{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FV3AB4YQDIJBETNAOKWA3PLFDY","short_pith_number":"pith:FV3AB4YQ","schema_version":"1.0","canonical_sha256":"2d7600f3101a12124da072ac0dbd651e0449e31864995283c4c286bcd7b24042","source":{"kind":"arxiv","id":"1304.2078","version":2},"attestation_state":"computed","paper":{"title":"Quasisymmetric rigidity of Sierpinski carpets $F_{n,p}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CV","authors_text":"Jinsong Zeng, Weixu Su","submitted_at":"2013-04-08T00:03:46Z","abstract_excerpt":"We study a new class of square Sierpi\\'nski carpets $F_{n,p}$ ($5\\leq n, 1\\leq p<\\frac{n}{2}-1$) on $\\mathbb{S}^2$, which are not quasisymmetrically equivalent to the standard Sierpi\\'{n}ski carpets. We prove that the group of quasisymmetric self-maps of each $F_{n,p}$ is the Euclidean isometry group.\n  We also establish that $F_{n,p}$ and $F_{n',p'}$ are quasisymmetrically equivalent if and only if $(n,p)=(n',p')$."},"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":"1304.2078","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-08T00:03:46Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"0534162baa06a90efacec3b0b000096bca79517635bcbf5dd2498193aa815543","abstract_canon_sha256":"2c1579301c406c4da0b38731d746166e4984e1f5d37e30dc393324d165881650"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:16.413373Z","signature_b64":"Yim0rUq8GQ4RViBxJeKh9EfFITfj43JXk80Gh+DnZWlUPSpapZZlD4nLX/2thC0WxlSjjzke78bZtUiXqpWODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d7600f3101a12124da072ac0dbd651e0449e31864995283c4c286bcd7b24042","last_reissued_at":"2026-05-18T01:37:16.412745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:16.412745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasisymmetric rigidity of Sierpinski carpets $F_{n,p}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CV","authors_text":"Jinsong Zeng, Weixu Su","submitted_at":"2013-04-08T00:03:46Z","abstract_excerpt":"We study a new class of square Sierpi\\'nski carpets $F_{n,p}$ ($5\\leq n, 1\\leq p<\\frac{n}{2}-1$) on $\\mathbb{S}^2$, which are not quasisymmetrically equivalent to the standard Sierpi\\'{n}ski carpets. We prove that the group of quasisymmetric self-maps of each $F_{n,p}$ is the Euclidean isometry group.\n  We also establish that $F_{n,p}$ and $F_{n',p'}$ are quasisymmetrically equivalent if and only if $(n,p)=(n',p')$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2078","kind":"arxiv","version":2},"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":"1304.2078","created_at":"2026-05-18T01:37:16.412833+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.2078v2","created_at":"2026-05-18T01:37:16.412833+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2078","created_at":"2026-05-18T01:37:16.412833+00:00"},{"alias_kind":"pith_short_12","alias_value":"FV3AB4YQDIJB","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FV3AB4YQDIJBETNA","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FV3AB4YQ","created_at":"2026-05-18T12:27:45.050594+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/FV3AB4YQDIJBETNAOKWA3PLFDY","json":"https://pith.science/pith/FV3AB4YQDIJBETNAOKWA3PLFDY.json","graph_json":"https://pith.science/api/pith-number/FV3AB4YQDIJBETNAOKWA3PLFDY/graph.json","events_json":"https://pith.science/api/pith-number/FV3AB4YQDIJBETNAOKWA3PLFDY/events.json","paper":"https://pith.science/paper/FV3AB4YQ"},"agent_actions":{"view_html":"https://pith.science/pith/FV3AB4YQDIJBETNAOKWA3PLFDY","download_json":"https://pith.science/pith/FV3AB4YQDIJBETNAOKWA3PLFDY.json","view_paper":"https://pith.science/paper/FV3AB4YQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.2078&json=true","fetch_graph":"https://pith.science/api/pith-number/FV3AB4YQDIJBETNAOKWA3PLFDY/graph.json","fetch_events":"https://pith.science/api/pith-number/FV3AB4YQDIJBETNAOKWA3PLFDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FV3AB4YQDIJBETNAOKWA3PLFDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FV3AB4YQDIJBETNAOKWA3PLFDY/action/storage_attestation","attest_author":"https://pith.science/pith/FV3AB4YQDIJBETNAOKWA3PLFDY/action/author_attestation","sign_citation":"https://pith.science/pith/FV3AB4YQDIJBETNAOKWA3PLFDY/action/citation_signature","submit_replication":"https://pith.science/pith/FV3AB4YQDIJBETNAOKWA3PLFDY/action/replication_record"}},"created_at":"2026-05-18T01:37:16.412833+00:00","updated_at":"2026-05-18T01:37:16.412833+00:00"}