{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5MYVJJ3JONNZGK362D5BIPVNFR","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":"2e7db2042b3fb7eb39870a7438de0d1cb3bc8e70d052c6dc43d2e1e2d0a50155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-05T06:55:27Z","title_canon_sha256":"7b4f52804ee083ba6740706c1bafb393c40428f5463fce0689602d5ee9e11978"},"schema_version":"1.0","source":{"id":"1104.0745","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0745","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0745v1","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0745","created_at":"2026-05-18T04:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"5MYVJJ3JONNZ","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5MYVJJ3JONNZGK36","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5MYVJJ3J","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:4b819407fac774c326a9230a57493a1e5bdc5c8603e114ebf77ef4ba56af39fd","target":"graph","created_at":"2026-05-18T04:25:02Z","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 second Dirac eigenvalue on Riemannian manifolds admitting a Killing spinor. In small dimensions the whole Dirac spectrum depends on special eigenvalues on functions and 1-forms. We compute and discuss the formulas in dimension $n = 7$.","authors_text":"Thomas Friedrich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-05T06:55:27Z","title":"The second Dirac eigenvalue of a nearly parallel $G_2$-manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0745","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":"sha256:47eb907f00bc9c33f397da961eed83eb2517fb94defa034c9cb414dade83bc19","target":"record","created_at":"2026-05-18T04:25:02Z","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":"2e7db2042b3fb7eb39870a7438de0d1cb3bc8e70d052c6dc43d2e1e2d0a50155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-05T06:55:27Z","title_canon_sha256":"7b4f52804ee083ba6740706c1bafb393c40428f5463fce0689602d5ee9e11978"},"schema_version":"1.0","source":{"id":"1104.0745","kind":"arxiv","version":1}},"canonical_sha256":"eb3154a769735b932b7ed0fa143ead2c59c52abe4f1ec199a28695086c285b39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb3154a769735b932b7ed0fa143ead2c59c52abe4f1ec199a28695086c285b39","first_computed_at":"2026-05-18T04:25:02.647233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:02.647233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vuZnvJBdB4pbVFAWsEiF0U+gw2OgsbLfyhT5daKHO3ud9jycXFGr2mYUGa+HQuLwo8gSDNe8pZHUol4inpwgAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:02.647958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0745","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47eb907f00bc9c33f397da961eed83eb2517fb94defa034c9cb414dade83bc19","sha256:4b819407fac774c326a9230a57493a1e5bdc5c8603e114ebf77ef4ba56af39fd"],"state_sha256":"cf2c64b1eb343ddd6a2a384519aad78527d29ff7c0097074ef951ef162d5656c"}