{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ND6JL6ANHT64JQYGAIUPQLCBOU","short_pith_number":"pith:ND6JL6AN","canonical_record":{"source":{"id":"1403.3489","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T05:40:56Z","cross_cats_sorted":["math.GN","math.MG"],"title_canon_sha256":"78b940de02c31ae19363810934c202f123e86f8e5b45d5609f241c2606caf566","abstract_canon_sha256":"1643e7bdb21f205c23683b0dd360213547563f46bd6985d514b62b1468fe0f91"},"schema_version":"1.0"},"canonical_sha256":"68fc95f80d3cfdc4c3060228f82c41751972538075cb337dbb282fa14799f19a","source":{"kind":"arxiv","id":"1403.3489","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3489","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3489v3","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3489","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"ND6JL6ANHT64","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"ND6JL6ANHT64JQYG","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"ND6JL6AN","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ND6JL6ANHT64JQYGAIUPQLCBOU","target":"record","payload":{"canonical_record":{"source":{"id":"1403.3489","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T05:40:56Z","cross_cats_sorted":["math.GN","math.MG"],"title_canon_sha256":"78b940de02c31ae19363810934c202f123e86f8e5b45d5609f241c2606caf566","abstract_canon_sha256":"1643e7bdb21f205c23683b0dd360213547563f46bd6985d514b62b1468fe0f91"},"schema_version":"1.0"},"canonical_sha256":"68fc95f80d3cfdc4c3060228f82c41751972538075cb337dbb282fa14799f19a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:04.303660Z","signature_b64":"nf203cN7XX5jlu7iMBLHCFWvKQqnvrJUnwoxrBo9ldS/YtivWeYT+KT8BBZMecrjmLMo813F/YLT67CWOfPCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68fc95f80d3cfdc4c3060228f82c41751972538075cb337dbb282fa14799f19a","last_reissued_at":"2026-05-18T02:45:04.303024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:04.303024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.3489","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fngwu+8jgxMm6oh2uN4vAp+kGVU2FFWOEZN3DZyQurN5e7FPuTcXhZ1v2ivjCzJ4OPxCBw4p1d8KhRv5V//kDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:47:13.711056Z"},"content_sha256":"a8c693017dcca52b9ce1dfa752c362be18f7b8ab28b8a29d6903552e5316be47","schema_version":"1.0","event_id":"sha256:a8c693017dcca52b9ce1dfa752c362be18f7b8ab28b8a29d6903552e5316be47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ND6JL6ANHT64JQYGAIUPQLCBOU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lipschitz equivalence of self-similar sets and hyperbolic boundaries II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.MG"],"primary_cat":"math.CO","authors_text":"Guo-Tai Deng, Jun Jason Luo, Ka-Sing Lau","submitted_at":"2014-03-14T05:40:56Z","abstract_excerpt":"In \\cite{LuLa13}, two of the authors initiated a study of Lipschitz equivalence of self-similar sets through the augmented trees, a class of hyperbolic graphs introduced by Kaimanovich \\cite{Ka03} and developed by Lau and Wang \\cite{LaWa09}. In this paper, we continue such investigation. We remove a major assumption in the main theorem in \\cite{LuLa13} by using a new notion of quasi-rearrangeable matrix, and show that the hyperbolic boundary of any simple augmented tree is Lipschitz equivalent to a Cantor-type set. We then apply this result to consider the Lipschitz equivalence of certain tota"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3489","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PuXXdM1UZAGBsGNLSVjZOmX+n6xCHw0O4P87iQhzVtIR10rMWUrP1RWSHMiFHSO8OaocpNS8gBJWtj8lLNjuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:47:13.711754Z"},"content_sha256":"fd72a68b10462637b6883fff2a21448df9b264bb4ee994224890f760dbbbbfef","schema_version":"1.0","event_id":"sha256:fd72a68b10462637b6883fff2a21448df9b264bb4ee994224890f760dbbbbfef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ND6JL6ANHT64JQYGAIUPQLCBOU/bundle.json","state_url":"https://pith.science/pith/ND6JL6ANHT64JQYGAIUPQLCBOU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ND6JL