{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NZNOHLMPZ7U7J36XHX3C3EJ5RF","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":"763ea4097a6f29b9c9f32108cbe5ab212cee9ab1aae483d267d77f507734746f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-13T08:27:36Z","title_canon_sha256":"42fde98c5460005ad0a5e0b733861980a023f43df8414fd387420ca900c80fc4"},"schema_version":"1.0","source":{"id":"1610.03975","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03975","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03975v3","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03975","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"NZNOHLMPZ7U7","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NZNOHLMPZ7U7J36X","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NZNOHLMP","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:692afeadf142ff416e690968fb17c6824f25daad20b35e2729d8854d607b2b29","target":"graph","created_at":"2026-05-18T00:05:39Z","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 expand upon previous work that examined behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations: that of a line and an ellipse and that of a line together with a $p$-sphere. With computer assistance we discover a beautiful geometry that illustrates phenomena which may affect the behavior of the iterates by slowing or inhibiting convergence for feasible cases. We prove local convergence near feasible points, and---seeking a better understanding of the behavior---we employ parallelization in order to study behavior graphically. Motivated by ","authors_text":"Anna Schneider, Brailey Sims, Jonathan M. Borwein, Matthew P. Skerritt, Scott B. Lindstrom","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-13T08:27:36Z","title":"Dynamics of the Douglas-Rachford Method for Ellipses and p-Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03975","kind":"arxiv","version":3},"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":"sha256:819f06f5ee11230fa75aa77f47619f0150c1bac309bd4d2155f564597410712b","target":"record","created_at":"2026-05-18T00:05:39Z","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":"763ea4097a6f29b9c9f32108cbe5ab212cee9ab1aae483d267d77f507734746f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-13T08:27:36Z","title_canon_sha256":"42fde98c5460005ad0a5e0b733861980a023f43df8414fd387420ca900c80fc4"},"schema_version":"1.0","source":{"id":"1610.03975","kind":"arxiv","version":3}},"canonical_sha256":"6e5ae3ad8fcfe9f4efd73df62d913d89731ace4767aeb8f8c40a2eaa0d0b02c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e5ae3ad8fcfe9f4efd73df62d913d89731ace4767aeb8f8c40a2eaa0d0b02c6","first_computed_at":"2026-05-18T00:05:39.928969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:39.928969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MThDq6cy6Blh6o3qaJKtyw2xJG43oJyRePFLZZlzSAuap6DjeLiwQK0pcPYCpjErF6yPN0ZndGiNKGSLLS9NDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:39.929504Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03975","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:819f06f5ee11230fa75aa77f47619f0150c1bac309bd4d2155f564597410712b","sha256:692afeadf142ff416e690968fb17c6824f25daad20b35e2729d8854d607b2b29"],"state_sha256":"f45b363933cf6d6c4bebc1d0b91b0c1fb4e1eb3b7889756eba178e90b261a00a"}