{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:VHHWICPYNUV5UFMS2JUE4HQOG5","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":"97d7a3af9d190dcb9f6bbcf1c3a072922325cbe125e0f0e8a9b458dbbf1d188c","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"hep-th","submitted_at":"2005-10-20T15:38:57Z","title_canon_sha256":"5a82d9ef17890d4a956e97b8fdbca993f5bc0c73bdecddd76745c24fa151d29f"},"schema_version":"1.0","source":{"id":"hep-th/0510176","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0510176","created_at":"2026-07-04T16:56:21Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0510176v2","created_at":"2026-07-04T16:56:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0510176","created_at":"2026-07-04T16:56:21Z"},{"alias_kind":"pith_short_12","alias_value":"VHHWICPYNUV5","created_at":"2026-07-04T16:56:21Z"},{"alias_kind":"pith_short_16","alias_value":"VHHWICPYNUV5UFMS","created_at":"2026-07-04T16:56:21Z"},{"alias_kind":"pith_short_8","alias_value":"VHHWICPY","created_at":"2026-07-04T16:56:21Z"}],"graph_snapshots":[{"event_id":"sha256:eaa489f91f2db73fc31e689e0f1f1189009e2780c1559eddef3d4e6f584143ef","target":"graph","created_at":"2026-07-04T16:56:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/0510176/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection $\\hat\\nabla$ with torsion $H$, the NS$\\otimes$NS three-form field strength, are Killing. We find that there are two classes of such backgrounds, the null and the timelike. The Killing spinors of the null backgrounds have stability subgroups $K\\ltimes\\bR^8$ in $Spin(9,1)$, for $K=Spin(7)$, SU(4), $Sp(2)$, $SU(2)\\times SU(2)$ and $\\{1\\}$, and the Killing spinors of the timelike backgrounds have stability subgroups $G_2$, SU(3), SU(2) and $\\{1\\}$. The former admit","authors_text":"G.Papadopoulos, P.Lohrmann, U.Gran","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2005-10-20T15:38:57Z","title":"The spinorial geometry of supersymmetric heterotic string backgrounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0510176","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":"sha256:96cd2279d123adaae463edde74ad5afe8f6f1a1d8dfe23dbed3390365381c878","target":"record","created_at":"2026-07-04T16:56:21Z","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":"97d7a3af9d190dcb9f6bbcf1c3a072922325cbe125e0f0e8a9b458dbbf1d188c","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"hep-th","submitted_at":"2005-10-20T15:38:57Z","title_canon_sha256":"5a82d9ef17890d4a956e97b8fdbca993f5bc0c73bdecddd76745c24fa151d29f"},"schema_version":"1.0","source":{"id":"hep-th/0510176","kind":"arxiv","version":2}},"canonical_sha256":"a9cf6409f86d2bda1592d2684e1e0e3757a2e14a4a66b48107f4dd7d7c5327ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9cf6409f86d2bda1592d2684e1e0e3757a2e14a4a66b48107f4dd7d7c5327ef","first_computed_at":"2026-07-04T16:56:21.620233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:56:21.620233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Grdr69IODDWEBT2wtqNZxXCxQjBDLxbxJqDkC9/xfSylg1XSfq6uF9TAnb45e0HeCzzfb02wvL1JBJ0z8dTCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:56:21.620709Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0510176","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96cd2279d123adaae463edde74ad5afe8f6f1a1d8dfe23dbed3390365381c878","sha256:eaa489f91f2db73fc31e689e0f1f1189009e2780c1559eddef3d4e6f584143ef"],"state_sha256":"173ce8e3e18387e4b0c2b7e47109870c79dcaf8e5e049c1105ce213495e8736c"}