{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:7CVLKKTDBJBTW42SHOSHHOBAZ3","short_pith_number":"pith:7CVLKKTD","canonical_record":{"source":{"id":"0903.3591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-20T19:12:49Z","cross_cats_sorted":[],"title_canon_sha256":"9c49870b62371a6a5e87896dde4c2b5f99b5ecb3973913548172e8f1cb6368e2","abstract_canon_sha256":"fe5d79a3ca62435c4a64abb4e38cbffe65000991441936ed3dcf6b4406649a4e"},"schema_version":"1.0"},"canonical_sha256":"f8aab52a630a433b73523ba473b820cec89e3cc6e227a6861f292b1521bd313e","source":{"kind":"arxiv","id":"0903.3591","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3591","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3591v2","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3591","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"7CVLKKTDBJBT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7CVLKKTDBJBTW42S","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7CVLKKTD","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:7CVLKKTDBJBTW42SHOSHHOBAZ3","target":"record","payload":{"canonical_record":{"source":{"id":"0903.3591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-20T19:12:49Z","cross_cats_sorted":[],"title_canon_sha256":"9c49870b62371a6a5e87896dde4c2b5f99b5ecb3973913548172e8f1cb6368e2","abstract_canon_sha256":"fe5d79a3ca62435c4a64abb4e38cbffe65000991441936ed3dcf6b4406649a4e"},"schema_version":"1.0"},"canonical_sha256":"f8aab52a630a433b73523ba473b820cec89e3cc6e227a6861f292b1521bd313e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:52.936064Z","signature_b64":"mTmhaiDr7roW2xh8y7dWyWgnhiZs/KxLC5QC/gt4zwbx/DkRXQzr+a/zD7MDiQZOdqSJ7FYGzn/uAzec09ZSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8aab52a630a433b73523ba473b820cec89e3cc6e227a6861f292b1521bd313e","last_reissued_at":"2026-05-18T02:35:52.935641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:52.935641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.3591","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":"2026-05-18T02:35:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eNcYwfroSyhBUUD3AZtAVmSSsBJjs0JNAgzHVOjKavEQefUWY97Gt2sMrDCnzH/P2TVFV7NDZeT2/wJSs8GgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:47:04.604471Z"},"content_sha256":"de4b0809de7bfacf10ba0fd320a39eb7a583ae1a438bb276002d77a5a9e8652e","schema_version":"1.0","event_id":"sha256:de4b0809de7bfacf10ba0fd320a39eb7a583ae1a438bb276002d77a5a9e8652e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:7CVLKKTDBJBTW42SHOSHHOBAZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The subconvexity problem for $\\GL_{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Akshay Venkatesh, Philippe Michel","submitted_at":"2009-03-20T19:12:49Z","abstract_excerpt":"Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of $\\GL_{1}$ and $\\GL_{2}$ automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino--Ikeda."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3591","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":"2026-05-18T02:35:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RCkaxNe1xTTiQb9bohcmSqHAh4z7+hVMXU68dVFc8IivvoYvMz6+Nsp8ylYZ4n/3V8XMuHcpfScDgfhAH7r4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:47:04.604828Z"},"content_sha256":"7c3c4b96e6817763c1ae7127484b767fcffea6e7a7f725b71c661c71a4e628e7","schema_version":"1.0","event_id":"sha256:7c3c4b96e6817763c1ae7127484b767fcffea6e7a7f725b71c661c71a4e628e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7CVLKKTDBJBTW42SHOSHHOBAZ3/bundle.json","state_url":"https://pith.science/pith/7CVLKKTDBJBTW42SHOSHHOBAZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7CVLKKTDBJBTW42SHOSHHOBAZ3/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":"2026-06-03T17:47:04Z","links":{"resolver":"https://pith.science/pith/7CVLKKTDBJBTW42SHOSHHOBAZ3","bundle":"https://pith.science/pith/7CVLKKTDBJBTW42SHOSHHOBAZ3/bundle.json","state":"https://pith.science/pith/7CVLKKTDBJBTW42SHOSHHOBAZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7CVLKKTDBJBTW42SHOSHHOBAZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7CVLKKTDBJBTW42SHOSHHOBAZ3","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":"fe5d79a3ca62435c4a64abb4e38cbffe65000991441936ed3dcf6b4406649a4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-20T19:12:49Z","title_canon_sha256":"9c49870b62371a6a5e87896dde4c2b5f99b5ecb3973913548172e8f1cb6368e2"},"schema_version":"1.0","source":{"id":"0903.3591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3591","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3591v2","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3591","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"7CVLKKTDBJBT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7CVLKKTDBJBTW42S","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7CVLKKTD","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:7c3c4b96e6817763c1ae7127484b767fcffea6e7a7f725b71c661c71a4e628e7","target":"graph","created_at":"2026-05-18T02:35:52Z","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":"Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of $\\GL_{1}$ and $\\GL_{2}$ automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino--Ikeda.","authors_text":"Akshay Venkatesh, Philippe Michel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-20T19:12:49Z","title":"The subconvexity problem for $\\GL_{2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3591","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:de4b0809de7bfacf10ba0fd320a39eb7a583ae1a438bb276002d77a5a9e8652e","target":"record","created_at":"2026-05-18T02:35:52Z","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":"fe5d79a3ca62435c4a64abb4e38cbffe65000991441936ed3dcf6b4406649a4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-20T19:12:49Z","title_canon_sha256":"9c49870b62371a6a5e87896dde4c2b5f99b5ecb3973913548172e8f1cb6368e2"},"schema_version":"1.0","source":{"id":"0903.3591","kind":"arxiv","version":2}},"canonical_sha256":"f8aab52a630a433b73523ba473b820cec89e3cc6e227a6861f292b1521bd313e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8aab52a630a433b73523ba473b820cec89e3cc6e227a6861f292b1521bd313e","first_computed_at":"2026-05-18T02:35:52.935641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:52.935641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mTmhaiDr7roW2xh8y7dWyWgnhiZs/KxLC5QC/gt4zwbx/DkRXQzr+a/zD7MDiQZOdqSJ7FYGzn/uAzec09ZSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:52.936064Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de4b0809de7bfacf10ba0fd320a39eb7a583ae1a438bb276002d77a5a9e8652e","sha256:7c3c4b96e6817763c1ae7127484b767fcffea6e7a7f725b71c661c71a4e628e7"],"state_sha256":"e691679fe97785672cfe6cffcb046a3872621ec408f1b9c78b0ed38c3929500a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f8n87ZrqoXkaVLSdaAqrYlLMEl7duWS/Wkv+80eet9Jqgm0OrdPX+ZYYicVOoNf1cLOBakN1f7Buw7aKCWOtDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:47:04.606779Z","bundle_sha256":"2a3f978572ed7e51689547c17e242172863324fbcfdc986c3c6d5e59d2c5f1bc"}}