{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7KMEX2OVW6GP7TN4SQD73SWSAC","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":"c4a3533604a1e8f6346e0960b5b8c59572b949064d888408a5dd97f5015f562e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-02T14:44:37Z","title_canon_sha256":"7ef0d24c42a7a929ae96d2d63b8eadd3c528c9d83e05c723a17233718f1809ee"},"schema_version":"1.0","source":{"id":"1807.00716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00716","created_at":"2026-05-18T00:11:51Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00716v1","created_at":"2026-05-18T00:11:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00716","created_at":"2026-05-18T00:11:51Z"},{"alias_kind":"pith_short_12","alias_value":"7KMEX2OVW6GP","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7KMEX2OVW6GP7TN4","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7KMEX2OV","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:1a2d8ee3ab1b29142c974c985d47478f247fb7c03e95febf6fbea8ca9fa6d831","target":"graph","created_at":"2026-05-18T00:11:51Z","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":"We investigate the Voronoi summation problem for ${\\rm GL}_n$ in the level aspect for $n\\geq 2$. Of particular interest are those primes at which the level and modulus are jointly ramified - a common occurrence in analytic number theory when using techniques such as the Petersson trace formula. Building on previous legacies, our formula stands as the most general of its kind; in particular we extend the results of Ichino-Templier. We also give (classical) refinements of our formula and study the $p$-adic generalisations of the Hankel transform.","authors_text":"Andrew Corbett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-02T14:44:37Z","title":"Voronoi summation for ${\\rm GL}_n$: collusion between level and modulus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00716","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":"sha256:2eff837abe87f44237fed5dcaaceb7f73b97cfcd7240c72a53a0f723b7554bef","target":"record","created_at":"2026-05-18T00:11:51Z","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":"c4a3533604a1e8f6346e0960b5b8c59572b949064d888408a5dd97f5015f562e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-02T14:44:37Z","title_canon_sha256":"7ef0d24c42a7a929ae96d2d63b8eadd3c528c9d83e05c723a17233718f1809ee"},"schema_version":"1.0","source":{"id":"1807.00716","kind":"arxiv","version":1}},"canonical_sha256":"fa984be9d5b78cffcdbc9407fdcad2009b8f7eb9ec7825abb1249e5da93748b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa984be9d5b78cffcdbc9407fdcad2009b8f7eb9ec7825abb1249e5da93748b9","first_computed_at":"2026-05-18T00:11:51.629728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:51.629728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TrBRqpFJQmnSO9ZkuOCgSrb3IgZH0NJUXQmXKHRHQodAbiddeJoxRG/cZ5QSZ+TDIoBFHFMcL4qAF0tTCvMsCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:51.630487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2eff837abe87f44237fed5dcaaceb7f73b97cfcd7240c72a53a0f723b7554bef","sha256:1a2d8ee3ab1b29142c974c985d47478f247fb7c03e95febf6fbea8ca9fa6d831"],"state_sha256":"1387f0ca8068f3ec3b0fe28190d38f433037f057aa978b3c4494cc282540444a"}