{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4G427GKVZQ47WCTYHUWSANMJEV","short_pith_number":"pith:4G427GKV","canonical_record":{"source":{"id":"1011.1961","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-09T02:36:29Z","cross_cats_sorted":[],"title_canon_sha256":"8a6dcc0a9b56517bf7dee4715580cb6b6e1d664b368371d285c50b7938c3c726","abstract_canon_sha256":"2511b69d73266afac6cb3f64be03835172f87adb14b55c9c87455d083636e1af"},"schema_version":"1.0"},"canonical_sha256":"e1b9af9955cc39fb0a783d2d20358925611ae95878cadd863589bd046cd712ec","source":{"kind":"arxiv","id":"1011.1961","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1961","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1961v2","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1961","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"4G427GKVZQ47","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4G427GKVZQ47WCTY","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4G427GKV","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4G427GKVZQ47WCTYHUWSANMJEV","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1961","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-09T02:36:29Z","cross_cats_sorted":[],"title_canon_sha256":"8a6dcc0a9b56517bf7dee4715580cb6b6e1d664b368371d285c50b7938c3c726","abstract_canon_sha256":"2511b69d73266afac6cb3f64be03835172f87adb14b55c9c87455d083636e1af"},"schema_version":"1.0"},"canonical_sha256":"e1b9af9955cc39fb0a783d2d20358925611ae95878cadd863589bd046cd712ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:01.524762Z","signature_b64":"vfewnv8iAsvkNrXhohzEnyd/2QC6XJGAMOWbsRUDYO0QoJopMfa+EuisOu5t8legVwpPy1ycWfpNiWJjxFzhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1b9af9955cc39fb0a783d2d20358925611ae95878cadd863589bd046cd712ec","last_reissued_at":"2026-05-18T02:58:01.524061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:01.524061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1961","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":"2026-05-18T02:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y4iaehlE14Dj5BulhhiIWoqJ1vrxM/x7dNF77y9Pq8N9l/+M8mvwTC1VBxoeTpF0RDeF2bIQ/rM+IOPixw39Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:01:41.539187Z"},"content_sha256":"89656e8159b2871f4043271ebe0b4bb7b89d541bea166a598804c453468f7731","schema_version":"1.0","event_id":"sha256:89656e8159b2871f4043271ebe0b4bb7b89d541bea166a598804c453468f7731"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4G427GKVZQ47WCTYHUWSANMJEV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A hybrid asymptotic formula for the second moment of Rankin-Selberg L-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gergely Harcos, Valentin Blomer","submitted_at":"2010-11-09T02:36:29Z","abstract_excerpt":"We consider the Rankin-Selberg L-functions associated with a fixed modular form of full level and holomorphic cuspidal newforms of large even weight, fixed level and fixed primitive nebentypus. We compute the second moment of this family in fairly general ranges, and obtain an asymptotic formula with a power saving error term. A special case treats the fourth moment of L-functions associated with holomorphic cusp forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1961","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":"2026-05-18T02:58:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TKdJfttbXIGLxec3glIdQh64IgDv116FGFX1GELKTHDvkbXT87mgrxZ/C3B4lq4BL/nUlePYEy3pFz1QcLEuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:01:41.539790Z"},"content_sha256":"db4cfd2cdf80b1b5ac6463057c2a783b929d7810c8d6870a92fbf40c7fb54b65","schema_version":"1.0","event_id":"sha256:db4cfd2cdf80b1b5ac6463057c2a783b929d7810c8d6870a92fbf40c7fb54b65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4G427GKVZQ47WCTYHUWSANMJEV/bundle.json","state_url":"https://pith.science/pith/4G427GKVZQ47WCTYHUWSANMJEV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4G427GKVZQ47WCTYHUWSANMJEV/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":"2026-05-26T13:01:41Z","links":{"resolver":"https://pith.science/pith/4G427GKVZQ47WCTYHUWSANMJEV","bundle":"https://pith.science/pith/4G427GKVZQ47WCTYHUWSANMJEV/bundle.json","state":"https://pith.science/pith/4G427GKVZQ47WCTYHUWSANMJEV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4G427GKVZQ47WCTYHUWSANMJEV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4G427GKVZQ47WCTYHUWSANMJEV","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":"2511b69d73266afac6cb3f64be03835172f87adb14b55c9c87455d083636e1af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-09T02:36:29Z","title_canon_sha256":"8a6dcc0a9b56517bf7dee4715580cb6b6e1d664b368371d285c50b7938c3c726"},"schema_version":"1.0","source":{"id":"1011.1961","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1961","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1961v2","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1961","created_at":"2026-05-18T02:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"4G427GKVZQ47","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4G427GKVZQ47WCTY","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4G427GKV","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:db4cfd2cdf80b1b5ac6463057c2a783b929d7810c8d6870a92fbf40c7fb54b65","target":"graph","created_at":"2026-05-18T02:58:01Z","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":"We consider the Rankin-Selberg L-functions associated with a fixed modular form of full level and holomorphic cuspidal newforms of large even weight, fixed level and fixed primitive nebentypus. We compute the second moment of this family in fairly general ranges, and obtain an asymptotic formula with a power saving error term. A special case treats the fourth moment of L-functions associated with holomorphic cusp forms.","authors_text":"Gergely Harcos, Valentin Blomer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-09T02:36:29Z","title":"A hybrid asymptotic formula for the second moment of Rankin-Selberg L-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1961","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":"sha256:89656e8159b2871f4043271ebe0b4bb7b89d541bea166a598804c453468f7731","target":"record","created_at":"2026-05-18T02:58:01Z","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":"2511b69d73266afac6cb3f64be03835172f87adb14b55c9c87455d083636e1af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-09T02:36:29Z","title_canon_sha256":"8a6dcc0a9b56517bf7dee4715580cb6b6e1d664b368371d285c50b7938c3c726"},"schema_version":"1.0","source":{"id":"1011.1961","kind":"arxiv","version":2}},"canonical_sha256":"e1b9af9955cc39fb0a783d2d20358925611ae95878cadd863589bd046cd712ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1b9af9955cc39fb0a783d2d20358925611ae95878cadd863589bd046cd712ec","first_computed_at":"2026-05-18T02:58:01.524061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:01.524061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vfewnv8iAsvkNrXhohzEnyd/2QC6XJGAMOWbsRUDYO0QoJopMfa+EuisOu5t8legVwpPy1ycWfpNiWJjxFzhCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:01.524762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1961","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89656e8159b2871f4043271ebe0b4bb7b89d541bea166a598804c453468f7731","sha256:db4cfd2cdf80b1b5ac6463057c2a783b929d7810c8d6870a92fbf40c7fb54b65"],"state_sha256":"e6da4dc2f4b5c0061db03f7d11f62d705324a9b98188f84382ee1628cc1940cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DLBX3t8BeRoj2obVGvLkt66L4o13EXX7Z4HUwQ9UEVTm3ifLH9BvhXZLh7AQsKmyccx4mHj5+rQNv67lk6bJBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:01:41.543304Z","bundle_sha256":"b6de6dd1230bdd6ccd46aa4cabb0e8caa4d719d5ef058beb5f641616486524ec"}}