{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UDL33LC345NO5R2EPMMLZLQFVV","short_pith_number":"pith:UDL33LC3","schema_version":"1.0","canonical_sha256":"a0d7bdac5be75aeec7447b18bcae05ad6c2872982a9ba4e4e8dc2fa862d3ee7e","source":{"kind":"arxiv","id":"1710.05018","version":1},"attestation_state":"computed","paper":{"title":"The distribution of symmetry of a naturally reductive nilpotent Lie group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Silvio Reggiani","submitted_at":"2017-10-13T17:38:11Z","abstract_excerpt":"We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides with the invariant distribution induced by the set of fixed vectors of the isotropy. This extends a known result on compact naturally reductive spaces. We also address the study of the quotient by the foliation of symmetry."},"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":"1710.05018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-13T17:38:11Z","cross_cats_sorted":[],"title_canon_sha256":"8ca399dfdcd237debabacb45da2f3d354919fe22981b42ea5ba1e25815cc1197","abstract_canon_sha256":"6c006e3bdbbe9c078a814c468df978b66d858bafb0ca88c161aeb9c32593eddf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:56.003351Z","signature_b64":"lR1if8j8OBGRbCA3Hj1zZixHIdCCiN0JRXwPPYM1R0bS2Md2zS9ii+z9duWTGSGYPdt7TRT7pjXNZzbXrEJzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0d7bdac5be75aeec7447b18bcae05ad6c2872982a9ba4e4e8dc2fa862d3ee7e","last_reissued_at":"2026-05-18T00:32:56.002807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:56.002807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The distribution of symmetry of a naturally reductive nilpotent Lie group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Silvio Reggiani","submitted_at":"2017-10-13T17:38:11Z","abstract_excerpt":"We show that the distribution of symmetry of a naturally reductive nilpotent Lie group coincides with the invariant distribution induced by the set of fixed vectors of the isotropy. This extends a known result on compact naturally reductive spaces. We also address the study of the quotient by the foliation of symmetry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05018","kind":"arxiv","version":1},"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":"1710.05018","created_at":"2026-05-18T00:32:56.002895+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.05018v1","created_at":"2026-05-18T00:32:56.002895+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05018","created_at":"2026-05-18T00:32:56.002895+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDL33LC345NO","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDL33LC345NO5R2E","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDL33LC3","created_at":"2026-05-18T12:31:46.661854+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/UDL33LC345NO5R2EPMMLZLQFVV","json":"https://pith.science/pith/UDL33LC345NO5R2EPMMLZLQFVV.json","graph_json":"https://pith.science/api/pith-number/UDL33LC345NO5R2EPMMLZLQFVV/graph.json","events_json":"https://pith.science/api/pith-number/UDL33LC345NO5R2EPMMLZLQFVV/events.json","paper":"https://pith.science/paper/UDL33LC3"},"agent_actions":{"view_html":"https://pith.science/pith/UDL33LC345NO5R2EPMMLZLQFVV","download_json":"https://pith.science/pith/UDL33LC345NO5R2EPMMLZLQFVV.json","view_paper":"https://pith.science/paper/UDL33LC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.05018&json=true","fetch_graph":"https://pith.science/api/pith-number/UDL33LC345NO5R2EPMMLZLQFVV/graph.json","fetch_events":"https://pith.science/api/pith-number/UDL33LC345NO5R2EPMMLZLQFVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDL33LC345NO5R2EPMMLZLQFVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDL33LC345NO5R2EPMMLZLQFVV/action/storage_attestation","attest_author":"https://pith.science/pith/UDL33LC345NO5R2EPMMLZLQFVV/action/author_attestation","sign_citation":"https://pith.science/pith/UDL33LC345NO5R2EPMMLZLQFVV/action/citation_signature","submit_replication":"https://pith.science/pith/UDL33LC345NO5R2EPMMLZLQFVV/action/replication_record"}},"created_at":"2026-05-18T00:32:56.002895+00:00","updated_at":"2026-05-18T00:32:56.002895+00:00"}