{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3ZIIG55FSOGOB3HC66GYFQGPUM","short_pith_number":"pith:3ZIIG55F","schema_version":"1.0","canonical_sha256":"de508377a5938ce0ece2f78d82c0cfa30bd9dba136dfd01e7c85c0282183bf15","source":{"kind":"arxiv","id":"2605.21159","version":1},"attestation_state":"computed","paper":{"title":"Mirror Symmetry of the Affine Toda Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.SG","authors_text":"Xin Jin, Zhiwei Yun","submitted_at":"2026-05-20T13:26:57Z","abstract_excerpt":"For a complex reductive group $G$, we prove a homological mirror symmetry between the wrapped Fukaya category of the affine Toda system for $G$ and coherent sheaves on the regular centralizer group scheme for the Langlands dual group $G^\\vee$. This can be interpreted as a geometric Langlands equivalence for $\\mathbb{P}^1$ with mildest wild ramification at $0$ and $\\infty$."},"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":"2605.21159","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2026-05-20T13:26:57Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"3ab8cfbb796a45414dd267aa9f9f18718cf694fbef766fdc76eac61f3daf5d1d","abstract_canon_sha256":"0319b315040833d99594006bcbee028bf10dcb272b19b573da5e9bf5fefce370"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:40.443240Z","signature_b64":"gC2YUd8by3bFFDPNISmdUDkb9h6U2ViP9qEIFNMOo9/r1nXZ5kdsNET2SkO7o15ksYU3tf1s8s911fzvtcYQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de508377a5938ce0ece2f78d82c0cfa30bd9dba136dfd01e7c85c0282183bf15","last_reissued_at":"2026-05-21T01:05:40.442668Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:40.442668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mirror Symmetry of the Affine Toda Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.SG","authors_text":"Xin Jin, Zhiwei Yun","submitted_at":"2026-05-20T13:26:57Z","abstract_excerpt":"For a complex reductive group $G$, we prove a homological mirror symmetry between the wrapped Fukaya category of the affine Toda system for $G$ and coherent sheaves on the regular centralizer group scheme for the Langlands dual group $G^\\vee$. This can be interpreted as a geometric Langlands equivalence for $\\mathbb{P}^1$ with mildest wild ramification at $0$ and $\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21159","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/2605.21159/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":"2605.21159","created_at":"2026-05-21T01:05:40.442770+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.21159v1","created_at":"2026-05-21T01:05:40.442770+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21159","created_at":"2026-05-21T01:05:40.442770+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ZIIG55FSOGO","created_at":"2026-05-21T01:05:40.442770+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ZIIG55FSOGOB3HC","created_at":"2026-05-21T01:05:40.442770+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ZIIG55F","created_at":"2026-05-21T01:05:40.442770+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/3ZIIG55FSOGOB3HC66GYFQGPUM","json":"https://pith.science/pith/3ZIIG55FSOGOB3HC66GYFQGPUM.json","graph_json":"https://pith.science/api/pith-number/3ZIIG55FSOGOB3HC66GYFQGPUM/graph.json","events_json":"https://pith.science/api/pith-number/3ZIIG55FSOGOB3HC66GYFQGPUM/events.json","paper":"https://pith.science/paper/3ZIIG55F"},"agent_actions":{"view_html":"https://pith.science/pith/3ZIIG55FSOGOB3HC66GYFQGPUM","download_json":"https://pith.science/pith/3ZIIG55FSOGOB3HC66GYFQGPUM.json","view_paper":"https://pith.science/paper/3ZIIG55F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.21159&json=true","fetch_graph":"https://pith.science/api/pith-number/3ZIIG55FSOGOB3HC66GYFQGPUM/graph.json","fetch_events":"https://pith.science/api/pith-number/3ZIIG55FSOGOB3HC66GYFQGPUM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ZIIG55FSOGOB3HC66GYFQGPUM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ZIIG55FSOGOB3HC66GYFQGPUM/action/storage_attestation","attest_author":"https://pith.science/pith/3ZIIG55FSOGOB3HC66GYFQGPUM/action/author_attestation","sign_citation":"https://pith.science/pith/3ZIIG55FSOGOB3HC66GYFQGPUM/action/citation_signature","submit_replication":"https://pith.science/pith/3ZIIG55FSOGOB3HC66GYFQGPUM/action/replication_record"}},"created_at":"2026-05-21T01:05:40.442770+00:00","updated_at":"2026-05-21T01:05:40.442770+00:00"}