{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NV3I5J4CPVX5QZXVR5FFLXWHHL","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":"dccb29372fe87c9764d7fa502270d32f23e837251b8ba286f7ffbeb073ec6179","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-11T08:26:48Z","title_canon_sha256":"24014e2dedcb316aded33af384953e9dd7ab82deb9713c1374bc61de8c3f9d2e"},"schema_version":"1.0","source":{"id":"1705.04066","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04066","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04066v1","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04066","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"pith_short_12","alias_value":"NV3I5J4CPVX5","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NV3I5J4CPVX5QZXV","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NV3I5J4C","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:b21e85db49c3ccd9fc3cbbcdabc84921a260abafa4592d0fa44592953e6e1d31","target":"graph","created_at":"2026-05-18T00:44:41Z","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 prove some geometric properties of sets in the first Heisenberg group whose Heisenberg Hausdorff dimension is the minimal or maximal possible in relation to their Euclidean one and the corresponding Hausdorff measures are positive and finite. In the first case we show that these sets must be in a sense horizontal and in the second case vertical. We show the sharpness of our results with some examples.","authors_text":"Laura Venieri, Pertti Mattila","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-11T08:26:48Z","title":"A comparison of Euclidean and Heisenberg Hausdorff measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04066","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:e75594da46f13fc4a9f4a52a3197520d0d46a0d6a8a63ef9f8bcf2222cffa5ba","target":"record","created_at":"2026-05-18T00:44:41Z","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":"dccb29372fe87c9764d7fa502270d32f23e837251b8ba286f7ffbeb073ec6179","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-05-11T08:26:48Z","title_canon_sha256":"24014e2dedcb316aded33af384953e9dd7ab82deb9713c1374bc61de8c3f9d2e"},"schema_version":"1.0","source":{"id":"1705.04066","kind":"arxiv","version":1}},"canonical_sha256":"6d768ea7827d6fd866f58f4a55dec73af1e5e4d4c658b84c2155488438e8ce8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d768ea7827d6fd866f58f4a55dec73af1e5e4d4c658b84c2155488438e8ce8e","first_computed_at":"2026-05-18T00:44:41.495306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:41.495306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rph+kePCVsjKpjEK1lR4eSEsR2HNVhc2Oli5Y5G9yLrek5Ik/5i+9rHsfLcHB8yUNrw4OUa+8USvjQVtyW6LAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:41.495742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04066","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e75594da46f13fc4a9f4a52a3197520d0d46a0d6a8a63ef9f8bcf2222cffa5ba","sha256:b21e85db49c3ccd9fc3cbbcdabc84921a260abafa4592d0fa44592953e6e1d31"],"state_sha256":"517a232ef2aaafe0bb3a9db6c985cdc7e089de5dd95d212ef5806e969c03593b"}