{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YRNLD6RM73M2GMB4OMFDGO6F66","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":"bc89acded06f321c08e9107119e4d686c0c03ef5f488941008074987edfd46bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-03-11T08:26:16Z","title_canon_sha256":"ea5c2591a0b0b1cb8077ac5c5b19f3876d680cd4d6bcdb63c401f5e15df4ca94"},"schema_version":"1.0","source":{"id":"1803.03923","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03923","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03923v1","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03923","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"YRNLD6RM73M2","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YRNLD6RM73M2GMB4","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YRNLD6RM","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:9ebfbc6bc881d4c38eeea336ea2a55a4e40d735fe0ca4271ae3d5a626d4f1e81","target":"graph","created_at":"2026-05-18T00:21:33Z","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":"A complete flag manifold is the quotient of a Lie group by its maximal torus. The rank of a flag manifold is the dimension of the maximal torus of the Lie group. The rank 2 complete flag manifolds are $SU(3)/T^2$, $Sp(2)/T^2$, $Spin(4)/T^2$, $Spin(5)/T^2$ and $G_2/T^2$. In this paper we calculate the cohomology of the free loop space of rank 2 complete flag manifolds.","authors_text":"Jelena Grbi\\'c, Matthew I. Burfitt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-03-11T08:26:16Z","title":"The cohomology of free loop spaces of rank 2 flag manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03923","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:faa404768ac5c44501ddf966ed28323939d434378b5cb52ea75a107bedaa1558","target":"record","created_at":"2026-05-18T00:21:33Z","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":"bc89acded06f321c08e9107119e4d686c0c03ef5f488941008074987edfd46bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-03-11T08:26:16Z","title_canon_sha256":"ea5c2591a0b0b1cb8077ac5c5b19f3876d680cd4d6bcdb63c401f5e15df4ca94"},"schema_version":"1.0","source":{"id":"1803.03923","kind":"arxiv","version":1}},"canonical_sha256":"c45ab1fa2cfed9a3303c730a333bc5f7bf66f00fd99d4b313624062ba2b30341","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c45ab1fa2cfed9a3303c730a333bc5f7bf66f00fd99d4b313624062ba2b30341","first_computed_at":"2026-05-18T00:21:33.464250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:33.464250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KpH4YrSkyAHWQgGGiEx2u6WjU4krBPovpDHChJfSBKHHMqiC3WKIGz9QE+x4+dBRmQ+EFf34L7MzfZ4kz8FvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:33.465104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03923","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faa404768ac5c44501ddf966ed28323939d434378b5cb52ea75a107bedaa1558","sha256:9ebfbc6bc881d4c38eeea336ea2a55a4e40d735fe0ca4271ae3d5a626d4f1e81"],"state_sha256":"ed8b4932c59806fdc39d3a5bf1919de9df8e16333521ab76958c89be199bd0b8"}