{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HJJ5M3GYGCE4ISXMSU4YZBP6PC","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":"54c18d10f3c8790be00629f50d54475aa38f13a2184fc04bbed18ee2dda409a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-03-17T15:41:32Z","title_canon_sha256":"d71f31ae400d1a69e26fa13264ac2565ab84fd54aae7e4110a727408a47fddd5"},"schema_version":"1.0","source":{"id":"2503.13295","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.13295","created_at":"2026-06-01T02:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"2503.13295v2","created_at":"2026-06-01T02:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.13295","created_at":"2026-06-01T02:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"HJJ5M3GYGCE4","created_at":"2026-06-01T02:03:20Z"},{"alias_kind":"pith_short_16","alias_value":"HJJ5M3GYGCE4ISXM","created_at":"2026-06-01T02:03:20Z"},{"alias_kind":"pith_short_8","alias_value":"HJJ5M3GY","created_at":"2026-06-01T02:03:20Z"}],"graph_snapshots":[{"event_id":"sha256:752a1db7626ff7570ee7251b80c7538ec933e65a4f59fd8cb2a8363d11dd76d8","target":"graph","created_at":"2026-06-01T02:03:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.13295/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we describe new noncommutative factorizations of functions related to $d$-th tensor powers of Carlitz's $\\mathbb F_q[\\theta]$-module for $d\\geq 1$, called higher sine functions. In recent work by the second author, factorizations of this type have been constructed for operators which are combinations of powers of a Frobenius endomorphism with coefficients ``in $\\operatorname{End}(\\operatorname{End}(\\mathbb G_a^d))$''. In the present paper we succeed in determining factorizations with coefficients ``in $\\operatorname{End}(\\mathbb G_a^d)$'' which are not easily deducible from previ","authors_text":"Federico Pellarin, Nathan Green","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-03-17T15:41:32Z","title":"Noncommutative factorizations of higher sine functions in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.13295","kind":"arxiv","version":2},"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:e8380133af3a735c7527aaadcd6c173af0646cd0a3d1c27aea1bde770a7c7667","target":"record","created_at":"2026-06-01T02:03:20Z","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":"54c18d10f3c8790be00629f50d54475aa38f13a2184fc04bbed18ee2dda409a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-03-17T15:41:32Z","title_canon_sha256":"d71f31ae400d1a69e26fa13264ac2565ab84fd54aae7e4110a727408a47fddd5"},"schema_version":"1.0","source":{"id":"2503.13295","kind":"arxiv","version":2}},"canonical_sha256":"3a53d66cd83089c44aec95398c85fe78b5073113d7afee3a3a08c1259b6bab78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a53d66cd83089c44aec95398c85fe78b5073113d7afee3a3a08c1259b6bab78","first_computed_at":"2026-06-01T02:03:20.021643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T02:03:20.021643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NyOqhsZKrOmnNhmsL4AFjYQPF+zn8pT3GmU0fk2Lw/PPPidhGuXFlgiJt+5qCL1McYRduNH3TSj9N0gkKWbYCA==","signature_status":"signed_v1","signed_at":"2026-06-01T02:03:20.022619Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.13295","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8380133af3a735c7527aaadcd6c173af0646cd0a3d1c27aea1bde770a7c7667","sha256:752a1db7626ff7570ee7251b80c7538ec933e65a4f59fd8cb2a8363d11dd76d8"],"state_sha256":"21a800d3e5de1adef2c2d5651d6006eabb85a4c2fbcd0fd3c1d30104c3f86a47"}