{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VJUSLR5C6K6YDB7QWO5WZ5B2FX","short_pith_number":"pith:VJUSLR5C","schema_version":"1.0","canonical_sha256":"aa6925c7a2f2bd8187f0b3bb6cf43a2dc007a79a04f861aed09190ca6a3486d5","source":{"kind":"arxiv","id":"1908.05975","version":2},"attestation_state":"computed","paper":{"title":"Diagram involutions and homogeneous Ricci-flat metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Diego Conti, Federico A. Rossi, Viviana del Barco","submitted_at":"2019-08-16T13:53:55Z","abstract_excerpt":"We introduce a combinatorial method to construct indefinite Ricci-flat metrics on nice nilpotent Lie groups.\n  We prove that every nilpotent Lie group of dimension $\\leq6$, every nice nilpotent Lie group of dimension $\\leq7$ and every two-step nilpotent Lie group attached to a graph admits such a metric. We construct infinite families of Ricci-flat nilmanifolds associated to parabolic nilradicals in the simple Lie groups ${\\rm SL}(n)$, ${\\rm SO}(p,q)$, ${\\rm Sp}(n,\\mathbb R)$. Most of these metrics are shown not to be flat."},"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":"1908.05975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-16T13:53:55Z","cross_cats_sorted":[],"title_canon_sha256":"4b7f17cbd9c87726c7b857e09f4734393691f066d0b66a4aba67c1eabb90dc3c","abstract_canon_sha256":"8637b8cfc865050bbaae9f504ffe6ed1fe7ee09469d1622c97c7537a238be5bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:17:24.694311Z","signature_b64":"ZxNSRnL45MsH32cxQ8TSuTw9JnY7Ajb90qxm3czptXjJpZBZcVbg3qa6BeLd4sjx5ytDPnWmVRKepww2jhbwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa6925c7a2f2bd8187f0b3bb6cf43a2dc007a79a04f861aed09190ca6a3486d5","last_reissued_at":"2026-07-05T01:17:24.693829Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:17:24.693829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diagram involutions and homogeneous Ricci-flat metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Diego Conti, Federico A. Rossi, Viviana del Barco","submitted_at":"2019-08-16T13:53:55Z","abstract_excerpt":"We introduce a combinatorial method to construct indefinite Ricci-flat metrics on nice nilpotent Lie groups.\n  We prove that every nilpotent Lie group of dimension $\\leq6$, every nice nilpotent Lie group of dimension $\\leq7$ and every two-step nilpotent Lie group attached to a graph admits such a metric. We construct infinite families of Ricci-flat nilmanifolds associated to parabolic nilradicals in the simple Lie groups ${\\rm SL}(n)$, ${\\rm SO}(p,q)$, ${\\rm Sp}(n,\\mathbb R)$. Most of these metrics are shown not to be flat."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05975","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.05975/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.05975","created_at":"2026-07-05T01:17:24.693885+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.05975v2","created_at":"2026-07-05T01:17:24.693885+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05975","created_at":"2026-07-05T01:17:24.693885+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJUSLR5C6K6Y","created_at":"2026-07-05T01:17:24.693885+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJUSLR5C6K6YDB7Q","created_at":"2026-07-05T01:17:24.693885+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJUSLR5C","created_at":"2026-07-05T01:17:24.693885+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/VJUSLR5C6K6YDB7QWO5WZ5B2FX","json":"https://pith.science/pith/VJUSLR5C6K6YDB7QWO5WZ5B2FX.json","graph_json":"https://pith.science/api/pith-number/VJUSLR5C6K6YDB7QWO5WZ5B2FX/graph.json","events_json":"https://pith.science/api/pith-number/VJUSLR5C6K6YDB7QWO5WZ5B2FX/events.json","paper":"https://pith.science/paper/VJUSLR5C"},"agent_actions":{"view_html":"https://pith.science/pith/VJUSLR5C6K6YDB7QWO5WZ5B2FX","download_json":"https://pith.science/pith/VJUSLR5C6K6YDB7QWO5WZ5B2FX.json","view_paper":"https://pith.science/paper/VJUSLR5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.05975&json=true","fetch_graph":"https://pith.science/api/pith-number/VJUSLR5C6K6YDB7QWO5WZ5B2FX/graph.json","fetch_events":"https://pith.science/api/pith-number/VJUSLR5C6K6YDB7QWO5WZ5B2FX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJUSLR5C6K6YDB7QWO5WZ5B2FX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJUSLR5C6K6YDB7QWO5WZ5B2FX/action/storage_attestation","attest_author":"https://pith.science/pith/VJUSLR5C6K6YDB7QWO5WZ5B2FX/action/author_attestation","sign_citation":"https://pith.science/pith/VJUSLR5C6K6YDB7QWO5WZ5B2FX/action/citation_signature","submit_replication":"https://pith.science/pith/VJUSLR5C6K6YDB7QWO5WZ5B2FX/action/replication_record"}},"created_at":"2026-07-05T01:17:24.693885+00:00","updated_at":"2026-07-05T01:17:24.693885+00:00"}