{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WQAYU5PO3SBITBE4KFX7XFV76H","short_pith_number":"pith:WQAYU5PO","schema_version":"1.0","canonical_sha256":"b4018a75eedc8289849c516ffb96bff1c0d9bc1d8721e3d8011e0d4c5f4557a0","source":{"kind":"arxiv","id":"1609.04296","version":1},"attestation_state":"computed","paper":{"title":"Lipschitz invariance of walk dimension on connected self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hui Rao, Qingsong Gu","submitted_at":"2016-09-14T14:32:40Z","abstract_excerpt":"Walk dimension is an important conception in analysis of fractals. In this paper we prove that the walk dimension of a connected compact set possessing an Alfors regular measure is an invariant under Lipschitz transforms. As an application, we show some generalized Sierpi\\'nski gaskets are not Lipschitz equivalent."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.04296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-14T14:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"e6fc4dddf634aefd73ff7f0f47e155895c2fa349e71edcac44a0aa8a71120b81","abstract_canon_sha256":"9b09e21cf987f79167063e3b39d9fc9f7b08e007d4693c582f457c0081383a7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:38.347923Z","signature_b64":"3RQT3joyKtjQ3OK1Jesl2QxEgFAeqOL+vT3otfeOIaiIwOHxEdOkMcl32emyWkYm6U2YxgasoktChzJl1e/lDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4018a75eedc8289849c516ffb96bff1c0d9bc1d8721e3d8011e0d4c5f4557a0","last_reissued_at":"2026-05-18T01:04:38.347398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:38.347398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lipschitz invariance of walk dimension on connected self-similar sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hui Rao, Qingsong Gu","submitted_at":"2016-09-14T14:32:40Z","abstract_excerpt":"Walk dimension is an important conception in analysis of fractals. In this paper we prove that the walk dimension of a connected compact set possessing an Alfors regular measure is an invariant under Lipschitz transforms. As an application, we show some generalized Sierpi\\'nski gaskets are not Lipschitz equivalent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04296","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.04296","created_at":"2026-05-18T01:04:38.347469+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.04296v1","created_at":"2026-05-18T01:04:38.347469+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04296","created_at":"2026-05-18T01:04:38.347469+00:00"},{"alias_kind":"pith_short_12","alias_value":"WQAYU5PO3SBI","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"WQAYU5PO3SBITBE4","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"WQAYU5PO","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WQAYU5PO3SBITBE4KFX7XFV76H","json":"https://pith.science/pith/WQAYU5PO3SBITBE4KFX7XFV76H.json","graph_json":"https://pith.science/api/pith-number/WQAYU5PO3SBITBE4KFX7XFV76H/graph.json","events_json":"https://pith.science/api/pith-number/WQAYU5PO3SBITBE4KFX7XFV76H/events.json","paper":"https://pith.science/paper/WQAYU5PO"},"agent_actions":{"view_html":"https://pith.science/pith/WQAYU5PO3SBITBE4KFX7XFV76H","download_json":"https://pith.science/pith/WQAYU5PO3SBITBE4KFX7XFV76H.json","view_paper":"https://pith.science/paper/WQAYU5PO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.04296&json=true","fetch_graph":"https://pith.science/api/pith-number/WQAYU5PO3SBITBE4KFX7XFV76H/graph.json","fetch_events":"https://pith.science/api/pith-number/WQAYU5PO3SBITBE4KFX7XFV76H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WQAYU5PO3SBITBE4KFX7XFV76H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WQAYU5PO3SBITBE4KFX7XFV76H/action/storage_attestation","attest_author":"https://pith.science/pith/WQAYU5PO3SBITBE4KFX7XFV76H/action/author_attestation","sign_citation":"https://pith.science/pith/WQAYU5PO3SBITBE4KFX7XFV76H/action/citation_signature","submit_replication":"https://pith.science/pith/WQAYU5PO3SBITBE4KFX7XFV76H/action/replication_record"}},"created_at":"2026-05-18T01:04:38.347469+00:00","updated_at":"2026-05-18T01:04:38.347469+00:00"}