{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4Y4ME4BVNYLBJLCK5L2XWJR4IO","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":"4355b8272b8542a5152b89e10f5de2c71421abb782aa152eb40823e0d566a1bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-06-10T09:26:01Z","title_canon_sha256":"293e18ba3d38bf125a1dd22d6044b342063a6bc00f9d20a39ae94bd5a8f9a9bc"},"schema_version":"1.0","source":{"id":"1306.2146","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2146","created_at":"2026-05-18T00:19:59Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2146v6","created_at":"2026-05-18T00:19:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2146","created_at":"2026-05-18T00:19:59Z"},{"alias_kind":"pith_short_12","alias_value":"4Y4ME4BVNYLB","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4Y4ME4BVNYLBJLCK","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4Y4ME4BV","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:0f93b953e9a72c7fdaa1de048523fe511f7b387a835e39f1f29edcb57c9bc089","target":"graph","created_at":"2026-05-18T00:19:59Z","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":"This article has been withdrawn in 2013.\n\nThe class of LOTS (linearly ordered topological spaces) contains many important spaces, like the set of real numbers, the set of rational numbers and the ordinals. Such spaces have rich topological properties, which are not necessarily hereditary.","authors_text":"Kyriakos Papadopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-06-10T09:26:01Z","title":"LOTS as Fixed Point Sets: An Application of Tarski's Fixed Point Theorem (draft)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2146","kind":"arxiv","version":6},"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:a943a3d9ae5144fddd5df0ec4795c045bafa24893a05c36dcae4747bd423220a","target":"record","created_at":"2026-05-18T00:19:59Z","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":"4355b8272b8542a5152b89e10f5de2c71421abb782aa152eb40823e0d566a1bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-06-10T09:26:01Z","title_canon_sha256":"293e18ba3d38bf125a1dd22d6044b342063a6bc00f9d20a39ae94bd5a8f9a9bc"},"schema_version":"1.0","source":{"id":"1306.2146","kind":"arxiv","version":6}},"canonical_sha256":"e638c270356e1614ac4aeaf57b263c43874dbd363858505ed9b8a0f7513f2e02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e638c270356e1614ac4aeaf57b263c43874dbd363858505ed9b8a0f7513f2e02","first_computed_at":"2026-05-18T00:19:59.742338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:59.742338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5myP8opqr8NVHoWQmWvdspqxFRSKTBsTyEN2RlzXZG/pBISFwzAU1c/uNEx/TJL1IUceU7KPrZPgKNkXYBofDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:59.742842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2146","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a943a3d9ae5144fddd5df0ec4795c045bafa24893a05c36dcae4747bd423220a","sha256:0f93b953e9a72c7fdaa1de048523fe511f7b387a835e39f1f29edcb57c9bc089"],"state_sha256":"a10aa86b53f53c2ae78f6a28411df5ba73dd9a2672cd5c5e0dca5626142d46b1"}