{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:3JBSSMXPRHAADN6P2TAEODCAU2","short_pith_number":"pith:3JBSSMXP","schema_version":"1.0","canonical_sha256":"da432932ef89c001b7cfd4c0470c40a6af5a9f29798daa2270dec70cf638a89e","source":{"kind":"arxiv","id":"1607.02244","version":3},"attestation_state":"computed","paper":{"title":"Rigidity of quasisymmetric mappings on self-affine carpets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Antti K\\\"aenm\\\"aki, Eino Rossi, Tuomo Ojala","submitted_at":"2016-07-08T06:15:06Z","abstract_excerpt":"We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show that horizontal self-affine carpets are minimal for the conformal Assouad dimension."},"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":"1607.02244","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-08T06:15:06Z","cross_cats_sorted":[],"title_canon_sha256":"d01d97517bbfde00332032d2eede3b0dd87217cc281e28a0f36459c81562d33e","abstract_canon_sha256":"b76599a422dd504b89f4474180c04eebb22913ec7481e82dff3c9faa3ae6cb36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:25.268028Z","signature_b64":"wU7U9KgA29C3wja15ni6sMhBYHIDRT6Z5Vm8ozNmEOf4OC7VVHoJbDEL7paNbI4CeLjvPKPlpHeTG4OrpLXCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da432932ef89c001b7cfd4c0470c40a6af5a9f29798daa2270dec70cf638a89e","last_reissued_at":"2026-05-18T00:12:25.267518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:25.267518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of quasisymmetric mappings on self-affine carpets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Antti K\\\"aenm\\\"aki, Eino Rossi, Tuomo Ojala","submitted_at":"2016-07-08T06:15:06Z","abstract_excerpt":"We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show that horizontal self-affine carpets are minimal for the conformal Assouad dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02244","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.02244","created_at":"2026-05-18T00:12:25.267588+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02244v3","created_at":"2026-05-18T00:12:25.267588+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02244","created_at":"2026-05-18T00:12:25.267588+00:00"},{"alias_kind":"pith_short_12","alias_value":"3JBSSMXPRHAA","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3JBSSMXPRHAADN6P","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3JBSSMXP","created_at":"2026-05-18T12:29:55.572404+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/3JBSSMXPRHAADN6P2TAEODCAU2","json":"https://pith.science/pith/3JBSSMXPRHAADN6P2TAEODCAU2.json","graph_json":"https://pith.science/api/pith-number/3JBSSMXPRHAADN6P2TAEODCAU2/graph.json","events_json":"https://pith.science/api/pith-number/3JBSSMXPRHAADN6P2TAEODCAU2/events.json","paper":"https://pith.science/paper/3JBSSMXP"},"agent_actions":{"view_html":"https://pith.science/pith/3JBSSMXPRHAADN6P2TAEODCAU2","download_json":"https://pith.science/pith/3JBSSMXPRHAADN6P2TAEODCAU2.json","view_paper":"https://pith.science/paper/3JBSSMXP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02244&json=true","fetch_graph":"https://pith.science/api/pith-number/3JBSSMXPRHAADN6P2TAEODCAU2/graph.json","fetch_events":"https://pith.science/api/pith-number/3JBSSMXPRHAADN6P2TAEODCAU2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3JBSSMXPRHAADN6P2TAEODCAU2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3JBSSMXPRHAADN6P2TAEODCAU2/action/storage_attestation","attest_author":"https://pith.science/pith/3JBSSMXPRHAADN6P2TAEODCAU2/action/author_attestation","sign_citation":"https://pith.science/pith/3JBSSMXPRHAADN6P2TAEODCAU2/action/citation_signature","submit_replication":"https://pith.science/pith/3JBSSMXPRHAADN6P2TAEODCAU2/action/replication_record"}},"created_at":"2026-05-18T00:12:25.267588+00:00","updated_at":"2026-05-18T00:12:25.267588+00:00"}