{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6GGF4LRC73NVG3K6ZILCQMVYDW","short_pith_number":"pith:6GGF4LRC","canonical_record":{"source":{"id":"2407.16562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-23T15:15:15Z","cross_cats_sorted":[],"title_canon_sha256":"0a745cffbc29c47e38cedfa6995939b0d5bfdd51c3dd36ced16bbe05eff9ff7c","abstract_canon_sha256":"da7d862ae9d0b9023d56e28ae009f9dc323fa3866a42e463eab219075e99355f"},"schema_version":"1.0"},"canonical_sha256":"f18c5e2e22fedb536d5eca162832b81dae5c459f2044216f3e289235d8bf115c","source":{"kind":"arxiv","id":"2407.16562","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.16562","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"2407.16562v1","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.16562","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"6GGF4LRC73NV","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"pith_short_16","alias_value":"6GGF4LRC73NVG3K6","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"pith_short_8","alias_value":"6GGF4LRC","created_at":"2026-07-05T08:47:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6GGF4LRC73NVG3K6ZILCQMVYDW","target":"record","payload":{"canonical_record":{"source":{"id":"2407.16562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-23T15:15:15Z","cross_cats_sorted":[],"title_canon_sha256":"0a745cffbc29c47e38cedfa6995939b0d5bfdd51c3dd36ced16bbe05eff9ff7c","abstract_canon_sha256":"da7d862ae9d0b9023d56e28ae009f9dc323fa3866a42e463eab219075e99355f"},"schema_version":"1.0"},"canonical_sha256":"f18c5e2e22fedb536d5eca162832b81dae5c459f2044216f3e289235d8bf115c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:47:35.150484Z","signature_b64":"6bOF50VaKgr7B7IGOTnM3TzxAfA6swhxYCg2xZ8g7eyOfLwYN3i0D24bpE0UrEfRuukLjpLK2G379G6V78JuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f18c5e2e22fedb536d5eca162832b81dae5c459f2044216f3e289235d8bf115c","last_reissued_at":"2026-07-05T08:47:35.150047Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:47:35.150047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.16562","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":"2026-07-05T08:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qLZ+Ihtl92pyqsXZRX9buaaZAuz0MZVuzsG+EVHU4E/4PGMSZl4d+aMUGPTE8czypO8kriQ7eMdyUXASskN+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:46:13.992097Z"},"content_sha256":"fb9335dd449ff4b8210267b7b9f03f72093f697c6ac399ad72676ff30afe2696","schema_version":"1.0","event_id":"sha256:fb9335dd449ff4b8210267b7b9f03f72093f697c6ac399ad72676ff30afe2696"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6GGF4LRC73NVG3K6ZILCQMVYDW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalised Einstein metrics on Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marco Freibert, Mateo Galdeano, Vicente Cort\\'es","submitted_at":"2024-07-23T15:15:15Z","abstract_excerpt":"We continue the systematic study of left-invariant generalised Einstein metrics on Lie groups initiated in arXiv:2206.01157. Our approach is based on a new reformulation of the corresponding algebraic system. For a fixed Lie algebra $\\mathfrak{g}$, the unknowns of the system consist of a scalar product $g$ and a $3$-form $H$ on $\\mathfrak{g}$ as well as a linear form $\\delta$ on $\\mathfrak{g}\\oplus\\mathfrak{g}^*$. As in arXiv:2206.01157, the Lie bracket of $\\mathfrak{g}$ is considered part of the unknowns. In the Riemannian case, we show that the generalised Einstein condition always reduces t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16562","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.16562/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oa8Tx3khGIzZrYckmsqMzp5uwFS0VKmsaI8ktv/a+yMkoExBE3hwK+B8mYVYyyHEaUDMhPK8dFkmfreG1c4pDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:46:13.992815Z"},"content_sha256":"e0c7e06de4d944baa610c13e950f3b1e4229476626d9b5754d98cde969728210","schema_version":"1.0","event_id":"sha256:e0c7e06de4d944baa610c13e950f3b1e4229476626d9b5754d98cde969728210"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6GGF4LRC73NVG3K6ZILCQMVYDW/bundle.json","state_url":"https://pith.science/pith/6GGF4LRC73NVG3K6ZILCQMVYDW