{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4DKX4PZM3XMZYWPAMNKZO6EYI5","short_pith_number":"pith:4DKX4PZM","schema_version":"1.0","canonical_sha256":"e0d57e3f2cddd99c59e0635597789847445ad401c278325e098aaefd7df5b9e1","source":{"kind":"arxiv","id":"2507.12829","version":1},"attestation_state":"computed","paper":{"title":"Cactus flower spaces and monodromy of Bethe vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"Joel Kamnitzer, Leonid Rybnikov","submitted_at":"2025-07-17T06:37:59Z","abstract_excerpt":"We continue the study of cactus flower moduli spaces $\\overline{F}_n$ and Gaudin models started in arXiv:2308.06880, arXiv:2407.06424. We show that isomorphism classes of operadic coverings of the real form $\\overline{F}_n(\\mathbb{R})$ are naturally one-to-one with equivalence classes of concrete coboundary monoidal categories (i.e. coboundary monoidal categories that admit a faithful monoidal functor to sets) with certain semisimplicity and finiteness conditions. Following the strategy of arXiv:1708.05105, for any complex semisimple Lie algebra $\\mathfrak{g}$, we recover Kashiwara $\\mathfrak{"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.12829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-07-17T06:37:59Z","cross_cats_sorted":["math.AG","math.QA"],"title_canon_sha256":"0348be5aead6807232ce15befe6c2f35380326b0257656798f743173ea1239ed","abstract_canon_sha256":"f2fea42f6217f550cc97140c0738ef84e678aeeee701489d3e8ddd055dbe8b6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:39.992735Z","signature_b64":"NxPmqD2HMdRs/SvLFg32rt/o7JeoqlynKNkymAUi32GWslIGENVepoUGl0uRfT745SesDicMItqQz2CCKIlNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0d57e3f2cddd99c59e0635597789847445ad401c278325e098aaefd7df5b9e1","last_reissued_at":"2026-07-05T11:38:39.992309Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:39.992309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cactus flower spaces and monodromy of Bethe vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"Joel Kamnitzer, Leonid Rybnikov","submitted_at":"2025-07-17T06:37:59Z","abstract_excerpt":"We continue the study of cactus flower moduli spaces $\\overline{F}_n$ and Gaudin models started in arXiv:2308.06880, arXiv:2407.06424. We show that isomorphism classes of operadic coverings of the real form $\\overline{F}_n(\\mathbb{R})$ are naturally one-to-one with equivalence classes of concrete coboundary monoidal categories (i.e. coboundary monoidal categories that admit a faithful monoidal functor to sets) with certain semisimplicity and finiteness conditions. Following the strategy of arXiv:1708.05105, for any complex semisimple Lie algebra $\\mathfrak{g}$, we recover Kashiwara $\\mathfrak{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12829","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.12829/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.12829","created_at":"2026-07-05T11:38:39.992381+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.12829v1","created_at":"2026-07-05T11:38:39.992381+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12829","created_at":"2026-07-05T11:38:39.992381+00:00"},{"alias_kind":"pith_short_12","alias_value":"4DKX4PZM3XMZ","created_at":"2026-07-05T11:38:39.992381+00:00"},{"alias_kind":"pith_short_16","alias_value":"4DKX4PZM3XMZYWPA","created_at":"2026-07-05T11:38:39.992381+00:00"},{"alias_kind":"pith_short_8","alias_value":"4DKX4PZM","created_at":"2026-07-05T11:38:39.992381+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4DKX4PZM3XMZYWPAMNKZO6EYI5","json":"https://pith.science/pith/4DKX4PZM3XMZYWPAMNKZO6EYI5.json","graph_json":"https://pith.science/api/pith-number/4DKX4PZM3XMZYWPAMNKZO6EYI5/graph.json","events_json":"https://pith.science/api/pith-number/4DKX4PZM3XMZYWPAMNKZO6EYI5/events.json","paper":"https://pith.science/paper/4DKX4PZM"},"agent_actions":{"view_html":"https://pith.science/pith/4DKX4PZM3XMZYWPAMNKZO6EYI5","download_json":"https://pith.science/pith/4DKX4PZM3XMZYWPAMNKZO6EYI5.json","view_paper":"https://pith.science/paper/4DKX4PZM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.12829&json=true","fetch_graph":"https://pith.science/api/pith-number/4DKX4PZM3XMZYWPAMNKZO6EYI5/graph.json","fetch_events":"https://pith.science/api/pith-number/4DKX4PZM3XMZYWPAMNKZO6EYI5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4DKX4PZM3XMZYWPAMNKZO6EYI5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4DKX4PZM3XMZYWPAMNKZO6EYI5/action/storage_attestation","attest_author":"https://pith.science/pith/4DKX4PZM3XMZYWPAMNKZO6EYI5/action/author_attestation","sign_citation":"https://pith.science/pith/4DKX4PZM3XMZYWPAMNKZO6EYI5/action/citation_signature","submit_replication":"https://pith.science/pith/4DKX4PZM3XMZYWPAMNKZO6EYI5/action/replication_record"}},"created_at":"2026-07-05T11:38:39.992381+00:00","updated_at":"2026-07-05T11:38:39.992381+00:00"}