{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HBSKVZJVR2OSQOAHIFIJH576CK","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":"65215d1182ebfc94069e3ca9e53de6364e2c26977d90fca12921dca95b299795","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-27T13:59:38Z","title_canon_sha256":"347e87ff1eb1c505c32d68a786b45eac17cd7950c189d6427dffc9052b898a5d"},"schema_version":"1.0","source":{"id":"1808.08849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08849","created_at":"2026-05-18T00:07:13Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08849v1","created_at":"2026-05-18T00:07:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08849","created_at":"2026-05-18T00:07:13Z"},{"alias_kind":"pith_short_12","alias_value":"HBSKVZJVR2OS","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HBSKVZJVR2OSQOAH","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HBSKVZJV","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:bd31cdc29350ef3aa62b009d9c90b60943ace5cdcc4e2ebaf9ce1ecd6b9997d1","target":"graph","created_at":"2026-05-18T00:07:13Z","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":"In this paper, we study a class $\\mathcal{A}(\\lambda ,n,m)$ of self-similar sets with $m$ exact overlaps generated by $n$ similitudes of the same ratio $ \\lambda $. We obtain a necessary condition for a self-similar set in $\\mathcal{A}(\\lambda ,n,m)$ to be Lipschitz equivalent to a self-similar set satisfying the strong separation condition, i.e., there exists an integer $ k\\geq 2$ such that $x^{2k}-mx^{k}+n$ is reducible, in particular, $m$ belongs to $\\{a^{i}:a\\in \\mathbb{N}$ with $i\\geq 2\\}.$","authors_text":"Kan Jiang, Lifeng Xi, Songjing Wang","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-27T13:59:38Z","title":"Lipschitz equivalence of self-similar sets with exact overlaps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08849","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":"sha256:1ed0e7388eb0a2996ef721e439ca7058a5535c6c7dcbd49ec7ec3300f809423d","target":"record","created_at":"2026-05-18T00:07:13Z","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":"65215d1182ebfc94069e3ca9e53de6364e2c26977d90fca12921dca95b299795","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-27T13:59:38Z","title_canon_sha256":"347e87ff1eb1c505c32d68a786b45eac17cd7950c189d6427dffc9052b898a5d"},"schema_version":"1.0","source":{"id":"1808.08849","kind":"arxiv","version":1}},"canonical_sha256":"3864aae5358e9d283807415093f7fe1298670702c358046bc0ce25a88e5f9059","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3864aae5358e9d283807415093f7fe1298670702c358046bc0ce25a88e5f9059","first_computed_at":"2026-05-18T00:07:13.056292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:13.056292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WGDBC1TmaqVoJfngrmuqO6jO3sP2u9iHCldpuybf9GWrDmIRqV0Pk4bnuA7Liv4kSKd0yLBjwXMemf/RidYJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:13.056920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.08849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ed0e7388eb0a2996ef721e439ca7058a5535c6c7dcbd49ec7ec3300f809423d","sha256:bd31cdc29350ef3aa62b009d9c90b60943ace5cdcc4e2ebaf9ce1ecd6b9997d1"],"state_sha256":"95a0a431bb69a3783578e256e179eda8315171b85534b3098c6406e78b0a7c83"}