{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:BYCYUUEW6ZXG63F2BOA4MZR4SR","short_pith_number":"pith:BYCYUUEW","canonical_record":{"source":{"id":"math/0202094","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2002-02-11T14:09:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c8e94161575df7397ea55676aad3a32afdd6f59dabe11f8901b7d9a9389e40dd","abstract_canon_sha256":"f9e95f595957bdc6d858b2940c1fee1a21b3df4c34bc251b052a59c92da85878"},"schema_version":"1.0"},"canonical_sha256":"0e058a5096f66e6f6cba0b81c6663c947f95147b4c679a555c912b7ff4ae3d7e","source":{"kind":"arxiv","id":"math/0202094","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0202094","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0202094v1","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0202094","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"BYCYUUEW6ZXG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"BYCYUUEW6ZXG63F2","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"BYCYUUEW","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:BYCYUUEW6ZXG63F2BOA4MZR4SR","target":"record","payload":{"canonical_record":{"source":{"id":"math/0202094","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2002-02-11T14:09:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c8e94161575df7397ea55676aad3a32afdd6f59dabe11f8901b7d9a9389e40dd","abstract_canon_sha256":"f9e95f595957bdc6d858b2940c1fee1a21b3df4c34bc251b052a59c92da85878"},"schema_version":"1.0"},"canonical_sha256":"0e058a5096f66e6f6cba0b81c6663c947f95147b4c679a555c912b7ff4ae3d7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:22.017908Z","signature_b64":"DbAthrvrnWI0kgzNrLbGqgAi+5tCvdi5pj2UOREhGwemtj4lvdJYbDuqtqFGC0lU3a5XIuus3OdQCb4WfQP9Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e058a5096f66e6f6cba0b81c6663c947f95147b4c679a555c912b7ff4ae3d7e","last_reissued_at":"2026-05-18T02:47:22.017217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:22.017217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0202094","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVKoGcHiqf1+rbObHtZzWiagqOqHbPBDDVwlQRxHnrJjygyfNuqlkvkBgh9gIhqClZXEHDktz8PQkIoAv+0iBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:53:07.662170Z"},"content_sha256":"89952aa19daf84dcc29777b19574373c9a37ad2478c8eefb9dd85ae7fe78fe0f","schema_version":"1.0","event_id":"sha256:89952aa19daf84dcc29777b19574373c9a37ad2478c8eefb9dd85ae7fe78fe0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:BYCYUUEW6ZXG63F2BOA4MZR4SR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connections on naturally reductive spaces, their Dirac operator and homogeneous models in string theory","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Ilka Agricola","submitted_at":"2002-02-11T14:09:41Z","abstract_excerpt":"Given a reductive homogeneous space M=G/H endowed with a naturally reductive metric, we study the one-parameter family of connections joining the canonical and the Levi-Civita connection (t=0, 1/2). We show that the Dirac operator D^t corresponding to t=1/3 is the so-called ``cubic'' Dirac operator recently introduced by B. Kostant, and derive the formula for its square for any t, thus generalizing the classical Parthasarathy formula on symmetric spaces. Applications include the existence of a new G-invariant first order differential operator on spinors and an eigenvalue estimate for the first"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202094","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"likuvXcET7LC2LQx7HX45v0uPX3Olp5A3vlVtiKuVWA0NgcKm6YLn4Jud2tOZmQSaP6BSHh+OuspKJlqhy3KDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:53:07.662535Z"},"content_sha256":"75e30a691e7352954685c6f6d9826053baee27b347feb31521893172eb79af74","schema_version":"1.0","event_id":"sha256:75e30a691e7352954685c6f6d9826053baee27b347feb31521893172eb79af74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BYCYUUEW6ZXG63F2BOA4MZR4SR/bundle.json","state_url":"https://pith.science/pith/BYCYUUEW6ZXG63F2BOA4MZR4SR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BYCYUUEW6ZXG63F2BOA4MZR4SR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T16:53:07Z","links":{"resolver":"https://pith.science/pith/BYCYUUEW6ZXG63F2BOA4MZR4SR","bundle":"https://pith.science/pith/BYCYUUEW6ZXG63F2BOA4MZR4SR/bundle.json","state":"https://pith.science/pith/BYCYUUEW6ZXG63F2BOA4MZR4SR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BYCYUUEW6ZXG63F2BOA4MZR4SR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:BYCYUUEW6ZXG63F2BOA4MZR4SR","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":"f9e95f595957bdc6d858b2940c1fee1a21b3df4c34bc251b052a59c92da85878","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.DG","submitted_at":"2002-02-11T14:09:41Z","title_canon_sha256":"c8e94161575df7397ea55676aad3a32afdd6f59dabe11f8901b7d9a9389e40dd"},"schema_version":"1.0","source":{"id":"math/0202094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0202094","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0202094v1","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0202094","created_at":"2026-05-18T02:47:22Z"},{"alias_kind":"pith_short_12","alias_value":"BYCYUUEW6ZXG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"BYCYUUEW6ZXG63F2","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"BYCYUUEW","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:75e30a691e7352954685c6f6d9826053baee27b347feb31521893172eb79af74","target":"graph","created_at":"2026-05-18T02:47:22Z","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"},"paper":{"abstract_excerpt":"Given a reductive homogeneous space M=G/H endowed with a naturally reductive metric, we study the one-parameter family of connections joining the canonical and the Levi-Civita connection (t=0, 1/2). We show that the Dirac operator D^t corresponding to t=1/3 is the so-called ``cubic'' Dirac operator recently introduced by B. Kostant, and derive the formula for its square for any t, thus generalizing the classical Parthasarathy formula on symmetric spaces. Applications include the existence of a new G-invariant first order differential operator on spinors and an eigenvalue estimate for the first","authors_text":"Ilka Agricola","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2002-02-11T14:09:41Z","title":"Connections on naturally reductive spaces, their Dirac operator and homogeneous models in string theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202094","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":"sha256:89952aa19daf84dcc29777b19574373c9a37ad2478c8eefb9dd85ae7fe78fe0f","target":"record","created_at":"2026-05-18T02:47:22Z","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":"f9e95f595957bdc6d858b2940c1fee1a21b3df4c34bc251b052a59c92da85878","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.DG","submitted_at":"2002-02-11T14:09:41Z","title_canon_sha256":"c8e94161575df7397ea55676aad3a32afdd6f59dabe11f8901b7d9a9389e40dd"},"schema_version":"1.0","source":{"id":"math/0202094","kind":"arxiv","version":1}},"canonical_sha256":"0e058a5096f66e6f6cba0b81c6663c947f95147b4c679a555c912b7ff4ae3d7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e058a5096f66e6f6cba0b81c6663c947f95147b4c679a555c912b7ff4ae3d7e","first_computed_at":"2026-05-18T02:47:22.017217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:22.017217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DbAthrvrnWI0kgzNrLbGqgAi+5tCvdi5pj2UOREhGwemtj4lvdJYbDuqtqFGC0lU3a5XIuus3OdQCb4WfQP9Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:22.017908Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0202094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89952aa19daf84dcc29777b19574373c9a37ad2478c8eefb9dd85ae7fe78fe0f","sha256:75e30a691e7352954685c6f6d9826053baee27b347feb31521893172eb79af74"],"state_sha256":"aa59acccd31ae166bbb1e4351d24dcbcc1ae172e981e49ee16a95fa14f4c51a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hUr8cfymT/WgsF0PN6Cz0mFx3mqA+wwq6f4VX4P4V08gdn7xJawocIvHMPcqm5D2CviuHBCqSEibWl/F4wx4Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:53:07.664539Z","bundle_sha256":"c0ee3df4a26dd95baec97929efbbf4624c217793856813ac1c5f9eb70c8414f1"}}