{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7OHB4PUXKX7IYYZ2QNDFWMUJNX","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":"a572707dba90c6c9464a150bee6d3a82e9f61df5e4186066af8d2e96e37dad5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-05-03T20:03:32Z","title_canon_sha256":"f3f16c00bc1fe6990d7ea2a94f849896e5c6715cbab48e0929450c218f2db754"},"schema_version":"1.0","source":{"id":"1305.0832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0832","created_at":"2026-05-18T03:26:31Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0832v1","created_at":"2026-05-18T03:26:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0832","created_at":"2026-05-18T03:26:31Z"},{"alias_kind":"pith_short_12","alias_value":"7OHB4PUXKX7I","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7OHB4PUXKX7IYYZ2","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7OHB4PUX","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:e8931cc60faa01fd9ec2f6a7097fcae9ca144221ab8af8d444105c939648e200","target":"graph","created_at":"2026-05-18T03:26:31Z","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":"Further extensions are given to the fixed point result (for implicit contractions) due to Altun and Simsek [Fixed Point Th. Appl., Volume 2010, Article ID 621469]. Some connections with related statements in the area due to Agarwal, El-Gebeily and O'Regan [Appl. Anal., 87 (2008), 109-116] are also discussed. Finally, the old approach in Turinici [An. St. Univ. \"A. I. Cuza\" Iasi, 22 (1976), 177-180] is presented, for historical reasons.","authors_text":"Mihai Turinici","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-05-03T20:03:32Z","title":"Implicit contractive maps in ordered metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0832","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":"sha256:97ad682d2fa1da4c99d304047a84e39ae05f58a92f1f624d464718e4dfbcf958","target":"record","created_at":"2026-05-18T03:26:31Z","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":"a572707dba90c6c9464a150bee6d3a82e9f61df5e4186066af8d2e96e37dad5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-05-03T20:03:32Z","title_canon_sha256":"f3f16c00bc1fe6990d7ea2a94f849896e5c6715cbab48e0929450c218f2db754"},"schema_version":"1.0","source":{"id":"1305.0832","kind":"arxiv","version":1}},"canonical_sha256":"fb8e1e3e9755fe8c633a83465b32896dee0caaecf834d19816af17cbdb856864","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb8e1e3e9755fe8c633a83465b32896dee0caaecf834d19816af17cbdb856864","first_computed_at":"2026-05-18T03:26:31.600992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:31.600992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2/7L84XdUc/dtfRm9m4ZlMJhsKF9P4mrYgk9bcHCqhjgYCF4cXtcT1VqbI/eIzgUbc86dorolU5h6Ph8r/YzAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:31.601744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97ad682d2fa1da4c99d304047a84e39ae05f58a92f1f624d464718e4dfbcf958","sha256:e8931cc60faa01fd9ec2f6a7097fcae9ca144221ab8af8d444105c939648e200"],"state_sha256":"1342f7aa7e3668192afca8b48ea020cc060b13f35b852502d3fc81706603cedd"}