{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2JR6YSCVICINNSQJSLGQ4EB3KG","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":"a923e60cee8e858eb569bd0f5de58cabec8358d8bd7271ea3149e3c1ed5f4f0c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T07:39:01Z","title_canon_sha256":"28ed5023dfaef461fe796c7f6e215c222beea358c920e917c8259dcaa61c6cd3"},"schema_version":"1.0","source":{"id":"2607.25383","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25383","created_at":"2026-07-29T01:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25383v1","created_at":"2026-07-29T01:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25383","created_at":"2026-07-29T01:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"2JR6YSCVICIN","created_at":"2026-07-29T01:25:12Z"},{"alias_kind":"pith_short_16","alias_value":"2JR6YSCVICINNSQJ","created_at":"2026-07-29T01:25:12Z"},{"alias_kind":"pith_short_8","alias_value":"2JR6YSCV","created_at":"2026-07-29T01:25:12Z"}],"graph_snapshots":[{"event_id":"sha256:4179e995392a4da1642b928133476038c45e755c609eb0311bf3f67c3fdd44aa","target":"graph","created_at":"2026-07-29T01:25:12Z","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/2607.25383/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"At the beginning of this century, Langlands introduced a strategy known as \\emph{Beyond Endoscopy} to attack the principle of functoriality. Altu\\u{g} studied $\\mathsf{GL}_2$ over $\\mathbb Q$ in the unramified setting for the standard representation. We consider the case with ramification at $S=\\{\\infty,q_1,\\dots,q_r\\}$ with $2\\in S$ and derive an asymptotic formula for the symmetric square representation adding some additional conditions on the test function so that the trace formula is simple. The limit is nonzero in general and we may detect the dihedral forms by using such limit form of th","authors_text":"Yuhao Cheng","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T07:39:01Z","title":"Beyond endoscopy for the symmetric square representation: The simple trace formula case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25383","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:f216df599de0ade405c6edf61213c2cfb5cd5638562094d083ae0279b21f5541","target":"record","created_at":"2026-07-29T01:25:12Z","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":"a923e60cee8e858eb569bd0f5de58cabec8358d8bd7271ea3149e3c1ed5f4f0c","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T07:39:01Z","title_canon_sha256":"28ed5023dfaef461fe796c7f6e215c222beea358c920e917c8259dcaa61c6cd3"},"schema_version":"1.0","source":{"id":"2607.25383","kind":"arxiv","version":1}},"canonical_sha256":"d263ec48554090d6ca0992cd0e103b51b1570eb7cdd88983cd2883c11287369f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d263ec48554090d6ca0992cd0e103b51b1570eb7cdd88983cd2883c11287369f","first_computed_at":"2026-07-29T01:25:12.723176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T01:25:12.723176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u120x3EJ+a674tOFWcqgSelNerVnihHmrElHeI0kIA9mGyahSlJT8m0ZWBbwOAkn+f3HkEcWRprhF6LzVfRhCA==","signature_status":"signed_v1","signed_at":"2026-07-29T01:25:12.723997Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.25383","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f216df599de0ade405c6edf61213c2cfb5cd5638562094d083ae0279b21f5541","sha256:4179e995392a4da1642b928133476038c45e755c609eb0311bf3f67c3fdd44aa"],"state_sha256":"a4883857c0fa4765850feec7e1b4af44907fcf06e84ee3767aeda8850aa6f02b"}