{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UQQUKDTTLSNDFQVSIUSRVLVBTV","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":"f29afa84b47c68bf6a5e34a249365de32e79ca496d6b8717027b4c66a61cd3f0","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-04T16:02:10Z","title_canon_sha256":"01579e082832b39d34e526740ecd5b9b856570752e09945bde1ff06e16a16393"},"schema_version":"1.0","source":{"id":"1410.1056","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1056","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1056v4","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1056","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"pith_short_12","alias_value":"UQQUKDTTLSND","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UQQUKDTTLSNDFQVS","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UQQUKDTT","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:5a3f21b6fc1b5124c5cda1e27161cac27ce31d61d4d58d8a06de6f8fd89c1dca","target":"graph","created_at":"2026-05-18T01:12:30Z","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 dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert's metric or Thompson's metric. We establish several Denjoy-Wolff type theorems that confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We also extend and put into a broader perspective results by Gaubert and Vigeral concerning the linear escape rate of such nonexpansive mappings.","authors_text":"Bas Lemmens, Brian Lins, Marten Wortel, Roger Nussbaum","cross_cats":["math.FA","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-04T16:02:10Z","title":"Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1056","kind":"arxiv","version":4},"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:d8c51f5df103d636869141b8fa0cd2a1a46b6b5655ff9a86d129503c3b7a341a","target":"record","created_at":"2026-05-18T01:12:30Z","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":"f29afa84b47c68bf6a5e34a249365de32e79ca496d6b8717027b4c66a61cd3f0","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-04T16:02:10Z","title_canon_sha256":"01579e082832b39d34e526740ecd5b9b856570752e09945bde1ff06e16a16393"},"schema_version":"1.0","source":{"id":"1410.1056","kind":"arxiv","version":4}},"canonical_sha256":"a421450e735c9a32c2b245251aaea19d65d6366089e6dc7a660017b92bd24e48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a421450e735c9a32c2b245251aaea19d65d6366089e6dc7a660017b92bd24e48","first_computed_at":"2026-05-18T01:12:30.956666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:30.956666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LTPBLhlTDpz2O85j/en1g/i2+Ze0JTyGf3xnxZCPMK4dDlzfreOsGhQfJ+45cY6kDzi/i5QQc7kuMXIgOExhBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:30.957000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1056","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8c51f5df103d636869141b8fa0cd2a1a46b6b5655ff9a86d129503c3b7a341a","sha256:5a3f21b6fc1b5124c5cda1e27161cac27ce31d61d4d58d8a06de6f8fd89c1dca"],"state_sha256":"92edd1fd911996a219baa0115ebc05782e68c47ff664d4583d6e1a6ffb7663f9"}