{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XV2L7KJ2ZOAJ2NSH6RMXOBPZQT","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":"5b44a1af4ddb04a489b834e317c576c4785d8ca2727e3eccf4b35fde89814626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-25T19:13:40Z","title_canon_sha256":"574ec850aaefb9ab1ca72fe47f5f4b3b21df201f454880ffc15582197fc8fd56"},"schema_version":"1.0","source":{"id":"1506.07851","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07851","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07851v2","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07851","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"XV2L7KJ2ZOAJ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XV2L7KJ2ZOAJ2NSH","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XV2L7KJ2","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:82a9e1656e84156a9e3307f786c616e29c46ee00b80dea4d15eb2645396889a8","target":"graph","created_at":"2026-05-18T00:51:34Z","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 consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain sub-self-affine sets. In addition to dimension results for the limit set, we manage to express the Assouad dimension of any closed subset of a self-conformal set by means of the Hausdorff dimension. As an interesting consequence of this, we show that a Furstenberg homogeneous self-similar set in the real line satisfies the weak separation condition. We also exhibit ","authors_text":"Antti K\\\"aenm\\\"aki, Eino Rossi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-25T19:13:40Z","title":"Weak separation condition, Assouad dimension, and Furstenberg homogeneity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07851","kind":"arxiv","version":2},"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:f861293fe9d17d56b1a2cdb972caf7898ad84054304e934f04924aa94a99f002","target":"record","created_at":"2026-05-18T00:51:34Z","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":"5b44a1af4ddb04a489b834e317c576c4785d8ca2727e3eccf4b35fde89814626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-06-25T19:13:40Z","title_canon_sha256":"574ec850aaefb9ab1ca72fe47f5f4b3b21df201f454880ffc15582197fc8fd56"},"schema_version":"1.0","source":{"id":"1506.07851","kind":"arxiv","version":2}},"canonical_sha256":"bd74bfa93acb809d3647f4597705f984d4161030ae2dbad1277dde3fd4d10985","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd74bfa93acb809d3647f4597705f984d4161030ae2dbad1277dde3fd4d10985","first_computed_at":"2026-05-18T00:51:34.312293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:34.312293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E/anWbT5iaspBZZ/vscQsgBodRhJRGuADK6FgP9p/o4zfmQ5Zi/+5blMf/Sup3oEOXAiYyJrtkpJ4+UVwvS9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:34.312675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07851","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f861293fe9d17d56b1a2cdb972caf7898ad84054304e934f04924aa94a99f002","sha256:82a9e1656e84156a9e3307f786c616e29c46ee00b80dea4d15eb2645396889a8"],"state_sha256":"9b3ce62d8c4e7e5861d0b3d5554012796a5b67490b1314a211b13df2249d6ed0"}