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6GGF4LRC73NVG3K6ZILCQMVYDW/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":"2026-08-17T20:46:13Z","links":{"resolver":"https://pith.science/pith/6GGF4LRC73NVG3K6ZILCQMVYDW","bundle":"https://pith.science/pith/6GGF4LRC73NVG3K6ZILCQMVYDW/bundle.json","state":"https://pith.science/pith/6GGF4LRC73NVG3K6ZILCQMVYDW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6GGF4LRC73NVG3K6ZILCQMVYDW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6GGF4LRC73NVG3K6ZILCQMVYDW","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":"da7d862ae9d0b9023d56e28ae009f9dc323fa3866a42e463eab219075e99355f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-23T15:15:15Z","title_canon_sha256":"0a745cffbc29c47e38cedfa6995939b0d5bfdd51c3dd36ced16bbe05eff9ff7c"},"schema_version":"1.0","source":{"id":"2407.16562","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.16562","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"2407.16562v1","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.16562","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"6GGF4LRC73NV","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"pith_short_16","alias_value":"6GGF4LRC73NVG3K6","created_at":"2026-07-05T08:47:35Z"},{"alias_kind":"pith_short_8","alias_value":"6GGF4LRC","created_at":"2026-07-05T08:47:35Z"}],"graph_snapshots":[{"event_id":"sha256:e0c7e06de4d944baa610c13e950f3b1e4229476626d9b5754d98cde969728210","target":"graph","created_at":"2026-07-05T08:47:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.16562/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We continue the systematic study of left-invariant generalised Einstein metrics on Lie groups initiated in arXiv:2206.01157. Our approach is based on a new reformulation of the corresponding algebraic system. For a fixed Lie algebra $\\mathfrak{g}$, the unknowns of the system consist of a scalar product $g$ and a $3$-form $H$ on $\\mathfrak{g}$ as well as a linear form $\\delta$ on $\\mathfrak{g}\\oplus\\mathfrak{g}^*$. As in arXiv:2206.01157, the Lie bracket of $\\mathfrak{g}$ is considered part of the unknowns. In the Riemannian case, we show that the generalised Einstein condition always reduces t","authors_text":"Marco Freibert, Mateo Galdeano, Vicente Cort\\'es","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-23T15:15:15Z","title":"Generalised Einstein metrics on Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16562","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:fb9335dd449ff4b8210267b7b9f03f72093f697c6ac399ad72676ff30afe2696","target":"record","created_at":"2026-07-05T08:47:35Z","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":"da7d862ae9d0b9023d56e28ae009f9dc323fa3866a42e463eab219075e99355f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-07-23T15:15:15Z","title_canon_sha256":"0a745cffbc29c47e38cedfa6995939b0d5bfdd51c3dd36ced16bbe05eff9ff7c"},"schema_version":"1.0","source":{"id":"2407.16562","kind":"arxiv","version":1}},"canonical_sha256":"f18c5e2e22fedb536d5eca162832b81dae5c459f2044216f3e289235d8bf115c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f18c5e2e22fedb536d5eca162832b81dae5c459f2044216f3e289235d8bf115c","first_computed_at":"2026-07-05T08:47:35.150047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:47:35.150047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6bOF50VaKgr7B7IGOTnM3TzxAfA6swhxYCg2xZ8g7eyOfLwYN3i0D24bpE0UrEfRuukLjpLK2G379G6V78JuAA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:47:35.150484Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.16562","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb9335dd449ff4b8210267b7b9f03f72093f697c6ac399ad72676ff30afe2696","sha256:e0c7e06de4d944baa610c13e950f3b1e4229476626d9b5754d98cde969728210"],"state_sha256":"a409f242ae9f40fb0da709de642a6aac7d41609ae109775618100a2369d35441"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gTXxDoRWPikaLCPSY7cqP+Wddw1IT8aC3kJEtDne/Q+NerJypI7u34QZWCATIvntA3QTulnHx/a6bwtztB+3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T20:46:13.996798Z","bundle_sha256":"de5d86703277e0c87a75df27e4d373fd76caeb4d8acec17a4b732831591b3471"}}