{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KNJNSXBC5IXGJ7ZQGRFYDCLWL4","short_pith_number":"pith:KNJNSXBC","canonical_record":{"source":{"id":"1205.1209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-06T12:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"84c7cdfae3d1428491533ae120e8419f5a6b52811351e5af57811de7207b4527","abstract_canon_sha256":"21b2111d6354b0b8f1ef9f911cb79eb71145b5ee7394e723945098a0e551941c"},"schema_version":"1.0"},"canonical_sha256":"5352d95c22ea2e64ff30344b8189765f2f53ad6c1879884e27584ff717fda3d0","source":{"kind":"arxiv","id":"1205.1209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1209","created_at":"2026-05-18T03:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1209v1","created_at":"2026-05-18T03:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1209","created_at":"2026-05-18T03:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"KNJNSXBC5IXG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KNJNSXBC5IXGJ7ZQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KNJNSXBC","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KNJNSXBC5IXGJ7ZQGRFYDCLWL4","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-06T12:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"84c7cdfae3d1428491533ae120e8419f5a6b52811351e5af57811de7207b4527","abstract_canon_sha256":"21b2111d6354b0b8f1ef9f911cb79eb71145b5ee7394e723945098a0e551941c"},"schema_version":"1.0"},"canonical_sha256":"5352d95c22ea2e64ff30344b8189765f2f53ad6c1879884e27584ff717fda3d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:08.616976Z","signature_b64":"7jLkeAfHc+DvtU12evffSOCT1XdkVxp10DNCzzeTfuT2lU3QEPpgsBKXY5ECfUz+QbdZ0TsT6YPbfavjii/nDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5352d95c22ea2e64ff30344b8189765f2f53ad6c1879884e27584ff717fda3d0","last_reissued_at":"2026-05-18T03:37:08.616113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:08.616113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1209","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":"2026-05-18T03:37:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jo0Bo6x5fJB3QKJYB6aqgntSVVAPuLWgbKWehRQ7avogpB3fDyBRVmb96EK/FZqwxDfwfx9CMx41bkHkGPO0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:27:40.816541Z"},"content_sha256":"f453eec2c5be05ba590a627e0c5f2eb1d68e710121df67425482d51033a76144","schema_version":"1.0","event_id":"sha256:f453eec2c5be05ba590a627e0c5f2eb1d68e710121df67425482d51033a76144"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KNJNSXBC5IXGJ7ZQGRFYDCLWL4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds for twisted symmetric square $L$-functions - III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ritabrata Munshi","submitted_at":"2012-05-06T12:00:00Z","abstract_excerpt":"Let $f$ be a newform, and let $\\chi$ be a primitive character of conductor $q^{\\ell}$. Assume that $q$ is an odd prime. In this paper we prove the subconvex bound $$ L(\\t1/2,\\Sym f\\otimes\\chi)\\ll_{f,q,\\varepsilon} q^{3\\ell(1/4-1/36+\\varepsilon)} $$ for any $\\varepsilon>0$. This can be compared with the recently established $t$-aspect subconvexity of the symmetric square $L$-functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1209","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":""},"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":"2026-05-18T03:37:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kYM7H+T8fiR0cojGwIEO48L0CYS0bk4rbfZFe56MewTIebiibRZgn3oRFvRI7jm+O6BTYxEzoNCn95GHi7u4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:27:40.817132Z"},"content_sha256":"a9c6e984c967697abb82b15a2c0614e6d62c29199ecd1cd18d7f347d6b3bd8d1","schema_version":"1.0","event_id":"sha256:a9c6e984c967697abb82b15a2c0614e6d62c29199ecd1cd18d7f347d6b3bd8d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNJNSXBC5IXGJ7ZQGRFYDCLWL4/bundle.json","state_url":"https://pith.science/pith/KNJNSXBC5IXGJ7ZQGRFYDCLWL4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNJNSXBC5IXGJ7ZQGRFYDCLWL4/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":"2026-07-01T22:27:40Z","links":{"resolver":"https://pith.science/pith/KNJNSXBC5IXGJ7ZQGRFYDCLWL4","bundle":"https://pith.science/pith/KNJNSXBC5IXGJ7ZQGRFYDCLWL4/bundle.json","state":"https://pith.science/pith/KNJNSXBC5IXGJ7ZQGRFYDCLWL4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNJNSXBC5IXGJ7ZQGRFYDCLWL4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KNJNSXBC5IXGJ7ZQGRFYDCLWL4","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":"21b2111d6354b0b8f1ef9f911cb79eb71145b5ee7394e723945098a0e551941c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-06T12:00:00Z","title_canon_sha256":"84c7cdfae3d1428491533ae120e8419f5a6b52811351e5af57811de7207b4527"},"schema_version":"1.0","source":{"id":"1205.1209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1209","created_at":"2026-05-18T03:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1209v1","created_at":"2026-05-18T03:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1209","created_at":"2026-05-18T03:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"KNJNSXBC5IXG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KNJNSXBC5IXGJ7ZQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KNJNSXBC","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:a9c6e984c967697abb82b15a2c0614e6d62c29199ecd1cd18d7f347d6b3bd8d1","target":"graph","created_at":"2026-05-18T03:37:08Z","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 $f$ be a newform, and let $\\chi$ be a primitive character of conductor $q^{\\ell}$. Assume that $q$ is an odd prime. In this paper we prove the subconvex bound $$ L(\\t1/2,\\Sym f\\otimes\\chi)\\ll_{f,q,\\varepsilon} q^{3\\ell(1/4-1/36+\\varepsilon)} $$ for any $\\varepsilon>0$. This can be compared with the recently established $t$-aspect subconvexity of the symmetric square $L$-functions.","authors_text":"Ritabrata Munshi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-06T12:00:00Z","title":"Bounds for twisted symmetric square $L$-functions - III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1209","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:f453eec2c5be05ba590a627e0c5f2eb1d68e710121df67425482d51033a76144","target":"record","created_at":"2026-05-18T03:37:08Z","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":"21b2111d6354b0b8f1ef9f911cb79eb71145b5ee7394e723945098a0e551941c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-06T12:00:00Z","title_canon_sha256":"84c7cdfae3d1428491533ae120e8419f5a6b52811351e5af57811de7207b4527"},"schema_version":"1.0","source":{"id":"1205.1209","kind":"arxiv","version":1}},"canonical_sha256":"5352d95c22ea2e64ff30344b8189765f2f53ad6c1879884e27584ff717fda3d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5352d95c22ea2e64ff30344b8189765f2f53ad6c1879884e27584ff717fda3d0","first_computed_at":"2026-05-18T03:37:08.616113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:08.616113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7jLkeAfHc+DvtU12evffSOCT1XdkVxp10DNCzzeTfuT2lU3QEPpgsBKXY5ECfUz+QbdZ0TsT6YPbfavjii/nDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:08.616976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f453eec2c5be05ba590a627e0c5f2eb1d68e710121df67425482d51033a76144","sha256:a9c6e984c967697abb82b15a2c0614e6d62c29199ecd1cd18d7f347d6b3bd8d1"],"state_sha256":"9a3690c858c095f501e38a68eb7509c1f560c3e1fa02c30909854ef584022c96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qLOPv9/k3X0ce+I+Gw2U52WuUjjKQ4KDVyDxn0QzbsP9qj9hi9o4Y90nPvouUhmHCyyBUM4RGiY28jXpuaqHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T22:27:40.820034Z","bundle_sha256":"96a2d25ea9f421edb9672da08ba03f274bb51296ae09e6effa4edc47f7ecd99a"}}