{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OVPMCD3RUKV74EPG7RJPZVGBGV","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":"c70e6dab0be0e85451c87fa46a101ac899460dd944c05e05f713616f11a01d6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-04T21:02:25Z","title_canon_sha256":"81b1939563072a81e492192443a9cf26071b53029bd905c244ca0de068345472"},"schema_version":"1.0","source":{"id":"1311.0887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0887","created_at":"2026-05-18T03:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0887v1","created_at":"2026-05-18T03:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0887","created_at":"2026-05-18T03:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"OVPMCD3RUKV7","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OVPMCD3RUKV74EPG","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OVPMCD3R","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:42500971faf8860d84c35d79db34465485055cc5bdb872891e6d63627522f1e4","target":"graph","created_at":"2026-05-18T03:07:56Z","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 study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\\nabla$ with skew torsion $T\\in\\Lambda^3 M$ in the situation where the tangent bundle splits under the holonomy of $\\nabla$ and the torsion of $\\nabla$ is of `split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.","authors_text":"Hwajeong Kim, Ilka Agricola","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-04T21:02:25Z","title":"A note on generalized Dirac eigenvalues for split holonomy and torsion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0887","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:dc0bb6834ea4a7dddda8a1590604e0527e3d8059dfcf2cbd0e1c55b4b0fe3d51","target":"record","created_at":"2026-05-18T03:07:56Z","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":"c70e6dab0be0e85451c87fa46a101ac899460dd944c05e05f713616f11a01d6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-04T21:02:25Z","title_canon_sha256":"81b1939563072a81e492192443a9cf26071b53029bd905c244ca0de068345472"},"schema_version":"1.0","source":{"id":"1311.0887","kind":"arxiv","version":1}},"canonical_sha256":"755ec10f71a2abfe11e6fc52fcd4c13543f9bf019a7a4531c0bf6d7ad6cfd0c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"755ec10f71a2abfe11e6fc52fcd4c13543f9bf019a7a4531c0bf6d7ad6cfd0c0","first_computed_at":"2026-05-18T03:07:56.193151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:56.193151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6q2RCAz+04QzqZwiWrD67PnNa/yTG6qcJh/5GU7/cbhPn92Tyi04nyZZPL9Ctf8LMI4I0k2kbDkhKaX/BrItBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:56.193743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc0bb6834ea4a7dddda8a1590604e0527e3d8059dfcf2cbd0e1c55b4b0fe3d51","sha256:42500971faf8860d84c35d79db34465485055cc5bdb872891e6d63627522f1e4"],"state_sha256":"347f7cfa0e4cd03116db8edc23d202700894eab1d6d5db20db465f9297616915"}