{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FQMLMVWRONG7NW5NFAPVA75WUA","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":"dbf6fdebc81692b4dec01119932df982d045f726457c9c7f8e58190ad2eeacc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-27T17:02:10Z","title_canon_sha256":"29b5fc621b344f0c10fac977d748972bb827014ef4875db184d3942d378dc366"},"schema_version":"1.0","source":{"id":"1506.08313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08313","created_at":"2026-05-18T01:37:46Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08313v1","created_at":"2026-05-18T01:37:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08313","created_at":"2026-05-18T01:37:46Z"},{"alias_kind":"pith_short_12","alias_value":"FQMLMVWRONG7","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FQMLMVWRONG7NW5N","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FQMLMVWR","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:7e6879c6928692ae8051576b3a427ee263b3ef070d83716b72f147a13dd8ed9a","target":"graph","created_at":"2026-05-18T01:37:46Z","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 [4] and [5], Folsom presents a family of modular units as higher-level analogues of the Rogers-Ramanujan $q$-continued fraction. These units are constructed from analytic solutions to the higher-order $q$-recurrence equations of Selberg. Here, we consider another family of modular units, which are quotients of Hall-Littlewood $q$-series that appear in the generalized Rogers-Ramanujan type identities of [6]. In analogy with the results of Folsom, we provide a formula for the rank of the subgroup these units generate and show that their specializations at the cusp $0$ generate a subgroup of t","authors_text":"Hannah Larson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-27T17:02:10Z","title":"Modular units from quotients of Rogers-Ramanujan type $q$-series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08313","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":"sha256:49141c51358a3c65412805ef5e9135f4ad8cd9adfea95daa08da2cf1ed454af5","target":"record","created_at":"2026-05-18T01:37:46Z","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":"dbf6fdebc81692b4dec01119932df982d045f726457c9c7f8e58190ad2eeacc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-27T17:02:10Z","title_canon_sha256":"29b5fc621b344f0c10fac977d748972bb827014ef4875db184d3942d378dc366"},"schema_version":"1.0","source":{"id":"1506.08313","kind":"arxiv","version":1}},"canonical_sha256":"2c18b656d1734df6dbad281f507fb6a02c0e3e826357927f7f92d1d941597d5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c18b656d1734df6dbad281f507fb6a02c0e3e826357927f7f92d1d941597d5d","first_computed_at":"2026-05-18T01:37:46.822872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:46.822872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LnHd8tJnLiqoRCbwKPX35BuoDir9s7lZyZLkpUTPk6cOY8mkZ3Nnpxs6WED2RhqpMWJcm8HEOthEDz60F6VqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:46.823228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49141c51358a3c65412805ef5e9135f4ad8cd9adfea95daa08da2cf1ed454af5","sha256:7e6879c6928692ae8051576b3a427ee263b3ef070d83716b72f147a13dd8ed9a"],"state_sha256":"d36f468ec77694a2b5c3ae75aec856b1ce18d6e2be6023edc5d38dad3c586aa2"}