{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6ZS2QUQVR2GZK3FIRB663LC5WE","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":"b2e7de47dee5a5b5b7f715cf5a9a171b54986399dab87094b6ad9473ed9cbb97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-12-31T03:06:07Z","title_canon_sha256":"e15192b49a6ba967b8a2d29ae4e68453ee13b3041b74b65cd5ddcda69d04a844"},"schema_version":"1.0","source":{"id":"1401.0074","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0074","created_at":"2026-05-18T01:45:34Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0074v1","created_at":"2026-05-18T01:45:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0074","created_at":"2026-05-18T01:45:34Z"},{"alias_kind":"pith_short_12","alias_value":"6ZS2QUQVR2GZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6ZS2QUQVR2GZK3FI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6ZS2QUQV","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:e393d9525bf625019e71c1d022a1209b2fea4cff8c538ff3fbb660429ec5e0e7","target":"graph","created_at":"2026-05-18T01:45:34Z","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":"An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting vector field. It shows that small metric perturbations, as measured using a Sobolev-type supremum norm on the space of Riemannian geometries on a fixed manifold, yield small perturbations in the approximate Killing field, as measured using a Hilbert-type square integral norm. It also discusses applications to the problem of computing the spin of a generic bla","authors_text":"Christopher Beetle, Shawn Wilder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-12-31T03:06:07Z","title":"Perturbative stability of the approximate Killing field eigenvalue problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0074","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":"sha256:9456e8010955d31de4f320d2058525b02ad1990f42c7a1539ff7a8081cb20ff9","target":"record","created_at":"2026-05-18T01:45:34Z","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":"b2e7de47dee5a5b5b7f715cf5a9a171b54986399dab87094b6ad9473ed9cbb97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-12-31T03:06:07Z","title_canon_sha256":"e15192b49a6ba967b8a2d29ae4e68453ee13b3041b74b65cd5ddcda69d04a844"},"schema_version":"1.0","source":{"id":"1401.0074","kind":"arxiv","version":1}},"canonical_sha256":"f665a852158e8d956ca8887dedac5db12f692e98e1fa27653441d8355cacf511","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f665a852158e8d956ca8887dedac5db12f692e98e1fa27653441d8355cacf511","first_computed_at":"2026-05-18T01:45:34.936452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:34.936452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C8Tbt8DZwYcXK+1ykzoGMz16cIvh596/iAdS68eIoH+WTM/4dk2AMSSFovwWJz/l0yjhZF5yngJlbLehrGbeDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:34.937090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0074","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9456e8010955d31de4f320d2058525b02ad1990f42c7a1539ff7a8081cb20ff9","sha256:e393d9525bf625019e71c1d022a1209b2fea4cff8c538ff3fbb660429ec5e0e7"],"state_sha256":"fddf2dae927f132afb232ef1d1ad9898403386b47d6c3d1a65bf33ba2f8c26b8"}