{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:IGWFZH22UR6ZZ63OPDC4SVBPKR","short_pith_number":"pith:IGWFZH22","canonical_record":{"source":{"id":"2305.10719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-05-18T05:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"b50505dd7bb1aa61e61fb5fc73f5e5cac5eb0e83205626f7255f5a4950a9bb34","abstract_canon_sha256":"dd28a83d6dcfe11937ad6230385a1bc67b7e094f798d92eea879e3d66d752451"},"schema_version":"1.0"},"canonical_sha256":"41ac5c9f5aa47d9cfb6e78c5c9542f5453c86f713127f235f528b9510f8353b4","source":{"kind":"arxiv","id":"2305.10719","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.10719","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"2305.10719v1","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.10719","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"IGWFZH22UR6Z","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"pith_short_16","alias_value":"IGWFZH22UR6ZZ63O","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"pith_short_8","alias_value":"IGWFZH22","created_at":"2026-07-05T06:11:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:IGWFZH22UR6ZZ63OPDC4SVBPKR","target":"record","payload":{"canonical_record":{"source":{"id":"2305.10719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-05-18T05:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"b50505dd7bb1aa61e61fb5fc73f5e5cac5eb0e83205626f7255f5a4950a9bb34","abstract_canon_sha256":"dd28a83d6dcfe11937ad6230385a1bc67b7e094f798d92eea879e3d66d752451"},"schema_version":"1.0"},"canonical_sha256":"41ac5c9f5aa47d9cfb6e78c5c9542f5453c86f713127f235f528b9510f8353b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:11:25.891201Z","signature_b64":"tU5XPawU82Pax23nopigXpsAPodxfQp2EV5CXWRp817u+Glo6AU1UXLmoY8o0DHutqDNuiVIYw3S9phZAVh8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41ac5c9f5aa47d9cfb6e78c5c9542f5453c86f713127f235f528b9510f8353b4","last_reissued_at":"2026-07-05T06:11:25.890825Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:11:25.890825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.10719","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:11:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z5L8ZI/YqUxJ7+ibwXJqSuRNURYaP1EtU0jW9Y+9ZLfKChGKo0roofTELIGJp/c1ihmx2nD5+7aOwtcEejtkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:23:36.775398Z"},"content_sha256":"d80bb2ebd59e51403c87e6988f467b0c5893276b3b31c7252cb5d791c513b5f5","schema_version":"1.0","event_id":"sha256:d80bb2ebd59e51403c87e6988f467b0c5893276b3b31c7252cb5d791c513b5f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:IGWFZH22UR6ZZ63OPDC4SVBPKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relative Trace Formula and Twisted $L$-functions: the Burgess Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liyang Yang","submitted_at":"2023-05-18T05:32:19Z","abstract_excerpt":"Let $F$ be a number field, $\\pi$ either a unitary cuspidal automorphic representation of $\\mathrm{GL}(2)/F$ or a unitary Eisenstein series, and $\\chi$ a unitary Hecke character of analytic conductor $C(\\chi).$ We develop a regularized relative trace formula to prove a refined hybrid subconvex bound for $L(1/2,\\pi\\times\\chi).$ In particular, we obtain the Burgess subconvex bound \\begin{align*} L(1/2,\\pi\\times\\chi)\\ll_{\\pi,F,\\varepsilon}C(\\chi)^{\\frac{1}{2}-\\frac{1}{8}+\\varepsilon}, \\end{align*} where the implied constant depends on $\\pi,$ $F$ and $\\varepsilon.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.10719","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.10719/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:11:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aQ1LSFiJXOoqs+LEB1at9S12JzIuFoI3OKmBEa3yxdwfvEpyJVC6ROlP8fuyQ4sXG25ypk/Zqf4VxlKgFv6wCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T07:23:36.776157Z"},"content_sha256":"6736b12d84c048cef46afcdb87db0ae1540ff4a8676c56b6aa431d8b65601a15","schema_version":"1.0","event_id":"sha256:6736b12d84c048cef46afcdb87db0ae1540ff4a8676c56b6aa431d8b65601a15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGWFZH22UR6ZZ63OPDC4SVBPKR/bundle.json","state_url":"https://pith.science/pith/IGWFZH22UR6ZZ63OPDC4SVBPKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGWFZH22UR6ZZ63OPDC4SVBPKR/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":"2026-08-18T07:23:36Z","links":{"resolver":"https://pith.science/pith/IGWFZH22UR6ZZ63OPDC4SVBPKR","bundle":"https://pith.science/pith/IGWFZH22UR6ZZ63OPDC4SVBPKR/bundle.json","state":"https://pith.science/pith/IGWFZH22UR6ZZ63OPDC4SVBPKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGWFZH22UR6ZZ63OPDC4SVBPKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:IGWFZH22UR6ZZ63OPDC4SVBPKR","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":"dd28a83d6dcfe11937ad6230385a1bc67b7e094f798d92eea879e3d66d752451","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-05-18T05:32:19Z","title_canon_sha256":"b50505dd7bb1aa61e61fb5fc73f5e5cac5eb0e83205626f7255f5a4950a9bb34"},"schema_version":"1.0","source":{"id":"2305.10719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.10719","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"arxiv_version","alias_value":"2305.10719v1","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.10719","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"pith_short_12","alias_value":"IGWFZH22UR6Z","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"pith_short_16","alias_value":"IGWFZH22UR6ZZ63O","created_at":"2026-07-05T06:11:25Z"},{"alias_kind":"pith_short_8","alias_value":"IGWFZH22","created_at":"2026-07-05T06:11:25Z"}],"graph_snapshots":[{"event_id":"sha256:6736b12d84c048cef46afcdb87db0ae1540ff4a8676c56b6aa431d8b65601a15","target":"graph","created_at":"2026-07-05T06:11:25Z","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/2305.10719/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $F$ be a number field, $\\pi$ either a unitary cuspidal automorphic representation of $\\mathrm{GL}(2)/F$ or a unitary Eisenstein series, and $\\chi$ a unitary Hecke character of analytic conductor $C(\\chi).$ We develop a regularized relative trace formula to prove a refined hybrid subconvex bound for $L(1/2,\\pi\\times\\chi).$ In particular, we obtain the Burgess subconvex bound \\begin{align*} L(1/2,\\pi\\times\\chi)\\ll_{\\pi,F,\\varepsilon}C(\\chi)^{\\frac{1}{2}-\\frac{1}{8}+\\varepsilon}, \\end{align*} where the implied constant depends on $\\pi,$ $F$ and $\\varepsilon.$","authors_text":"Liyang Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-05-18T05:32:19Z","title":"Relative Trace Formula and Twisted $L$-functions: the Burgess Bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.10719","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:d80bb2ebd59e51403c87e6988f467b0c5893276b3b31c7252cb5d791c513b5f5","target":"record","created_at":"2026-07-05T06:11:25Z","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":"dd28a83d6dcfe11937ad6230385a1bc67b7e094f798d92eea879e3d66d752451","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-05-18T05:32:19Z","title_canon_sha256":"b50505dd7bb1aa61e61fb5fc73f5e5cac5eb0e83205626f7255f5a4950a9bb34"},"schema_version":"1.0","source":{"id":"2305.10719","kind":"arxiv","version":1}},"canonical_sha256":"41ac5c9f5aa47d9cfb6e78c5c9542f5453c86f713127f235f528b9510f8353b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41ac5c9f5aa47d9cfb6e78c5c9542f5453c86f713127f235f528b9510f8353b4","first_computed_at":"2026-07-05T06:11:25.890825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:11:25.890825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tU5XPawU82Pax23nopigXpsAPodxfQp2EV5CXWRp817u+Glo6AU1UXLmoY8o0DHutqDNuiVIYw3S9phZAVh8Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:11:25.891201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.10719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d80bb2ebd59e51403c87e6988f467b0c5893276b3b31c7252cb5d791c513b5f5","sha256:6736b12d84c048cef46afcdb87db0ae1540ff4a8676c56b6aa431d8b65601a15"],"state_sha256":"09f6fd03d63297042659102f4d16305ec8800208db9709b34c89dc799978fd25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvJD5THt6ZItmhX6tumqqIvF5DzYUehCEaJUHjZxXF2wIbD6twytAt5TYfUrwCwkGOSNDZs+GC6D3rSZv/o1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T07:23:36.782522Z","bundle_sha256":"f492188b9333c64e71c5cce7e1f9dd827b1caa736305ede3bb9876b47b449204"}}