{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JYSDCR2XJSV5VUMDRY3GQH3X5D","short_pith_number":"pith:JYSDCR2X","canonical_record":{"source":{"id":"1709.10342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-29T11:43:41Z","cross_cats_sorted":[],"title_canon_sha256":"f754d432c1332f35358f78abcb94c2c4a5c5bbb3fe6354b23c204c22ec03f679","abstract_canon_sha256":"40c891cd8de27997cb6766de84268411f409f630f1d8eec1ee5c261493a18cff"},"schema_version":"1.0"},"canonical_sha256":"4e243147574cabdad1838e36681f77e8dc2352b45497ab0dbb2bb4d335566341","source":{"kind":"arxiv","id":"1709.10342","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10342","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10342v1","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10342","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"JYSDCR2XJSV5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JYSDCR2XJSV5VUMD","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JYSDCR2X","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JYSDCR2XJSV5VUMDRY3GQH3X5D","target":"record","payload":{"canonical_record":{"source":{"id":"1709.10342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-29T11:43:41Z","cross_cats_sorted":[],"title_canon_sha256":"f754d432c1332f35358f78abcb94c2c4a5c5bbb3fe6354b23c204c22ec03f679","abstract_canon_sha256":"40c891cd8de27997cb6766de84268411f409f630f1d8eec1ee5c261493a18cff"},"schema_version":"1.0"},"canonical_sha256":"4e243147574cabdad1838e36681f77e8dc2352b45497ab0dbb2bb4d335566341","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:03.463433Z","signature_b64":"EYzhko/EJSQv5NifPC0oHB2FhKzzes3Il+MUNPfrqm6aiZYC8tQyZ+J+Cpb5nJDAd4dtcpP4isl4CaEnNbMVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e243147574cabdad1838e36681f77e8dc2352b45497ab0dbb2bb4d335566341","last_reissued_at":"2026-05-18T00:34:03.462907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:03.462907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.10342","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cDQIZ4vAvzeAyBmWxdt6+U1IYmWZfqMO8/+142BbLlji/Q/nAyqqd1y82YeYdsVYVodguCi9IUpa5a/EZBe/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:14:52.044020Z"},"content_sha256":"3edcc124da6e8cdc0181896fe860977a1f40b26cfeed08d592105db8737e52a1","schema_version":"1.0","event_id":"sha256:3edcc124da6e8cdc0181896fe860977a1f40b26cfeed08d592105db8737e52a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JYSDCR2XJSV5VUMDRY3GQH3X5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Ricci negative solvmanifolds and their nilradicals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jonas Der\\'e, Jorge Lauret","submitted_at":"2017-09-29T11:43:41Z","abstract_excerpt":"In the homogeneous case, the only curvature behavior which is still far from being understood is Ricci negative. In this paper, we study which nilpotent Lie algebras admit a Ricci negative solvable extension. Different unexpected behaviors were found. On the other hand, given a nilpotent Lie algebra, we consider the space of all the derivations such that the corresponding solvable extension has a metric with negative Ricci curvature. Using the nice convexity properties of the moment map for the variety of nilpotent Lie algebras, we obtain a useful characterization of such derivations and some "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10342","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ie8uciMvpwklila4Z7YYNLl5nLJ65pwfpz+OgnqnK1qMD45A6tfJG4R8Od3Rv3NedpYAV36VtnnYhmvXlILoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:14:52.044540Z"},"content_sha256":"52ad884b907ef446dcd2b7cbf3d5e081a4e74dd49c45895d4bd38c0aebcadccc","schema_version":"1.0","event_id":"sha256:52ad884b907ef446dcd2b7cbf3d5e081a4e74dd49c45895d4bd38c0aebcadccc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JYSDCR2XJSV5VUMDRY3GQH3X5D/bundle.json","state_url":"https://pith.science/pith/JYSDCR2XJSV5VUMDRY3GQH3X5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JYSDCR2XJSV5VUMDRY3GQH3X5D/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T01:14:52Z","links":{"resolver":"https://pith.science/pith/JYSDCR2XJSV5VUMDRY3GQH3X5D","bundle":"https://pith.science/pith/JYSDCR2XJSV5VUMDRY3GQH3X5D/bundle.json","state":"https://pith.science/pith/JYSDCR2XJSV5VUMDRY3GQH3X5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JYSDCR2XJSV5VUMDRY3GQH3X5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JYSDCR2XJSV5VUMDRY3GQH3X5D","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":"40c891cd8de27997cb6766de84268411f409f630f1d8eec1ee5c261493a18cff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-29T11:43:41Z","title_canon_sha256":"f754d432c1332f35358f78abcb94c2c4a5c5bbb3fe6354b23c204c22ec03f679"},"schema_version":"1.0","source":{"id":"1709.10342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10342","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10342v1","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10342","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"JYSDCR2XJSV5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JYSDCR2XJSV5VUMD","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JYSDCR2X","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:52ad884b907ef446dcd2b7cbf3d5e081a4e74dd49c45895d4bd38c0aebcadccc","target":"graph","created_at":"2026-05-18T00:34:03Z","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 the homogeneous case, the only curvature behavior which is still far from being understood is Ricci negative. In this paper, we study which nilpotent Lie algebras admit a Ricci negative solvable extension. Different unexpected behaviors were found. On the other hand, given a nilpotent Lie algebra, we consider the space of all the derivations such that the corresponding solvable extension has a metric with negative Ricci curvature. Using the nice convexity properties of the moment map for the variety of nilpotent Lie algebras, we obtain a useful characterization of such derivations and some ","authors_text":"Jonas Der\\'e, Jorge Lauret","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-29T11:43:41Z","title":"On Ricci negative solvmanifolds and their nilradicals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10342","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":"sha256:3edcc124da6e8cdc0181896fe860977a1f40b26cfeed08d592105db8737e52a1","target":"record","created_at":"2026-05-18T00:34:03Z","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":"40c891cd8de27997cb6766de84268411f409f630f1d8eec1ee5c261493a18cff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-29T11:43:41Z","title_canon_sha256":"f754d432c1332f35358f78abcb94c2c4a5c5bbb3fe6354b23c204c22ec03f679"},"schema_version":"1.0","source":{"id":"1709.10342","kind":"arxiv","version":1}},"canonical_sha256":"4e243147574cabdad1838e36681f77e8dc2352b45497ab0dbb2bb4d335566341","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e243147574cabdad1838e36681f77e8dc2352b45497ab0dbb2bb4d335566341","first_computed_at":"2026-05-18T00:34:03.462907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:03.462907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EYzhko/EJSQv5NifPC0oHB2FhKzzes3Il+MUNPfrqm6aiZYC8tQyZ+J+Cpb5nJDAd4dtcpP4isl4CaEnNbMVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:03.463433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.10342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3edcc124da6e8cdc0181896fe860977a1f40b26cfeed08d592105db8737e52a1","sha256:52ad884b907ef446dcd2b7cbf3d5e081a4e74dd49c45895d4bd38c0aebcadccc"],"state_sha256":"ec2b4acd7b1a94941e81a60780ecd1dfda30a44de438284a646c8333ef080b9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XN9fOQoIV3EyPFIzIutNooinhRbf5UxjKH80f8UtLdb3oD+braurI6W5TaLWUbLp3AgFIoW+Gc14Lyv0n/kVCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T01:14:52.047218Z","bundle_sha256":"83333b25eb715134d90555ef48ea80ff0f2c35783c188059a13ba513597ea28c"}}