{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OFW3XNFXYOQZRXDHUCVANNB3XV","short_pith_number":"pith:OFW3XNFX","canonical_record":{"source":{"id":"1312.3611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-12T20:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"1160e3ead6051afa1281b85bd190fd33e82ec1dd4aa70347fa3d20c42e5f962d","abstract_canon_sha256":"207a8f20fc22eca66b9f4112456861e7abe717c63ba0a94750b02af4d4cbbd94"},"schema_version":"1.0"},"canonical_sha256":"716dbbb4b7c3a198dc67a0aa06b43bbd4b9a5c35c61b4fa01905678c724af0a7","source":{"kind":"arxiv","id":"1312.3611","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3611","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3611v2","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3611","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"OFW3XNFXYOQZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OFW3XNFXYOQZRXDH","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OFW3XNFX","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OFW3XNFXYOQZRXDHUCVANNB3XV","target":"record","payload":{"canonical_record":{"source":{"id":"1312.3611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-12T20:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"1160e3ead6051afa1281b85bd190fd33e82ec1dd4aa70347fa3d20c42e5f962d","abstract_canon_sha256":"207a8f20fc22eca66b9f4112456861e7abe717c63ba0a94750b02af4d4cbbd94"},"schema_version":"1.0"},"canonical_sha256":"716dbbb4b7c3a198dc67a0aa06b43bbd4b9a5c35c61b4fa01905678c724af0a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:38.828620Z","signature_b64":"PKDFNac/D+p3fZZVSDd2iabNTlJLvZSRAsNouB4PdhfiienGXuAF5R/Dppku7RjJ8AyvQPxYhe+onU9GqPS+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"716dbbb4b7c3a198dc67a0aa06b43bbd4b9a5c35c61b4fa01905678c724af0a7","last_reissued_at":"2026-05-18T02:49:38.828252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:38.828252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.3611","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NdWHiorpCPA39KRaIALawm9OqWi7XATYpcb7yfbxZrH/68HHgA2AFrH0OBvwZRz4CCVwbxWBYn2Fmpc79dEJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:46:22.890094Z"},"content_sha256":"3cb0380d9790504fa1e3e8686e4424fe32fd23f0a5347956f79e8c3b40e28a72","schema_version":"1.0","event_id":"sha256:3cb0380d9790504fa1e3e8686e4424fe32fd23f0a5347956f79e8c3b40e28a72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OFW3XNFXYOQZRXDHUCVANNB3XV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A nonabelian trace formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jayce R. Getz, P. Edward Herman","submitted_at":"2013-12-12T20:18:18Z","abstract_excerpt":"Let $E/F$ be an extension of number fields with $\\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\\mathrm{GL}_2$ along such an extension. Motivated by this we prove a trace formula whose spectral side is a weighted sum over cuspidal automorphic representations of $\\mathrm{GL}_2(\\mathbb{A}_E)$ that are isomorphic to their $\\mathrm{Gal}(E/F)$-conjugates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3611","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4N2EeZ3tBGPZF5fGhNRvAvwS1go60tni85GQwqCSkiZlTj7/Zm/mGKjxj+UbID2yXF+gQI+2ohuPIxc5/reYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:46:22.890736Z"},"content_sha256":"82e379b3a1c5de1a513df11b7e88c3d37ccc514ccb14ece1af4d0755c1c2d8de","schema_version":"1.0","event_id":"sha256:82e379b3a1c5de1a513df11b7e88c3d37ccc514ccb14ece1af4d0755c1c2d8de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFW3XNFXYOQZRXDHUCVANNB3XV/bundle.json","state_url":"https://pith.science/pith/OFW3XNFXYOQZRXDHUCVANNB3XV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFW3XNFXYOQZRXDHUCVANNB3XV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T10:46:22Z","links":{"resolver":"https://pith.science/pith/OFW3XNFXYOQZRXDHUCVANNB3XV","bundle":"https://pith.science/pith/OFW3XNFXYOQZRXDHUCVANNB3XV/bundle.json","state":"https://pith.science/pith/OFW3XNFXYOQZRXDHUCVANNB3XV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFW3XNFXYOQZRXDHUCVANNB3XV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OFW3XNFXYOQZRXDHUCVANNB3XV","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":"207a8f20fc22eca66b9f4112456861e7abe717c63ba0a94750b02af4d4cbbd94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-12T20:18:18Z","title_canon_sha256":"1160e3ead6051afa1281b85bd190fd33e82ec1dd4aa70347fa3d20c42e5f962d"},"schema_version":"1.0","source":{"id":"1312.3611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3611","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3611v2","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3611","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"OFW3XNFXYOQZ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OFW3XNFXYOQZRXDH","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OFW3XNFX","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:82e379b3a1c5de1a513df11b7e88c3d37ccc514ccb14ece1af4d0755c1c2d8de","target":"graph","created_at":"2026-05-18T02:49:38Z","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":"Let $E/F$ be an extension of number fields with $\\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\\mathrm{GL}_2$ along such an extension. Motivated by this we prove a trace formula whose spectral side is a weighted sum over cuspidal automorphic representations of $\\mathrm{GL}_2(\\mathbb{A}_E)$ that are isomorphic to their $\\mathrm{Gal}(E/F)$-conjugates.","authors_text":"Jayce R. Getz, P. Edward Herman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-12T20:18:18Z","title":"A nonabelian trace formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3611","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":"sha256:3cb0380d9790504fa1e3e8686e4424fe32fd23f0a5347956f79e8c3b40e28a72","target":"record","created_at":"2026-05-18T02:49:38Z","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":"207a8f20fc22eca66b9f4112456861e7abe717c63ba0a94750b02af4d4cbbd94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-12T20:18:18Z","title_canon_sha256":"1160e3ead6051afa1281b85bd190fd33e82ec1dd4aa70347fa3d20c42e5f962d"},"schema_version":"1.0","source":{"id":"1312.3611","kind":"arxiv","version":2}},"canonical_sha256":"716dbbb4b7c3a198dc67a0aa06b43bbd4b9a5c35c61b4fa01905678c724af0a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"716dbbb4b7c3a198dc67a0aa06b43bbd4b9a5c35c61b4fa01905678c724af0a7","first_computed_at":"2026-05-18T02:49:38.828252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:38.828252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PKDFNac/D+p3fZZVSDd2iabNTlJLvZSRAsNouB4PdhfiienGXuAF5R/Dppku7RjJ8AyvQPxYhe+onU9GqPS+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:38.828620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cb0380d9790504fa1e3e8686e4424fe32fd23f0a5347956f79e8c3b40e28a72","sha256:82e379b3a1c5de1a513df11b7e88c3d37ccc514ccb14ece1af4d0755c1c2d8de"],"state_sha256":"1dad61dacd7b0dbf51ea2c4d8cce6a00b447c53a17b505080fbc42ec1f9cf7f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EtjfCRxMwrSbJfx5S5qlFxaf15Uv5+HAlF2Gb6fB+sysPuZ1km+cSjAc1zmkhDQinRkbxHNiK7g8Js2+Kla4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:46:22.893695Z","bundle_sha256":"3010d4c713eb23e8b93ec99c3466e5d4bd81aa666f846d87c4c6563a4e99af54"}}