{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3J7YFCXMSXPA2HXWXPZYWFGDD6","short_pith_number":"pith:3J7YFCXM","canonical_record":{"source":{"id":"1402.0080","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-01T11:41:28Z","cross_cats_sorted":[],"title_canon_sha256":"d8ad8e0559ea885a0092aad90516119a6ca5b2834f05c7b2bb19062a8f7aa452","abstract_canon_sha256":"d3bffc55a6452a0553f4d0b77601773d0a3013ba28c3bdf35480e0cad9a7d32e"},"schema_version":"1.0"},"canonical_sha256":"da7f828aec95de0d1ef6bbf38b14c31fa6ffa4a903a5180bff7b57ddc1843edb","source":{"kind":"arxiv","id":"1402.0080","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0080","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0080v4","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0080","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"3J7YFCXMSXPA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3J7YFCXMSXPA2HXW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3J7YFCXM","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3J7YFCXMSXPA2HXWXPZYWFGDD6","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0080","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-01T11:41:28Z","cross_cats_sorted":[],"title_canon_sha256":"d8ad8e0559ea885a0092aad90516119a6ca5b2834f05c7b2bb19062a8f7aa452","abstract_canon_sha256":"d3bffc55a6452a0553f4d0b77601773d0a3013ba28c3bdf35480e0cad9a7d32e"},"schema_version":"1.0"},"canonical_sha256":"da7f828aec95de0d1ef6bbf38b14c31fa6ffa4a903a5180bff7b57ddc1843edb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:53.836365Z","signature_b64":"fhdBh1L+py7Og9+SZPc4JgyQnb8YMpoxUx9pC04WMuguWRvPES6nDaBnM1QXeZtkGy8/caC36u0lWbklIygICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da7f828aec95de0d1ef6bbf38b14c31fa6ffa4a903a5180bff7b57ddc1843edb","last_reissued_at":"2026-05-18T02:42:53.835937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:53.835937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0080","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ujNW4KD7Uy+GOWKuyrGLL+W54NZngNZ3F0YXRXxwNnvXXDfcJq0q9RQQ4B0Io75ivYo0Luo0TOaDWipLstEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:07:42.136952Z"},"content_sha256":"0c4861d578193e9a59bb7cef9361a12f861bd4f9213dd87f5bf3019082c1bdd4","schema_version":"1.0","event_id":"sha256:0c4861d578193e9a59bb7cef9361a12f861bd4f9213dd87f5bf3019082c1bdd4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3J7YFCXMSXPA2HXWXPZYWFGDD6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bilipschitz embedding of homogeneous fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Fan L\\\"u, Li-Feng Xi, Man-Li Lou, Zhi-Ying Wen","submitted_at":"2014-02-01T11:41:28Z","abstract_excerpt":"In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0080","kind":"arxiv","version":4},"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":"2026-05-18T02:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vosyRVi4QK+jAgrhkg+Wpo1AbFEVjsCrnttBlYj367vcGmZHrbeX+AliUZ+EPf7Xrlz0hUkXW1EZAmeGf6k4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:07:42.137285Z"},"content_sha256":"36d66f265c3b88b175878e65bf25df90a0d2983a3170384a4ae7696ef66896ba","schema_version":"1.0","event_id":"sha256:36d66f265c3b88b175878e65bf25df90a0d2983a3170384a4ae7696ef66896ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3J7YFCXMSXPA2HXWXPZYWFGDD6/bundle.json","state_url":"https://pith.science/pith/3J7YFCXMSXPA2HXWXPZYWFGDD6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3J7YFCXMSXPA2HXWXPZYWFGDD6/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":"2026-06-23T05:07:42Z","links":{"resolver":"https://pith.science/pith/3J7YFCXMSXPA2HXWXPZYWFGDD6","bundle":"https://pith.science/pith/3J7YFCXMSXPA2HXWXPZYWFGDD6/bundle.json","state":"https://pith.science/pith/3J7YFCXMSXPA2HXWXPZYWFGDD6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3J7YFCXMSXPA2HXWXPZYWFGDD6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3J7YFCXMSXPA2HXWXPZYWFGDD6","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":"d3bffc55a6452a0553f4d0b77601773d0a3013ba28c3bdf35480e0cad9a7d32e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-01T11:41:28Z","title_canon_sha256":"d8ad8e0559ea885a0092aad90516119a6ca5b2834f05c7b2bb19062a8f7aa452"},"schema_version":"1.0","source":{"id":"1402.0080","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0080","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0080v4","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0080","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"3J7YFCXMSXPA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3J7YFCXMSXPA2HXW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3J7YFCXM","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:36d66f265c3b88b175878e65bf25df90a0d2983a3170384a4ae7696ef66896ba","target":"graph","created_at":"2026-05-18T02:42:53Z","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 introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.","authors_text":"Fan L\\\"u, Li-Feng Xi, Man-Li Lou, Zhi-Ying Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-01T11:41:28Z","title":"Bilipschitz embedding of homogeneous fractals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0080","kind":"arxiv","version":4},"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":"sha256:0c4861d578193e9a59bb7cef9361a12f861bd4f9213dd87f5bf3019082c1bdd4","target":"record","created_at":"2026-05-18T02:42:53Z","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":"d3bffc55a6452a0553f4d0b77601773d0a3013ba28c3bdf35480e0cad9a7d32e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-01T11:41:28Z","title_canon_sha256":"d8ad8e0559ea885a0092aad90516119a6ca5b2834f05c7b2bb19062a8f7aa452"},"schema_version":"1.0","source":{"id":"1402.0080","kind":"arxiv","version":4}},"canonical_sha256":"da7f828aec95de0d1ef6bbf38b14c31fa6ffa4a903a5180bff7b57ddc1843edb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da7f828aec95de0d1ef6bbf38b14c31fa6ffa4a903a5180bff7b57ddc1843edb","first_computed_at":"2026-05-18T02:42:53.835937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:53.835937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fhdBh1L+py7Og9+SZPc4JgyQnb8YMpoxUx9pC04WMuguWRvPES6nDaBnM1QXeZtkGy8/caC36u0lWbklIygICA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:53.836365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0080","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c4861d578193e9a59bb7cef9361a12f861bd4f9213dd87f5bf3019082c1bdd4","sha256:36d66f265c3b88b175878e65bf25df90a0d2983a3170384a4ae7696ef66896ba"],"state_sha256":"2814468d76ef8d3fb2496d61a84ab7bb45a0b67bd24dac193a7900301b1fd260"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+GOk6Cel547/bbLYSDEPkrLlFCD7KELLUNlju51AoMFMrr5Jf9p2trUfjaci8uocCk2ancrWbMMYIn6v9VRwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:07:42.139208Z","bundle_sha256":"c8fe99e6ac260ca2a86777e093a91b489f0772d9731445556108a7e34034d920"}}