{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RMDNXBHOTSLPTXKWPVOMCWLUHF","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":"b129f1f3244275869ced0b7451bcfca8957f6b595bd2c412cd826aa876221aa5","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-07-23T21:01:20Z","title_canon_sha256":"8dfec8b97690c376e920713194116fe48e3292ef2a6dc7d9fee10f7665302f77"},"schema_version":"1.0","source":{"id":"2607.21815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21815","created_at":"2026-07-27T00:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21815v1","created_at":"2026-07-27T00:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21815","created_at":"2026-07-27T00:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"RMDNXBHOTSLP","created_at":"2026-07-27T00:20:22Z"},{"alias_kind":"pith_short_16","alias_value":"RMDNXBHOTSLPTXKW","created_at":"2026-07-27T00:20:22Z"},{"alias_kind":"pith_short_8","alias_value":"RMDNXBHO","created_at":"2026-07-27T00:20:22Z"}],"graph_snapshots":[{"event_id":"sha256:3ddaba2677761ee8140b6e0c033c23b79c1150de1645e7737da430957bf84abf","target":"graph","created_at":"2026-07-27T00:20:22Z","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/2607.21815/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We find a system of differential equations on an initial data surface whose solutions are in bijection with unit vector fields on the Einstein $\\Lambda$-vacuum development that are proportional to a Killing vector. We refer to these conditions as the \\textit{unit Killing initial data} (uKID) equations, analogous to the classical \\textit{Killing initial data} (KID) equations. The uKID equations can be useful in a setting where only the unit-normalized part of the Killing vector is geometrically distinguished. We eliminate the scaling degree of freedom of a general Killing vector to obtain the s","authors_text":"Igor Khavkine, Salvador Mengual Sendra","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-07-23T21:01:20Z","title":"Unit Killing Initial Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21815","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":"sha256:5f6b5470dfa80c16b104163e16e564c518592b6dd3aa4d4ed1e46be7d69a9ebb","target":"record","created_at":"2026-07-27T00:20:22Z","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":"b129f1f3244275869ced0b7451bcfca8957f6b595bd2c412cd826aa876221aa5","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-07-23T21:01:20Z","title_canon_sha256":"8dfec8b97690c376e920713194116fe48e3292ef2a6dc7d9fee10f7665302f77"},"schema_version":"1.0","source":{"id":"2607.21815","kind":"arxiv","version":1}},"canonical_sha256":"8b06db84ee9c96f9dd567d5cc159743977a78837c11dfe3a257310595f742793","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b06db84ee9c96f9dd567d5cc159743977a78837c11dfe3a257310595f742793","first_computed_at":"2026-07-27T00:20:22.371610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-27T00:20:22.371610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lJUB7K8f+ixOHdPmqnwPhlWqHD+PmxqRmTjEfw6Zz/GBG4uhxGp3CQ94OWYYQDhco15LJTeqOwibiC+Jd5v9Dg==","signature_status":"signed_v1","signed_at":"2026-07-27T00:20:22.372389Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.21815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f6b5470dfa80c16b104163e16e564c518592b6dd3aa4d4ed1e46be7d69a9ebb","sha256:3ddaba2677761ee8140b6e0c033c23b79c1150de1645e7737da430957bf84abf"],"state_sha256":"3e35c87283f61c1ec6a3fcb30e41a7715e4dbdbe9004ed26960e4257374c5271"}