{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:NXKBGHAKYK2DYC3UPHRQQ63YJI","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":"e4c554acc76f877334695ee19926ba0dd2507971f5ce35d6f7dc84a2ee0744ce","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.DG","submitted_at":"2001-05-16T16:31:00Z","title_canon_sha256":"f53695eaa6affd3bbc4b25d775dc98e1a0a5fb98bf45742d6a3e66801cd4aca5"},"schema_version":"1.0","source":{"id":"math/0105133","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0105133","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0105133v4","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0105133","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"NXKBGHAKYK2D","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"NXKBGHAKYK2DYC3U","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"NXKBGHAK","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:8c6566aafc3f97e60a6b0b25d70391e09597900747192c570a37c7ba928d3d50","target":"graph","created_at":"2026-05-18T01:05:37Z","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":"Consider the infinite dimensional flag manifold $LK/T$ corresponding to the simple Lie group $K$ of rank $l$ and with maximal torus $T$. We show that, for $K$ of type $A$, $B$ or $C$, if we endow the space $H^*(LK/T)\\otimes \\bR[q_1,...,q_{l+1}]$ (where $q_1,...,q_{l+1}$ are multiplicative variables) with an $\\bR[\\{q_j\\}]$-bilinear product satisfying some simple properties analogous to the quantum product on $QH^*(K/T)$, then the isomorphism type of the resulting ring is determined by the integrals of motion of a certain periodic Toda lattice system, in exactly the same way as the isomorphism t","authors_text":"Augustin-Liviu Mare","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2001-05-16T16:31:00Z","title":"Quantum cohomology of the infinite dimensional generalized flag manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0105133","kind":"arxiv","version":4},"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":"sha256:21ceb27ab60a8b35984d99c71686fc2f1d1de1cf821ef713eab42c7b32099d20","target":"record","created_at":"2026-05-18T01:05:37Z","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":"e4c554acc76f877334695ee19926ba0dd2507971f5ce35d6f7dc84a2ee0744ce","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.DG","submitted_at":"2001-05-16T16:31:00Z","title_canon_sha256":"f53695eaa6affd3bbc4b25d775dc98e1a0a5fb98bf45742d6a3e66801cd4aca5"},"schema_version":"1.0","source":{"id":"math/0105133","kind":"arxiv","version":4}},"canonical_sha256":"6dd4131c0ac2b43c0b7479e3087b784a122767f4b78f3b928672c2e391ab4093","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dd4131c0ac2b43c0b7479e3087b784a122767f4b78f3b928672c2e391ab4093","first_computed_at":"2026-05-18T01:05:37.799917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:37.799917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aYzclPGBw2+bnH7twzn2oGEEawTljLScNKy0oDTrwEU+FgZEuyamHlNdt6zH6XFvx4lzWC/9c8y6tmUS4wVuCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:37.800409Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0105133","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21ceb27ab60a8b35984d99c71686fc2f1d1de1cf821ef713eab42c7b32099d20","sha256:8c6566aafc3f97e60a6b0b25d70391e09597900747192c570a37c7ba928d3d50"],"state_sha256":"a8a0c2025d42a5a31384eb7d195a37e1b240abe1bfcbaf90ad6e077ba9aa0fd9"}