{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MEOPJQTU5RHJYNAOQYB57SA666","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":"3a79dbe35b35ff08fa97edaaef126804130d010bbaad431943f4b68c348a2b63","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-31T08:04:21Z","title_canon_sha256":"e01742535b1b1fdd6cfb174f148be8e3d69a0224948b94e3088a0fa89555110b"},"schema_version":"1.0","source":{"id":"1801.10334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10334","created_at":"2026-05-18T00:24:41Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10334v1","created_at":"2026-05-18T00:24:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10334","created_at":"2026-05-18T00:24:41Z"},{"alias_kind":"pith_short_12","alias_value":"MEOPJQTU5RHJ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MEOPJQTU5RHJYNAO","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MEOPJQTU","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:f9fb7457b894a5e51fc9deff511f76c27f7b4f8198166e285fabd76aedc611ac","target":"graph","created_at":"2026-05-18T00:24:41Z","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":"Let $K$ be a homogeneous self-similar set satisfying the strong separation condition. This paper is concerned with the quantitative recurrence properties of the natural map $T: K\\rightarrow K$ induced by the shift. Let $\\mu$ be the natural self-similar measure supported on $K$. For a positive function $\\varphi$ defined on $\\mathbb{N}$, we show that the $\\mu$-measure of the following set \\begin{equation*}\n  R(\\varphi):=\\{x\\in K: |T^n x-x|<\\varphi(n) \\; \\text{for infinitely many} \\; n\\in\\mathbb{N}\\} \\end{equation*} is null or full according to convergence or divergence of a certain series. Moreo","authors_text":"Min Wu, Wen Wu, Yuanyang Chang","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-31T08:04:21Z","title":"Quantitative recurrence properties and homogeneous self-similar sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10334","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":"sha256:7d968c2f23c89130da6aa0cf61bf893bbc2f290d24321189102ba788a653b13a","target":"record","created_at":"2026-05-18T00:24:41Z","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":"3a79dbe35b35ff08fa97edaaef126804130d010bbaad431943f4b68c348a2b63","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-31T08:04:21Z","title_canon_sha256":"e01742535b1b1fdd6cfb174f148be8e3d69a0224948b94e3088a0fa89555110b"},"schema_version":"1.0","source":{"id":"1801.10334","kind":"arxiv","version":1}},"canonical_sha256":"611cf4c274ec4e9c340e8603dfc81ef796d9408a61207370e363d33e1ceee1b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"611cf4c274ec4e9c340e8603dfc81ef796d9408a61207370e363d33e1ceee1b8","first_computed_at":"2026-05-18T00:24:41.067978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:41.067978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LzgKVn2wCjOXs4V+VWJSYPNyrDvdGPbEPFwPD16m4SwwX1aW9Tbx+Kisg5U/chTgyHyR2LrTRwAGlrvvUgcFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:41.068484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.10334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d968c2f23c89130da6aa0cf61bf893bbc2f290d24321189102ba788a653b13a","sha256:f9fb7457b894a5e51fc9deff511f76c27f7b4f8198166e285fabd76aedc611ac"],"state_sha256":"9ba49f54b0ff6b5775004a7339ec2c8c63ca2d70ff43b6df5c0c466fb54d92fa"}