6ANHT64JQYGAIUPQLCBOU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T14:47:13Z","links":{"resolver":"https://pith.science/pith/ND6JL6ANHT64JQYGAIUPQLCBOU","bundle":"https://pith.science/pith/ND6JL6ANHT64JQYGAIUPQLCBOU/bundle.json","state":"https://pith.science/pith/ND6JL6ANHT64JQYGAIUPQLCBOU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ND6JL6ANHT64JQYGAIUPQLCBOU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ND6JL6ANHT64JQYGAIUPQLCBOU","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":"1643e7bdb21f205c23683b0dd360213547563f46bd6985d514b62b1468fe0f91","cross_cats_sorted":["math.GN","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T05:40:56Z","title_canon_sha256":"78b940de02c31ae19363810934c202f123e86f8e5b45d5609f241c2606caf566"},"schema_version":"1.0","source":{"id":"1403.3489","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3489","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3489v3","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3489","created_at":"2026-05-18T02:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"ND6JL6ANHT64","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"ND6JL6ANHT64JQYG","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"ND6JL6AN","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:fd72a68b10462637b6883fff2a21448df9b264bb4ee994224890f760dbbbbfef","target":"graph","created_at":"2026-05-18T02:45:04Z","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 \\cite{LuLa13}, two of the authors initiated a study of Lipschitz equivalence of self-similar sets through the augmented trees, a class of hyperbolic graphs introduced by Kaimanovich \\cite{Ka03} and developed by Lau and Wang \\cite{LaWa09}. In this paper, we continue such investigation. We remove a major assumption in the main theorem in \\cite{LuLa13} by using a new notion of quasi-rearrangeable matrix, and show that the hyperbolic boundary of any simple augmented tree is Lipschitz equivalent to a Cantor-type set. We then apply this result to consider the Lipschitz equivalence of certain tota","authors_text":"Guo-Tai Deng, Jun Jason Luo, Ka-Sing Lau","cross_cats":["math.GN","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T05:40:56Z","title":"Lipschitz equivalence of self-similar sets and hyperbolic boundaries II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3489","kind":"arxiv","version":3},"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:a8c693017dcca52b9ce1dfa752c362be18f7b8ab28b8a29d6903552e5316be47","target":"record","created_at":"2026-05-18T02:45:04Z","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":"1643e7bdb21f205c23683b0dd360213547563f46bd6985d514b62b1468fe0f91","cross_cats_sorted":["math.GN","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-14T05:40:56Z","title_canon_sha256":"78b940de02c31ae19363810934c202f123e86f8e5b45d5609f241c2606caf566"},"schema_version":"1.0","source":{"id":"1403.3489","kind":"arxiv","version":3}},"canonical_sha256":"68fc95f80d3cfdc4c3060228f82c41751972538075cb337dbb282fa14799f19a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68fc95f80d3cfdc4c3060228f82c41751972538075cb337dbb282fa14799f19a","first_computed_at":"2026-05-18T02:45:04.303024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:04.303024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nf203cN7XX5jlu7iMBLHCFWvKQqnvrJUnwoxrBo9ldS/YtivWeYT+KT8BBZMecrjmLMo813F/YLT67CWOfPCBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:04.303660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3489","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8c693017dcca52b9ce1dfa752c362be18f7b8ab28b8a29d6903552e5316be47","sha256:fd72a68b10462637b6883fff2a21448df9b264bb4ee994224890f760dbbbbfef"],"state_sha256":"576ebdbceb3faeab071ad5a6482ae6fbc8f522ba0dfa49fddd3fa069738f8eb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Og2EPe52O79ruI4c9gs1fKvErfAbxXKztwcR/rPqUC8JTSY/0NjEEkKRyHjAIWeKM7PddI3WxHW6dfdwmMAvDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:47:13.715519Z","bundle_sha256":"a08e9f72124d86abddbd532a884ddc5837b3896bb1ecbec138e54a6470ad929f"}}