{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:32CIMATBWA3W2CBQIVTOBB267M","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":"fde7a4832308bceaf3fd25ff0038794ab9d2c130124e5068d149ec1f0e8779a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-01T14:51:46Z","title_canon_sha256":"034f22026f2ba5b9e1a46851483f761566b00c0d0a7bc561336ece28ee3f00e7"},"schema_version":"1.0","source":{"id":"1808.00344","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00344","created_at":"2026-05-17T23:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00344v2","created_at":"2026-05-17T23:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00344","created_at":"2026-05-17T23:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"32CIMATBWA3W","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"32CIMATBWA3W2CBQ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"32CIMATB","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:152b787ebcb586ea9e07bf58fb76a99e99bef32cd2245354fe1c822c9103b1d5","target":"graph","created_at":"2026-05-17T23:54:11Z","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 this note we show that the bi-invariant Einstein metric on the compact Lie group $G_{2}$ is dynamically unstable as a fixed point of the Ricci flow. This completes the stability analysis for the bi-invariant metrics on the compact, connected, simple Lie groups. Interestingly, $G_{2}$ is the only unstable exceptional group.","authors_text":"Stuart James Hall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-01T14:51:46Z","title":"The canonical Einstein metric on $G_{2}$ is dynamically unstable under the Ricci flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00344","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":"sha256:1dfff78457081c0622ed7645e896dbc1f5945ed6af0b33da2052d9d6915a8c8b","target":"record","created_at":"2026-05-17T23:54:11Z","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":"fde7a4832308bceaf3fd25ff0038794ab9d2c130124e5068d149ec1f0e8779a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-01T14:51:46Z","title_canon_sha256":"034f22026f2ba5b9e1a46851483f761566b00c0d0a7bc561336ece28ee3f00e7"},"schema_version":"1.0","source":{"id":"1808.00344","kind":"arxiv","version":2}},"canonical_sha256":"de84860261b0376d08304566e0875efb08dfdbcd782d83f2abe5e380178872a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de84860261b0376d08304566e0875efb08dfdbcd782d83f2abe5e380178872a5","first_computed_at":"2026-05-17T23:54:11.206467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:11.206467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"spINkX6iuiyPcR/JioNuQJibc5ngG+d4VSEswquGrR6g9Nwha0RYZheqsXqKTxBUpuzyVEYnpp7YUbS8Y5mXAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:11.207158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.00344","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dfff78457081c0622ed7645e896dbc1f5945ed6af0b33da2052d9d6915a8c8b","sha256:152b787ebcb586ea9e07bf58fb76a99e99bef32cd2245354fe1c822c9103b1d5"],"state_sha256":"4acf8ef2dcce32d73d5b65457c8f4db2e6f5bb6878916be66ed4806ee49c803e"}