca49b47a32e7080f98f848925823ddf89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32476dbff2e0d8fdd24060bbd9c5c6cca49b47a32e7080f98f848925823ddf89","first_computed_at":"2026-05-18T03:18:50.648618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:50.648618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxryJvOUr9zeBfQBC9uDjSlQ1k8E1B1LHlLLdWXrdkF5aJWnSmwMOVW/2QsvMhbLiPBI0UyZl/47Tl/qWocgBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:50.649231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c4f574ce605865438505ae37ec54bd666a72b11db850e9fb299bbc476553025","sha256:ef5babd12c36fed8fc19571c153565eff26b0abfe113867de44501c2ed09d058"],"state_sha256":"ab30c49fe146396b8ef3e3006bdc9709d5e6beef737acf3c330b70e0676d1516"}