{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:B7YXKZYWAXEBQEENKBMZG7WVFW","short_pith_number":"pith:B7YXKZYW","canonical_record":{"source":{"id":"1202.4068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-18T10:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"49a295671671a9ec2341289cc8b12c959a6aa36a4ab47f0218f9436ce2139680","abstract_canon_sha256":"f30428fa91e7d7975058a565ed7ccca2db590b4719124115a88f3355943c784f"},"schema_version":"1.0"},"canonical_sha256":"0ff175671605c818108d5059937ed52dae44f0757cfaeae4669c1dbfc86f8d02","source":{"kind":"arxiv","id":"1202.4068","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4068","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4068v1","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4068","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"B7YXKZYWAXEB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B7YXKZYWAXEBQEEN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B7YXKZYW","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:B7YXKZYWAXEBQEENKBMZG7WVFW","target":"record","payload":{"canonical_record":{"source":{"id":"1202.4068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-18T10:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"49a295671671a9ec2341289cc8b12c959a6aa36a4ab47f0218f9436ce2139680","abstract_canon_sha256":"f30428fa91e7d7975058a565ed7ccca2db590b4719124115a88f3355943c784f"},"schema_version":"1.0"},"canonical_sha256":"0ff175671605c818108d5059937ed52dae44f0757cfaeae4669c1dbfc86f8d02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:01.444012Z","signature_b64":"xZKMeaMqhb6HmsxtbCxOsA646x0+DKbCFRyKjYEkrJVOEHxMtUXHXgxWRdVBacFc6B2UmjHhZvu4doxlCxNbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ff175671605c818108d5059937ed52dae44f0757cfaeae4669c1dbfc86f8d02","last_reissued_at":"2026-05-18T04:02:01.442841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:01.442841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.4068","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":"2026-05-18T04:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XjxfBOez/BIOcm/5FEMhOOQqGe7QZDFR2XBpC+W4qi9uSeJM1qctv1Y+5KOjkRiPh/Awm32FKoRawfKTjEEgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:16:06.331138Z"},"content_sha256":"ad456f135bee4268cf6b8c5f61bec636c83deb6487e303f9fca7b98b867973f2","schema_version":"1.0","event_id":"sha256:ad456f135bee4268cf6b8c5f61bec636c83deb6487e303f9fca7b98b867973f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:B7YXKZYWAXEBQEENKBMZG7WVFW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The circle method and bounds for $L$-functions - I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ritabrata Munshi","submitted_at":"2012-02-18T10:42:24Z","abstract_excerpt":"Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\\chi$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\\otimes \\chi)$ we establish the hybrid subconvex bound $$ L(1/2+it,f\\otimes\\chi)\\ll (M(3+|t|))^{1/2-1/18+\\varepsilon}, $$ for $t\\in \\mathbb R$. The implied constant depends only on the form $f$ and $\\varepsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4068","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":"2026-05-18T04:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DsiYtNwcunBmH4w+YmFNc4TaQ/Pi5YugCfLPBs/6qIWdg2IVN21UxfjMehCIxnAEllyqhNBN9qivHE3oDZSmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:16:06.331525Z"},"content_sha256":"cd3c732a79e3ad7ef6f489ad7995e77d22974aff7fd5658caffc799688675249","schema_version":"1.0","event_id":"sha256:cd3c732a79e3ad7ef6f489ad7995e77d22974aff7fd5658caffc799688675249"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B7YXKZYWAXEBQEENKBMZG7WVFW/bundle.json","state_url":"https://pith.science/pith/B7YXKZYWAXEBQEENKBMZG7WVFW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B7YXKZYWAXEBQEENKBMZG7WVFW/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":"2026-07-01T23:16:06Z","links":{"resolver":"https://pith.science/pith/B7YXKZYWAXEBQEENKBMZG7WVFW","bundle":"https://pith.science/pith/B7YXKZYWAXEBQEENKBMZG7WVFW/bundle.json","state":"https://pith.science/pith/B7YXKZYWAXEBQEENKBMZG7WVFW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B7YXKZYWAXEBQEENKBMZG7WVFW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B7YXKZYWAXEBQEENKBMZG7WVFW","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":"f30428fa91e7d7975058a565ed7ccca2db590b4719124115a88f3355943c784f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-18T10:42:24Z","title_canon_sha256":"49a295671671a9ec2341289cc8b12c959a6aa36a4ab47f0218f9436ce2139680"},"schema_version":"1.0","source":{"id":"1202.4068","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4068","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4068v1","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4068","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"B7YXKZYWAXEB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B7YXKZYWAXEBQEEN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B7YXKZYW","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:cd3c732a79e3ad7ef6f489ad7995e77d22974aff7fd5658caffc799688675249","target":"graph","created_at":"2026-05-18T04:02:01Z","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 Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\\chi$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\\otimes \\chi)$ we establish the hybrid subconvex bound $$ L(1/2+it,f\\otimes\\chi)\\ll (M(3+|t|))^{1/2-1/18+\\varepsilon}, $$ for $t\\in \\mathbb R$. The implied constant depends only on the form $f$ and $\\varepsilon$.","authors_text":"Ritabrata Munshi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-18T10:42:24Z","title":"The circle method and bounds for $L$-functions - I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4068","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:ad456f135bee4268cf6b8c5f61bec636c83deb6487e303f9fca7b98b867973f2","target":"record","created_at":"2026-05-18T04:02:01Z","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":"f30428fa91e7d7975058a565ed7ccca2db590b4719124115a88f3355943c784f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-02-18T10:42:24Z","title_canon_sha256":"49a295671671a9ec2341289cc8b12c959a6aa36a4ab47f0218f9436ce2139680"},"schema_version":"1.0","source":{"id":"1202.4068","kind":"arxiv","version":1}},"canonical_sha256":"0ff175671605c818108d5059937ed52dae44f0757cfaeae4669c1dbfc86f8d02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ff175671605c818108d5059937ed52dae44f0757cfaeae4669c1dbfc86f8d02","first_computed_at":"2026-05-18T04:02:01.442841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:01.442841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xZKMeaMqhb6HmsxtbCxOsA646x0+DKbCFRyKjYEkrJVOEHxMtUXHXgxWRdVBacFc6B2UmjHhZvu4doxlCxNbAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:01.444012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4068","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad456f135bee4268cf6b8c5f61bec636c83deb6487e303f9fca7b98b867973f2","sha256:cd3c732a79e3ad7ef6f489ad7995e77d22974aff7fd5658caffc799688675249"],"state_sha256":"3b0f0273fa303610c92cf1aa2010db2259855ddb1e83aeaff420a8d090fe9c89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVcLgrvagqK1OkBJL6j7j5YeC9BlSXyxcRIG5r/QOSNo6UjP1gmF+lBFm/Uz5oboLwMuTwR5FkSu4zT9F0WECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T23:16:06.333690Z","bundle_sha256":"f9044b0d8c590d725d18ec26a649ad403324aee7b6da8afd9477f594f50368f8"}}