{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:U7LIX6UI2L2W26FRNUPAXSUF7F","short_pith_number":"pith:U7LIX6UI","canonical_record":{"source":{"id":"1205.6109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T13:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"47bf2b7359485d0e2fce01ce96e010cc5eda85d948be813c3772b6cc09950727","abstract_canon_sha256":"3cfa441ef7f60e737b6840845f3ea42c49672550b1a44054793d9c9b50241d24"},"schema_version":"1.0"},"canonical_sha256":"a7d68bfa88d2f56d78b16d1e0bca85f97dc3d3ea488cf8b8f51b201f68de2967","source":{"kind":"arxiv","id":"1205.6109","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6109","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6109v2","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6109","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"U7LIX6UI2L2W","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U7LIX6UI2L2W26FR","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U7LIX6UI","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:U7LIX6UI2L2W26FRNUPAXSUF7F","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T13:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"47bf2b7359485d0e2fce01ce96e010cc5eda85d948be813c3772b6cc09950727","abstract_canon_sha256":"3cfa441ef7f60e737b6840845f3ea42c49672550b1a44054793d9c9b50241d24"},"schema_version":"1.0"},"canonical_sha256":"a7d68bfa88d2f56d78b16d1e0bca85f97dc3d3ea488cf8b8f51b201f68de2967","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:36.915665Z","signature_b64":"DUiQWRDxojPrRb7oW7+9qyUw4c69mSG+CbYcS9ZvQ6Nbru5XarKm2PY0Rk2HlCSxpFqMtI6RIhZdwLih5yXoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7d68bfa88d2f56d78b16d1e0bca85f97dc3d3ea488cf8b8f51b201f68de2967","last_reissued_at":"2026-05-18T03:54:36.914937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:36.914937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6109","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UxIE+RKnayPDMOXRYsbzsjZJ6zRPEKSGEMKikFxN5sWPt89UhiKh89pwLvcFSF0Y1dIiHoofNxcUQ/VnuBLgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:09:08.367654Z"},"content_sha256":"fe8d92b9e44ab794c844947fc1a9377c0d4ad8163a80177e5d199e6ba5bcd080","schema_version":"1.0","event_id":"sha256:fe8d92b9e44ab794c844947fc1a9377c0d4ad8163a80177e5d199e6ba5bcd080"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:U7LIX6UI2L2W26FRNUPAXSUF7F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nilsolitons of H-type in the Lorentzian setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kensuke Onda, Phillip E. Parker","submitted_at":"2012-05-28T13:27:43Z","abstract_excerpt":"It is known that all left-invariant pseudo-Riemannian metrics on $H_3$ are algebraic Ricci solitons. We consider generalizations of Riemannian $H$-type, namely pseudo$H$-type and $pH$-type. We study algebraic Ricci solitons of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups of both types."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6109","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":""},"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":"2026-05-18T03:54:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X0XeWi7JBDYKByXZiFFaSMrgTytvTxx+oFwZHrWe0nZlc544yzg50RX1TQc/lnrKamMN4HycOPYzT6jhHcSNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:09:08.368002Z"},"content_sha256":"8561cd7e0cbc945b6654b94a894611be14dbbf18f65091783b2eda0687487379","schema_version":"1.0","event_id":"sha256:8561cd7e0cbc945b6654b94a894611be14dbbf18f65091783b2eda0687487379"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U7LIX6UI2L2W26FRNUPAXSUF7F/bundle.json","state_url":"https://pith.science/pith/U7LIX6UI2L2W26FRNUPAXSUF7F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U7LIX6UI2L2W26FRNUPAXSUF7F/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":"2026-05-31T06:09:08Z","links":{"resolver":"https://pith.science/pith/U7LIX6UI2L2W26FRNUPAXSUF7F","bundle":"https://pith.science/pith/U7LIX6UI2L2W26FRNUPAXSUF7F/bundle.json","state":"https://pith.science/pith/U7LIX6UI2L2W26FRNUPAXSUF7F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U7LIX6UI2L2W26FRNUPAXSUF7F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:U7LIX6UI2L2W26FRNUPAXSUF7F","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":"3cfa441ef7f60e737b6840845f3ea42c49672550b1a44054793d9c9b50241d24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T13:27:43Z","title_canon_sha256":"47bf2b7359485d0e2fce01ce96e010cc5eda85d948be813c3772b6cc09950727"},"schema_version":"1.0","source":{"id":"1205.6109","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6109","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6109v2","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6109","created_at":"2026-05-18T03:54:36Z"},{"alias_kind":"pith_short_12","alias_value":"U7LIX6UI2L2W","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"U7LIX6UI2L2W26FR","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"U7LIX6UI","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:8561cd7e0cbc945b6654b94a894611be14dbbf18f65091783b2eda0687487379","target":"graph","created_at":"2026-05-18T03:54:36Z","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":"It is known that all left-invariant pseudo-Riemannian metrics on $H_3$ are algebraic Ricci solitons. We consider generalizations of Riemannian $H$-type, namely pseudo$H$-type and $pH$-type. We study algebraic Ricci solitons of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups of both types.","authors_text":"Kensuke Onda, Phillip E. Parker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T13:27:43Z","title":"Nilsolitons of H-type in the Lorentzian setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6109","kind":"arxiv","version":2},"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:fe8d92b9e44ab794c844947fc1a9377c0d4ad8163a80177e5d199e6ba5bcd080","target":"record","created_at":"2026-05-18T03:54:36Z","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":"3cfa441ef7f60e737b6840845f3ea42c49672550b1a44054793d9c9b50241d24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T13:27:43Z","title_canon_sha256":"47bf2b7359485d0e2fce01ce96e010cc5eda85d948be813c3772b6cc09950727"},"schema_version":"1.0","source":{"id":"1205.6109","kind":"arxiv","version":2}},"canonical_sha256":"a7d68bfa88d2f56d78b16d1e0bca85f97dc3d3ea488cf8b8f51b201f68de2967","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7d68bfa88d2f56d78b16d1e0bca85f97dc3d3ea488cf8b8f51b201f68de2967","first_computed_at":"2026-05-18T03:54:36.914937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:36.914937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DUiQWRDxojPrRb7oW7+9qyUw4c69mSG+CbYcS9ZvQ6Nbru5XarKm2PY0Rk2HlCSxpFqMtI6RIhZdwLih5yXoBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:36.915665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6109","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe8d92b9e44ab794c844947fc1a9377c0d4ad8163a80177e5d199e6ba5bcd080","sha256:8561cd7e0cbc945b6654b94a894611be14dbbf18f65091783b2eda0687487379"],"state_sha256":"6eefaf800fa0bc5c59fe134b873ae31a57f8845a551afb19549ca34b91b1a8f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nKwXegO2JJIF26M9r5dWNrSCpZ7GGTUoYlhugAJrqRYcM5zLmGFNXL8KmLDAABL98wT4n9/MG1F+Zo2vtRVUDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:09:08.370204Z","bundle_sha256":"a5caab8f78b72e13f57589568df618115a847f68779132d4ac6a310d62d3a01b"}}