{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ATYVBQKYC3QDRLR2MQBBOTCHLG","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":"5f26b6c0794210895e44917b3551df3cab1e489709602ca4d3898627dc4b8341","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-08-25T08:27:38Z","title_canon_sha256":"70c7d22c66ce7fd51e1ae79999f4096c8ba042400b184426b7d29358e101af36"},"schema_version":"1.0","source":{"id":"1508.06062","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06062","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06062v1","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06062","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"ATYVBQKYC3QD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ATYVBQKYC3QDRLR2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ATYVBQKY","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:a1790b8382f7c2eab9557bd8f6c360a258a1af19800819adc6b56d7b49199c8d","target":"graph","created_at":"2026-05-18T01:34:46Z","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":"We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in `Fractured fractals and broken dreams' by David and Semmes, or equivalently, Question 22 and hence also Question 24 in `Thirty-three yes or no questions about mappings, measures, and metrics' by Heinonen and Semmes.\n  The non-minimality of the Heisenberg group is shown by giving an example of an Ahlfors $4$-regular metric space $X$ having big pieces of itself such that no Lipschitz map from a subset of $X$ to the Heisenberg group has image with positive measure, and by providing a Lipschitz map from","authors_text":"Enrico Le Donne, Sean Li, Tapio Rajala","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-08-25T08:27:38Z","title":"Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06062","kind":"arxiv","version":1},"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":"sha256:202e95f835f1b61cb015f813d9b8e6cd845828f8f6abc13f7c294a064616879a","target":"record","created_at":"2026-05-18T01:34:46Z","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":"5f26b6c0794210895e44917b3551df3cab1e489709602ca4d3898627dc4b8341","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-08-25T08:27:38Z","title_canon_sha256":"70c7d22c66ce7fd51e1ae79999f4096c8ba042400b184426b7d29358e101af36"},"schema_version":"1.0","source":{"id":"1508.06062","kind":"arxiv","version":1}},"canonical_sha256":"04f150c15816e038ae3a6402174c47599e0d0ca64f2c5ef2f01dc9bcc4473a56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04f150c15816e038ae3a6402174c47599e0d0ca64f2c5ef2f01dc9bcc4473a56","first_computed_at":"2026-05-18T01:34:46.971543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:46.971543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NpuF+8mtPo8KpfNSmGO/BcaOFTJTfEPszikTiRlc+ZcsGIjC+MH/moe8yO+wppnSIdWYnhFusB6hzMUwhU/0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:46.972204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06062","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:202e95f835f1b61cb015f813d9b8e6cd845828f8f6abc13f7c294a064616879a","sha256:a1790b8382f7c2eab9557bd8f6c360a258a1af19800819adc6b56d7b49199c8d"],"state_sha256":"a2aebbbe45abb8b7d7e2c30f1d332fc2f50a6fc57ae94fb385ce24d7f17bff8c"}