{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BVIIC7M3JN5ONDRKKPKNPMIXTX","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":"c97115ddd24d92d7e6a826a95e7fbcf2631401dc0f2983b80e015927bbd7a647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-04-25T13:46:48Z","title_canon_sha256":"af7fd490d4b2feb34d728408897ae402722e2df82389332a553e949c015827f6"},"schema_version":"1.0","source":{"id":"0704.3373","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3373","created_at":"2026-05-18T03:26:21Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3373v6","created_at":"2026-05-18T03:26:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3373","created_at":"2026-05-18T03:26:21Z"},{"alias_kind":"pith_short_12","alias_value":"BVIIC7M3JN5O","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BVIIC7M3JN5ONDRK","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BVIIC7M3","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:3b96f351dfd995cbd3227b43d203fa839378b6365776fb57adc62cda5843a97e","target":"graph","created_at":"2026-05-18T03:26:21Z","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":"We investigate the validity of the isometry extension property for (Riemannian) Einstein metrics on manifolds with boundary. Given a metric on the boundary, this is the issue of whether any Killing field of the boundary metric extends to a Killing field of any bulk or filling Einstein metric inducing the given data on the boundary. Under a mild condition on the fundamental group, this is proved to be the case at least when the Killing field preserves the mean curvature of the boundary.","authors_text":"Michael T. Anderson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-04-25T13:46:48Z","title":"Extension of symmetries on Einstein manifolds with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3373","kind":"arxiv","version":6},"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":"sha256:2aa5244cd87e58d2a4f7367d2e1ff0ccc4e5be94c147c8d4715cd2ee75d29ae4","target":"record","created_at":"2026-05-18T03:26:21Z","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":"c97115ddd24d92d7e6a826a95e7fbcf2631401dc0f2983b80e015927bbd7a647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-04-25T13:46:48Z","title_canon_sha256":"af7fd490d4b2feb34d728408897ae402722e2df82389332a553e949c015827f6"},"schema_version":"1.0","source":{"id":"0704.3373","kind":"arxiv","version":6}},"canonical_sha256":"0d50817d9b4b7ae68e2a53d4d7b1179ddb8e43c080faaf38690f90fdc4a47a80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d50817d9b4b7ae68e2a53d4d7b1179ddb8e43c080faaf38690f90fdc4a47a80","first_computed_at":"2026-05-18T03:26:21.097016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:21.097016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Raquwei++Uk1o/ZJCzgKeLmm1sQuc/NqoBQSgcxnsyGq8jft28wr0DTcDIsTyCCNPqp7CMCV95wV5XbBF7JWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:21.097769Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.3373","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2aa5244cd87e58d2a4f7367d2e1ff0ccc4e5be94c147c8d4715cd2ee75d29ae4","sha256:3b96f351dfd995cbd3227b43d203fa839378b6365776fb57adc62cda5843a97e"],"state_sha256":"d3ac2e55b3005f37296285c89782c19021d367db92b8b5d2f254ca1cbdf16c7c"}