{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JOLM4ZVQNMNELV2LCBRBVUEYPR","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":"69f85ba0b4038d46297d217989eb513c61d1ca29dd49a7a170b46f04afddfedb","cross_cats_sorted":["math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-05-16T06:34:08Z","title_canon_sha256":"93bc462367e87dd775038732d2fef37215ca3ba790a644bed56bf986ecde785a"},"schema_version":"1.0","source":{"id":"1205.3563","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3563","created_at":"2026-05-18T03:35:41Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3563v2","created_at":"2026-05-18T03:35:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3563","created_at":"2026-05-18T03:35:41Z"},{"alias_kind":"pith_short_12","alias_value":"JOLM4ZVQNMNE","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JOLM4ZVQNMNELV2L","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JOLM4ZVQ","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:f046e74bfe8f28db5b6cd54df2a3c1e8101ecc639d7af16a928d2a8ed25422b8","target":"graph","created_at":"2026-05-18T03:35:41Z","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":"In [9] Kaimanovich introduced the concept of augmented tree on the symbolic space of a self-similar set. It is hyperbolic in the sense of Gromov, and it was shown in [13] that under the open set condition, a self-similar set can be identified with the hyperbolic boundary of the tree. In the paper, we investigate in detail a class of simple augmented trees and the Lipschitz equivalence of such trees. The main purpose is to use this to study the Lipschitz equivalence problem of the totally disconnected self-similar sets which has been undergoing some extensive development recently.","authors_text":"Jun Jason Luo, Ka-Sing Lau","cross_cats":["math.GN","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-05-16T06:34:08Z","title":"Lipschitz equivalence of self-similar sets and hyperbolic boundaries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3563","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:b1cba41c309beb21f0502574b04704fa5bb6dc9fa2eaa0cd809436dc6b11671d","target":"record","created_at":"2026-05-18T03:35:41Z","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":"69f85ba0b4038d46297d217989eb513c61d1ca29dd49a7a170b46f04afddfedb","cross_cats_sorted":["math.GN","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-05-16T06:34:08Z","title_canon_sha256":"93bc462367e87dd775038732d2fef37215ca3ba790a644bed56bf986ecde785a"},"schema_version":"1.0","source":{"id":"1205.3563","kind":"arxiv","version":2}},"canonical_sha256":"4b96ce66b06b1a45d74b10621ad0987c5429f2ac587a47a8722ab0d27934bbe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b96ce66b06b1a45d74b10621ad0987c5429f2ac587a47a8722ab0d27934bbe5","first_computed_at":"2026-05-18T03:35:41.044847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:41.044847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uU3PvNhIgTk1VGtzjcCtTQEe0E5lNd2S23bSXHeS0c8PULLqfsFr+90Ksp0tVW7075cNBFckg9BiZKoG1zRVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:41.045543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3563","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1cba41c309beb21f0502574b04704fa5bb6dc9fa2eaa0cd809436dc6b11671d","sha256:f046e74bfe8f28db5b6cd54df2a3c1e8101ecc639d7af16a928d2a8ed25422b8"],"state_sha256":"db4e090085b6b910fe498904e66de52e5521e314546f7db1eddd455699b5fd9f"}