{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:62PSIUNJPTMRTK67IUOJAYRHPL","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":"c796506466cec509f120be5274634e882edec5bfcca9d6d48c724ca839c67241","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-01T13:17:20Z","title_canon_sha256":"a523a4ebc0429d7018325cf5055077667419db68a639f0dcb9408f516ad668af"},"schema_version":"1.0","source":{"id":"1702.00241","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00241","created_at":"2026-05-18T00:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00241v3","created_at":"2026-05-18T00:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00241","created_at":"2026-05-18T00:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"62PSIUNJPTMR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"62PSIUNJPTMRTK67","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"62PSIUNJ","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:ce3fcaa21aeb646f638dc52292cce8627a029cebce9c307a5e2d978d6ac20798","target":"graph","created_at":"2026-05-18T00:49:31Z","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":"In \\cite{gjha} we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim is to extend the study to other kinds of intrinsic measures on sub-Riemannian manifolds, namely Popp's measure and general (i.e., non spherical) Hausdorff measures. The second is to explore some consequences of \\cite{gjha} on metric measure spaces based on sub-Riemannian manifolds.","authors_text":"Fr\\'ed\\'eric Jean, Roberta Ghezzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-01T13:17:20Z","title":"On measures in sub-Riemannian geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00241","kind":"arxiv","version":3},"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":"sha256:7500d75eb0bf7d04498e25211e5ede34fe470cd3c8943d6b5037d945bd1d9b60","target":"record","created_at":"2026-05-18T00:49:31Z","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":"c796506466cec509f120be5274634e882edec5bfcca9d6d48c724ca839c67241","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-01T13:17:20Z","title_canon_sha256":"a523a4ebc0429d7018325cf5055077667419db68a639f0dcb9408f516ad668af"},"schema_version":"1.0","source":{"id":"1702.00241","kind":"arxiv","version":3}},"canonical_sha256":"f69f2451a97cd919abdf451c9062277ae465577cd7a9e12c63a5527acd3d21e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f69f2451a97cd919abdf451c9062277ae465577cd7a9e12c63a5527acd3d21e3","first_computed_at":"2026-05-18T00:49:31.494640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:31.494640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S1TUocYPTfpKNoLBm3x8KziLw7grXbL4k3rvYRmdTAyOt3x9e2gu6yzh7OZTAZyfqAlOmYiZLHq1UEXl75EPAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:31.495211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00241","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7500d75eb0bf7d04498e25211e5ede34fe470cd3c8943d6b5037d945bd1d9b60","sha256:ce3fcaa21aeb646f638dc52292cce8627a029cebce9c307a5e2d978d6ac20798"],"state_sha256":"68cc169c263ec7d77d44e93ac5e4e577939ee6647ecf638ee45730512be8bc51"}