{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MM5CVMWIWK2VKNGHZ6PMRPWZS6","short_pith_number":"pith:MM5CVMWI","canonical_record":{"source":{"id":"1905.07001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-16T19:14:14Z","cross_cats_sorted":[],"title_canon_sha256":"a9dadbea2d9698a003572a68ad49fcb39ce280657497bf2e59d41b571ab0d344","abstract_canon_sha256":"b6801088e2fe9755d82f16527c9a0917f767c1f37cb0843fa599c301514b00a6"},"schema_version":"1.0"},"canonical_sha256":"633a2ab2c8b2b55534c7cf9ec8bed9979437ca0bb501f9018049a7e94a1b522b","source":{"kind":"arxiv","id":"1905.07001","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07001","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07001v2","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07001","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"pith_short_12","alias_value":"MM5CVMWIWK2V","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"pith_short_16","alias_value":"MM5CVMWIWK2VKNGH","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"pith_short_8","alias_value":"MM5CVMWI","created_at":"2026-07-05T00:51:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MM5CVMWIWK2VKNGHZ6PMRPWZS6","target":"record","payload":{"canonical_record":{"source":{"id":"1905.07001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-16T19:14:14Z","cross_cats_sorted":[],"title_canon_sha256":"a9dadbea2d9698a003572a68ad49fcb39ce280657497bf2e59d41b571ab0d344","abstract_canon_sha256":"b6801088e2fe9755d82f16527c9a0917f767c1f37cb0843fa599c301514b00a6"},"schema_version":"1.0"},"canonical_sha256":"633a2ab2c8b2b55534c7cf9ec8bed9979437ca0bb501f9018049a7e94a1b522b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:51:19.800151Z","signature_b64":"fEcvZOyLekweehwbbYSNG8iP/fDPeyguS6OjiYjdku9hQvbAGq7FMz4H+4jeTDWg4BjM4mMiUybw56rviBbFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"633a2ab2c8b2b55534c7cf9ec8bed9979437ca0bb501f9018049a7e94a1b522b","last_reissued_at":"2026-07-05T00:51:19.799599Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:51:19.799599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.07001","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":"2026-07-05T00:51:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Sn17rpRIQIUIgkTtDUbT/hAQ0CRXDoifVgU8yb7spvRg0zqKRMwSOpBEBgFwflwXXmerz/ucBt5IE0tm3O7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:36:24.454226Z"},"content_sha256":"e206aea400da5deb225e4bb29396c1b2983b269c15e933607b11c3f443276ccd","schema_version":"1.0","event_id":"sha256:e206aea400da5deb225e4bb29396c1b2983b269c15e933607b11c3f443276ccd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MM5CVMWIWK2VKNGHZ6PMRPWZS6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equidistribution of Gross points over rational function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ahmad El-Guindy, Guchao Zeng, Matthew Papanikolas, Riad Masri","submitted_at":"2019-05-16T19:14:14Z","abstract_excerpt":"In this paper we prove a sparse equidistribution theorem for Gross points over the rational function field $\\mathbb{F}_q(t)$. We apply this result to study the reduction map from CM Drinfeld modules to supersingular Drinfeld modules. Our proofs rely crucially on a period formula due to M. Papikian and F.-T. Wei/J. Yu, and a Lindel\\\"of-type bound for central values of Rankin-Selberg $L$-functions associated to twists of automorphic forms of Drinfeld-type by ideal class group characters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07001","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.07001/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":"2026-07-05T00:51:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"whagBei0FnzqcoR7eh+qKQLXubBxdtBm/D7C7dmkBHyV6OsqL+c1yYAC3EFpEPmuPs9jkxPfeSm3rUXvJ4VOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T07:36:24.454782Z"},"content_sha256":"f8bbfd53047f2e017d159735ec2179b6b2e5c3980adc5a42737b679d0d5c30aa","schema_version":"1.0","event_id":"sha256:f8bbfd53047f2e017d159735ec2179b6b2e5c3980adc5a42737b679d0d5c30aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MM5CVMWIWK2VKNGHZ6PMRPWZS6/bundle.json","state_url":"https://pith.science/pith/MM5CVMWIWK2VKNGHZ6PMRPWZS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MM5CVMWIWK2VKNGHZ6PMRPWZS6/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":"2026-08-12T07:36:24Z","links":{"resolver":"https://pith.science/pith/MM5CVMWIWK2VKNGHZ6PMRPWZS6","bundle":"https://pith.science/pith/MM5CVMWIWK2VKNGHZ6PMRPWZS6/bundle.json","state":"https://pith.science/pith/MM5CVMWIWK2VKNGHZ6PMRPWZS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MM5CVMWIWK2VKNGHZ6PMRPWZS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MM5CVMWIWK2VKNGHZ6PMRPWZS6","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":"b6801088e2fe9755d82f16527c9a0917f767c1f37cb0843fa599c301514b00a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-16T19:14:14Z","title_canon_sha256":"a9dadbea2d9698a003572a68ad49fcb39ce280657497bf2e59d41b571ab0d344"},"schema_version":"1.0","source":{"id":"1905.07001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07001","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07001v2","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07001","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"pith_short_12","alias_value":"MM5CVMWIWK2V","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"pith_short_16","alias_value":"MM5CVMWIWK2VKNGH","created_at":"2026-07-05T00:51:19Z"},{"alias_kind":"pith_short_8","alias_value":"MM5CVMWI","created_at":"2026-07-05T00:51:19Z"}],"graph_snapshots":[{"event_id":"sha256:f8bbfd53047f2e017d159735ec2179b6b2e5c3980adc5a42737b679d0d5c30aa","target":"graph","created_at":"2026-07-05T00:51:19Z","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/1905.07001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we prove a sparse equidistribution theorem for Gross points over the rational function field $\\mathbb{F}_q(t)$. We apply this result to study the reduction map from CM Drinfeld modules to supersingular Drinfeld modules. Our proofs rely crucially on a period formula due to M. Papikian and F.-T. Wei/J. Yu, and a Lindel\\\"of-type bound for central values of Rankin-Selberg $L$-functions associated to twists of automorphic forms of Drinfeld-type by ideal class group characters.","authors_text":"Ahmad El-Guindy, Guchao Zeng, Matthew Papanikolas, Riad Masri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-16T19:14:14Z","title":"Equidistribution of Gross points over rational function fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07001","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:e206aea400da5deb225e4bb29396c1b2983b269c15e933607b11c3f443276ccd","target":"record","created_at":"2026-07-05T00:51:19Z","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":"b6801088e2fe9755d82f16527c9a0917f767c1f37cb0843fa599c301514b00a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-05-16T19:14:14Z","title_canon_sha256":"a9dadbea2d9698a003572a68ad49fcb39ce280657497bf2e59d41b571ab0d344"},"schema_version":"1.0","source":{"id":"1905.07001","kind":"arxiv","version":2}},"canonical_sha256":"633a2ab2c8b2b55534c7cf9ec8bed9979437ca0bb501f9018049a7e94a1b522b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"633a2ab2c8b2b55534c7cf9ec8bed9979437ca0bb501f9018049a7e94a1b522b","first_computed_at":"2026-07-05T00:51:19.799599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:51:19.799599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fEcvZOyLekweehwbbYSNG8iP/fDPeyguS6OjiYjdku9hQvbAGq7FMz4H+4jeTDWg4BjM4mMiUybw56rviBbFAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:51:19.800151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e206aea400da5deb225e4bb29396c1b2983b269c15e933607b11c3f443276ccd","sha256:f8bbfd53047f2e017d159735ec2179b6b2e5c3980adc5a42737b679d0d5c30aa"],"state_sha256":"260bef738c76fa7d801de97748f9672ed8524f3221ca5984c84f43ff4d78ec6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nzj5FNmwpsSc7Y1U02KVf8xksxcKKOLz97GfD7SFuW9ySmGIpQAtpKRXDozx07QsLrCLA3rk6l0QXY3lznTOCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T07:36:24.460380Z","bundle_sha256":"0fd8bda3644e003f7485c6c9c3bf3e339df4139c271da1f1a2ed08e62864a14d"}}