{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4NKIMDM63Q4QIHPF3DCPSM3CVR","short_pith_number":"pith:4NKIMDM6","canonical_record":{"source":{"id":"1812.05203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-13T00:07:12Z","cross_cats_sorted":[],"title_canon_sha256":"c4c5e81a285e273bfb2a6218ff1e0820e010401e704d01f9b7f418b61189374c","abstract_canon_sha256":"0f3e075aac81dc75d028b0abeae0a8f7a22d8b403f0d5c5b31d90817b7a4621f"},"schema_version":"1.0"},"canonical_sha256":"e354860d9edc39041de5d8c4f93362ac730e495db3d8b1efbf367cf76f6ce4cd","source":{"kind":"arxiv","id":"1812.05203","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05203","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05203v1","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05203","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"4NKIMDM63Q4Q","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4NKIMDM63Q4QIHPF","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4NKIMDM6","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4NKIMDM63Q4QIHPF3DCPSM3CVR","target":"record","payload":{"canonical_record":{"source":{"id":"1812.05203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-13T00:07:12Z","cross_cats_sorted":[],"title_canon_sha256":"c4c5e81a285e273bfb2a6218ff1e0820e010401e704d01f9b7f418b61189374c","abstract_canon_sha256":"0f3e075aac81dc75d028b0abeae0a8f7a22d8b403f0d5c5b31d90817b7a4621f"},"schema_version":"1.0"},"canonical_sha256":"e354860d9edc39041de5d8c4f93362ac730e495db3d8b1efbf367cf76f6ce4cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:24.217056Z","signature_b64":"ZnmBNfuD69DzhZpUasiFsvKbOn8tMvV9cw5zlpoX45AfudqvII1JRLaxAoxQtPRQ9vvfmLdf9ItkZeTmSU8QBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e354860d9edc39041de5d8c4f93362ac730e495db3d8b1efbf367cf76f6ce4cd","last_reissued_at":"2026-05-17T23:58:24.216501Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:24.216501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.05203","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":"2026-05-17T23:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2J5yX384zbsBzE59zn5mNC6Yqz0utXpZ+NSgvNMA3uZq+ZnSFKwpNibyRddPpZyDEx2K3Um23jZqy0agVv4xBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:06:39.513733Z"},"content_sha256":"7061e25581ff1556476ccbbe15a68a1180f116898664f905e6e7cd67433f8b93","schema_version":"1.0","event_id":"sha256:7061e25581ff1556476ccbbe15a68a1180f116898664f905e6e7cd67433f8b93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4NKIMDM63Q4QIHPF3DCPSM3CVR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Langlands Program and Ramanujan Conjecture: a survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Luis Alberto Lomel\\'i","submitted_at":"2018-12-13T00:07:12Z","abstract_excerpt":"We present topics in the Langlands Program to graduate students and a wider mathematically mature audience. We study both global and local aspects in characteristic zero as well as characteristic $p$. We look at modern approaches to the generalized Ramanujan conjecture, which is an open problem over number fields, and present known cases over function fields. In particular, we study automorphic $L$-functions via the Langlands-Shahidi method. Hopefully, our approach to the Langlands Program can help guide the interested reader into an exciting field of mathematical research."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05203","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":"2026-05-17T23:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8oNyfzdX+GmiX1ULw24SepYugjLzp4+o/dPLIcrN9KpMr4VriYxVVvPO1a/j6Wq9MVHxsSYIbpk5iL020s1VDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:06:39.514094Z"},"content_sha256":"de70b55b22f64b42a9c23cbe8fb53818719b6268164e93a9a79389c7983bb8e7","schema_version":"1.0","event_id":"sha256:de70b55b22f64b42a9c23cbe8fb53818719b6268164e93a9a79389c7983bb8e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NKIMDM63Q4QIHPF3DCPSM3CVR/bundle.json","state_url":"https://pith.science/pith/4NKIMDM63Q4QIHPF3DCPSM3CVR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NKIMDM63Q4QIHPF3DCPSM3CVR/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":"2026-06-11T21:06:39Z","links":{"resolver":"https://pith.science/pith/4NKIMDM63Q4QIHPF3DCPSM3CVR","bundle":"https://pith.science/pith/4NKIMDM63Q4QIHPF3DCPSM3CVR/bundle.json","state":"https://pith.science/pith/4NKIMDM63Q4QIHPF3DCPSM3CVR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NKIMDM63Q4QIHPF3DCPSM3CVR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4NKIMDM63Q4QIHPF3DCPSM3CVR","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":"0f3e075aac81dc75d028b0abeae0a8f7a22d8b403f0d5c5b31d90817b7a4621f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-13T00:07:12Z","title_canon_sha256":"c4c5e81a285e273bfb2a6218ff1e0820e010401e704d01f9b7f418b61189374c"},"schema_version":"1.0","source":{"id":"1812.05203","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05203","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05203v1","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05203","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"4NKIMDM63Q4Q","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4NKIMDM63Q4QIHPF","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4NKIMDM6","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:de70b55b22f64b42a9c23cbe8fb53818719b6268164e93a9a79389c7983bb8e7","target":"graph","created_at":"2026-05-17T23:58:24Z","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 present topics in the Langlands Program to graduate students and a wider mathematically mature audience. We study both global and local aspects in characteristic zero as well as characteristic $p$. We look at modern approaches to the generalized Ramanujan conjecture, which is an open problem over number fields, and present known cases over function fields. In particular, we study automorphic $L$-functions via the Langlands-Shahidi method. Hopefully, our approach to the Langlands Program can help guide the interested reader into an exciting field of mathematical research.","authors_text":"Luis Alberto Lomel\\'i","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-13T00:07:12Z","title":"Langlands Program and Ramanujan Conjecture: a survey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05203","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":"sha256:7061e25581ff1556476ccbbe15a68a1180f116898664f905e6e7cd67433f8b93","target":"record","created_at":"2026-05-17T23:58:24Z","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":"0f3e075aac81dc75d028b0abeae0a8f7a22d8b403f0d5c5b31d90817b7a4621f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-13T00:07:12Z","title_canon_sha256":"c4c5e81a285e273bfb2a6218ff1e0820e010401e704d01f9b7f418b61189374c"},"schema_version":"1.0","source":{"id":"1812.05203","kind":"arxiv","version":1}},"canonical_sha256":"e354860d9edc39041de5d8c4f93362ac730e495db3d8b1efbf367cf76f6ce4cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e354860d9edc39041de5d8c4f93362ac730e495db3d8b1efbf367cf76f6ce4cd","first_computed_at":"2026-05-17T23:58:24.216501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:24.216501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZnmBNfuD69DzhZpUasiFsvKbOn8tMvV9cw5zlpoX45AfudqvII1JRLaxAoxQtPRQ9vvfmLdf9ItkZeTmSU8QBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:24.217056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.05203","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7061e25581ff1556476ccbbe15a68a1180f116898664f905e6e7cd67433f8b93","sha256:de70b55b22f64b42a9c23cbe8fb53818719b6268164e93a9a79389c7983bb8e7"],"state_sha256":"6ba7c6fa3f01991c4eaf19893a2d9584d4d18af5e737e67ed33ec58e56193ff3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"heWvSh15qGBi3L/q23yxN3pV+Ad7A48LOslA+p5ZAh/o11iqYcARNYogWieQbvH1OnHUmtIhDmfPRDudQS9YCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:06:39.516417Z","bundle_sha256":"d6415084a038e1d32d0954b5287b154d18edeee6458086a59edf01d3f732a803"}}