{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:N5T3CLRRT2WPTFFBVAN2UVZKTT","short_pith_number":"pith:N5T3CLRR","canonical_record":{"source":{"id":"1804.06402","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-17T17:59:02Z","cross_cats_sorted":[],"title_canon_sha256":"aeb39621e802d1f23f5865af8f8eadd46b67f6bfcde4947b46f56fb3c5d03ad2","abstract_canon_sha256":"3894fc867e9027fbc25625b82b3049e03c4c6084f4073f6eaaffcdf8b3f7bb70"},"schema_version":"1.0"},"canonical_sha256":"6f67b12e319eacf994a1a81baa572a9ccffc26a6670dc0dbc4e85c49d40cfa26","source":{"kind":"arxiv","id":"1804.06402","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06402","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06402v3","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06402","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"N5T3CLRRT2WP","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"pith_short_16","alias_value":"N5T3CLRRT2WPTFFB","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"pith_short_8","alias_value":"N5T3CLRR","created_at":"2026-07-05T04:22:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:N5T3CLRRT2WPTFFBVAN2UVZKTT","target":"record","payload":{"canonical_record":{"source":{"id":"1804.06402","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-17T17:59:02Z","cross_cats_sorted":[],"title_canon_sha256":"aeb39621e802d1f23f5865af8f8eadd46b67f6bfcde4947b46f56fb3c5d03ad2","abstract_canon_sha256":"3894fc867e9027fbc25625b82b3049e03c4c6084f4073f6eaaffcdf8b3f7bb70"},"schema_version":"1.0"},"canonical_sha256":"6f67b12e319eacf994a1a81baa572a9ccffc26a6670dc0dbc4e85c49d40cfa26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:22:48.286811Z","signature_b64":"ChfaU36+Su7vMthQSHcxO23WdRg9mNJCpBlLz6S3P9v8kjF6+rX+o2edIefGWEiVq/wcsfQBokheJVsBANWXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f67b12e319eacf994a1a81baa572a9ccffc26a6670dc0dbc4e85c49d40cfa26","last_reissued_at":"2026-07-05T04:22:48.286341Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:22:48.286341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.06402","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fSlodyxU5EVTnv8aMGiDZ7nyJJ4mFQrg6i7nLOSnxXm1+fVFs+yPn0pxS+/kVGD9bi+CaYQUnb4aSwBEhsuLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:02:14.181550Z"},"content_sha256":"b8e4d231524c9ddee905f52d7465ed042b75768eeb1a5dfd7a5aa560371954c2","schema_version":"1.0","event_id":"sha256:b8e4d231524c9ddee905f52d7465ed042b75768eeb1a5dfd7a5aa560371954c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:N5T3CLRRT2WPTFFBVAN2UVZKTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeros of Rankin-Selberg $L$-functions at the edge of the critical strip","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Asif Zaman, Farrell Brumley, Jesse Thorner","submitted_at":"2018-04-17T17:59:02Z","abstract_excerpt":"Let $\\pi$ and $\\pi_0$ be unitary cuspidal automorphic representations. We prove log-free zero density estimates for Rankin-Selberg $L$-functions of the form $L(s,\\pi\\times\\pi_0)$, where $\\pi$ varies in a given family and $\\pi_0$ is fixed. These estimates are unconditional in many cases of interest; they hold in full generality assuming an average form of the generalized Ramanujan conjecture. We consider applications of these estimates related to mass equidistribution for Hecke-Maass forms, the rarity of Landau-Siegel zeros of Rankin-Selberg $L$-functions, the Chebotarev density theorem, and $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06402","kind":"arxiv","version":3},"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/1804.06402/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":"2026-07-05T04:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KrL5lH8AWfFyjpikPWuwtLNvDWm5EttfQ0/HF5ieHJIWkJa8uRi+IXnAzdKLf7+UQGw4w5fGdyM1ekvyx5QgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:02:14.182053Z"},"content_sha256":"e201d053eb0b4ca74cb03879b49bd0843dba7d267f901b23a8a409c4ffc094cc","schema_version":"1.0","event_id":"sha256:e201d053eb0b4ca74cb03879b49bd0843dba7d267f901b23a8a409c4ffc094cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N5T3CLRRT2WPTFFBVAN2UVZKTT/bundle.json","state_url":"https://pith.science/pith/N5T3CLRRT2WPTFFBVAN2UVZKTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N5T3CLRRT2WPTFFBVAN2UVZKTT/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":"2026-08-16T15:02:14Z","links":{"resolver":"https://pith.science/pith/N5T3CLRRT2WPTFFBVAN2UVZKTT","bundle":"https://pith.science/pith/N5T3CLRRT2WPTFFBVAN2UVZKTT/bundle.json","state":"https://pith.science/pith/N5T3CLRRT2WPTFFBVAN2UVZKTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N5T3CLRRT2WPTFFBVAN2UVZKTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:N5T3CLRRT2WPTFFBVAN2UVZKTT","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":"3894fc867e9027fbc25625b82b3049e03c4c6084f4073f6eaaffcdf8b3f7bb70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-17T17:59:02Z","title_canon_sha256":"aeb39621e802d1f23f5865af8f8eadd46b67f6bfcde4947b46f56fb3c5d03ad2"},"schema_version":"1.0","source":{"id":"1804.06402","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06402","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06402v3","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06402","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"N5T3CLRRT2WP","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"pith_short_16","alias_value":"N5T3CLRRT2WPTFFB","created_at":"2026-07-05T04:22:48Z"},{"alias_kind":"pith_short_8","alias_value":"N5T3CLRR","created_at":"2026-07-05T04:22:48Z"}],"graph_snapshots":[{"event_id":"sha256:e201d053eb0b4ca74cb03879b49bd0843dba7d267f901b23a8a409c4ffc094cc","target":"graph","created_at":"2026-07-05T04:22:48Z","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/1804.06402/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\pi$ and $\\pi_0$ be unitary cuspidal automorphic representations. We prove log-free zero density estimates for Rankin-Selberg $L$-functions of the form $L(s,\\pi\\times\\pi_0)$, where $\\pi$ varies in a given family and $\\pi_0$ is fixed. These estimates are unconditional in many cases of interest; they hold in full generality assuming an average form of the generalized Ramanujan conjecture. We consider applications of these estimates related to mass equidistribution for Hecke-Maass forms, the rarity of Landau-Siegel zeros of Rankin-Selberg $L$-functions, the Chebotarev density theorem, and $\\","authors_text":"Asif Zaman, Farrell Brumley, Jesse Thorner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-17T17:59:02Z","title":"Zeros of Rankin-Selberg $L$-functions at the edge of the critical strip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06402","kind":"arxiv","version":3},"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:b8e4d231524c9ddee905f52d7465ed042b75768eeb1a5dfd7a5aa560371954c2","target":"record","created_at":"2026-07-05T04:22:48Z","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":"3894fc867e9027fbc25625b82b3049e03c4c6084f4073f6eaaffcdf8b3f7bb70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-04-17T17:59:02Z","title_canon_sha256":"aeb39621e802d1f23f5865af8f8eadd46b67f6bfcde4947b46f56fb3c5d03ad2"},"schema_version":"1.0","source":{"id":"1804.06402","kind":"arxiv","version":3}},"canonical_sha256":"6f67b12e319eacf994a1a81baa572a9ccffc26a6670dc0dbc4e85c49d40cfa26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f67b12e319eacf994a1a81baa572a9ccffc26a6670dc0dbc4e85c49d40cfa26","first_computed_at":"2026-07-05T04:22:48.286341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:22:48.286341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ChfaU36+Su7vMthQSHcxO23WdRg9mNJCpBlLz6S3P9v8kjF6+rX+o2edIefGWEiVq/wcsfQBokheJVsBANWXDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:22:48.286811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06402","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8e4d231524c9ddee905f52d7465ed042b75768eeb1a5dfd7a5aa560371954c2","sha256:e201d053eb0b4ca74cb03879b49bd0843dba7d267f901b23a8a409c4ffc094cc"],"state_sha256":"b229be87e7cfd3d6775500bc1a5d19011241bb3167b957f865d499270179990d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXk7Ghwv/jYOLMBecXzXTcMSHrCSrT60VtTV+yrR9zh3zpcZBwOAxx9zRngHjyBwrjtQm/XIkmuq9IcYoah5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:02:14.186351Z","bundle_sha256":"3aa1b32f487ed9d8db0d81f66dbd32c5f803c6d0a0cf5affcf267d9f4b379eec"}}