{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VMTHLZPROMXB63BGDXQ7WWP44R","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":"4412df39a140ee59694d7f3dea141a8be7dff0d7f618f9a8172417daa80735bd","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-20T05:20:00Z","title_canon_sha256":"30ee7d6c6acdaef56ae727aabc4de220d1970722b3b3e5bfa6698bbb58dc69bb"},"schema_version":"1.0","source":{"id":"2605.20719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20719","created_at":"2026-05-21T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20719v1","created_at":"2026-05-21T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20719","created_at":"2026-05-21T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"VMTHLZPROMXB","created_at":"2026-05-21T01:04:50Z"},{"alias_kind":"pith_short_16","alias_value":"VMTHLZPROMXB63BG","created_at":"2026-05-21T01:04:50Z"},{"alias_kind":"pith_short_8","alias_value":"VMTHLZPR","created_at":"2026-05-21T01:04:50Z"}],"graph_snapshots":[{"event_id":"sha256:d3e14ecd4b31b591d4ae9db3d50801a289300b620a476fd21aac2981276a31db","target":"graph","created_at":"2026-05-21T01:04:50Z","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/2605.20719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We continue our work on $\\mathsf{GL}_2$ over $\\mathbb{Q}$ in the ramified setting for \\emph{Beyond Endoscopy}. We establish asymptotic formulas for each term of the trace formula when summing over $n<X$, using arbitrary smooth test functions at the places in $S=\\{\\infty,q_1,\\dots, q_r\\}$ where $2\\in S$, for the standard representation, up to an error of $o(X)$. This yields an identity depending on a parameter $X$, leading to certain identities that can be regarded as a limit form of the trace formula for $\\mathsf{GL}_2$ over $\\mathbb{Q}$. On the spectral side, we employ the contour shift metho","authors_text":"Yuhao Cheng","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-20T05:20:00Z","title":"Beyond endoscopy for $\\mathsf{GL}_2$ over $\\mathbb{Q}$ with ramification 4: contribution of non-elliptic parts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20719","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:e7d09d3f1d7a46cef3fca1be7c0f48c8ef637f4eaf8211a4d43bb6829635dec7","target":"record","created_at":"2026-05-21T01:04:50Z","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":"4412df39a140ee59694d7f3dea141a8be7dff0d7f618f9a8172417daa80735bd","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-20T05:20:00Z","title_canon_sha256":"30ee7d6c6acdaef56ae727aabc4de220d1970722b3b3e5bfa6698bbb58dc69bb"},"schema_version":"1.0","source":{"id":"2605.20719","kind":"arxiv","version":1}},"canonical_sha256":"ab2675e5f1732e1f6c261de1fb59fce451d73f00c616ab1419dae52223864075","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab2675e5f1732e1f6c261de1fb59fce451d73f00c616ab1419dae52223864075","first_computed_at":"2026-05-21T01:04:50.638435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:50.638435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lfmxff5kGe7RqBLyelCMozWBKwseN04aE/7JVz4mL39gVC9VXVAJNM8VY4Kw1/CgD+hswRKl2VSPULjEI2jQBQ==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:50.639052Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7d09d3f1d7a46cef3fca1be7c0f48c8ef637f4eaf8211a4d43bb6829635dec7","sha256:d3e14ecd4b31b591d4ae9db3d50801a289300b620a476fd21aac2981276a31db"],"state_sha256":"8c6da8abe3ecb931ef0a08d96f32e2bd02a9462958993eb15a4200130b575010"}