{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:34LLUJ24BY2KAWXQ6576BDE2LQ","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":"2e8b9b810a211a922de4f1aa4d6016b5552e9f7061d2a98978006c2d61aba241","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-09-10T13:18:21Z","title_canon_sha256":"56d7f4dde92e7da43c90d88aa28854b10aa4fb0cfa689aadc7e02deb1ab6ddf0"},"schema_version":"1.0","source":{"id":"1209.1978","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1978","created_at":"2026-05-18T03:42:10Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1978v4","created_at":"2026-05-18T03:42:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1978","created_at":"2026-05-18T03:42:10Z"},{"alias_kind":"pith_short_12","alias_value":"34LLUJ24BY2K","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"34LLUJ24BY2KAWXQ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"34LLUJ24","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:2820d8fcd95bb93776613a09f48a66f182af16217e1aa63544ac4b769e6affa5","target":"graph","created_at":"2026-05-18T03:42:10Z","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":"In the theory of the Nil-DAHA Fourier transform, the inner products of q-Hermite polynomials for the measure function multiplied by a level one theta function are the key. They are used to obtain expansions of products of any number of such theta functions in terms of the q-Hermite polynomials. An ample family of modular functions satisfying Rogers-Ramanujan type identities for arbitrary (reduced, twisted) affine root systems is obtained as an application. A relation to Rogers dilogarithm and Nahm's conjecture is discussed. Some of our q-series can be identified with known ones, but their inte","authors_text":"Boris Feigin, Ivan Cherednik","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-09-10T13:18:21Z","title":"Rogers-Ramanujan type identities and Nil-DAHA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1978","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":"sha256:0af3705bb5313ed6030618d73caf9b28bce59edafc3e14779196e525e869e8ed","target":"record","created_at":"2026-05-18T03:42:10Z","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":"2e8b9b810a211a922de4f1aa4d6016b5552e9f7061d2a98978006c2d61aba241","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-09-10T13:18:21Z","title_canon_sha256":"56d7f4dde92e7da43c90d88aa28854b10aa4fb0cfa689aadc7e02deb1ab6ddf0"},"schema_version":"1.0","source":{"id":"1209.1978","kind":"arxiv","version":4}},"canonical_sha256":"df16ba275c0e34a05af0f77fe08c9a5c395c437fb3fd1a91b02ed56f34062122","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df16ba275c0e34a05af0f77fe08c9a5c395c437fb3fd1a91b02ed56f34062122","first_computed_at":"2026-05-18T03:42:10.984343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:10.984343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YekzF+BKAW6a5XeBPwHdR8dHg/mX1fKp5TSdNRbF8ZDwKkHQ8FtdC07yk3J077sKD5YCNYzJqRfDnwnPctvSAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:10.985057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1978","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0af3705bb5313ed6030618d73caf9b28bce59edafc3e14779196e525e869e8ed","sha256:2820d8fcd95bb93776613a09f48a66f182af16217e1aa63544ac4b769e6affa5"],"state_sha256":"7b64f08c939862dae5eeefd43e8a79402b3e8924a18a64745e351385bd62436a"}