{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5QKYXJHQUHDDCEDUJ45YDTMHPD","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":"82f7905f4a21be8ed3b6b01ed113efc0c191983cc6dbe71ec3659cf84cc2f617","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-12-02T20:42:58Z","title_canon_sha256":"fead3097f9c101fbc3fdbb2090372004902b311fd29ef89406c45c66944d9f7d"},"schema_version":"1.0","source":{"id":"1312.0587","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0587","created_at":"2026-05-18T03:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0587v1","created_at":"2026-05-18T03:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0587","created_at":"2026-05-18T03:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"5QKYXJHQUHDD","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5QKYXJHQUHDDCEDU","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5QKYXJHQ","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:7db5077f5387ea83d3a888b5b44e17e8c282abccde293f3c6439e9a81d571b78","target":"graph","created_at":"2026-05-18T03:05:37Z","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":"A family f_1,...,f_n of operators on a complete metric space X is called contractive if there exists lambda < 1 such that for any x,y in X we have d(f_i(x),f_i(y)) leq lambda d(x,y) for some i. Stein conjectured that for any contractive family there is some composition of the operators f_i that has a fixed point. Austin gave a counterexample to this, and asked if Stein's conjecture is true if we restrict to compact spaces. Our aim in this paper is to show that, even for compact spaces, Stein's conjecture is false.","authors_text":"Luka Milicevic","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-12-02T20:42:58Z","title":"Contractive Families on Compact Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0587","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":"sha256:5237ce0330291e13a27a26eb6091a4c72ac7d8a35bd433f92369eaf33620899f","target":"record","created_at":"2026-05-18T03:05:37Z","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":"82f7905f4a21be8ed3b6b01ed113efc0c191983cc6dbe71ec3659cf84cc2f617","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-12-02T20:42:58Z","title_canon_sha256":"fead3097f9c101fbc3fdbb2090372004902b311fd29ef89406c45c66944d9f7d"},"schema_version":"1.0","source":{"id":"1312.0587","kind":"arxiv","version":1}},"canonical_sha256":"ec158ba4f0a1c63110744f3b81cd8778eeb1717c43daafb837782ea24a905c62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec158ba4f0a1c63110744f3b81cd8778eeb1717c43daafb837782ea24a905c62","first_computed_at":"2026-05-18T03:05:37.166823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:37.166823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c1u9CwXEne1cs/WXY2EHaf2jb+qnMZvVN9bCMKP8tBwuPlPRWnr5srn8/zDu9ivIGsfPYEKuJErX0hNLEijJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:37.167646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0587","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5237ce0330291e13a27a26eb6091a4c72ac7d8a35bd433f92369eaf33620899f","sha256:7db5077f5387ea83d3a888b5b44e17e8c282abccde293f3c6439e9a81d571b78"],"state_sha256":"29fb18cee6c9244a5b5f2472656bd02160f29fe9fdae37ddf54916e2202a0312"}