{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:32KUAUPBBK5EYOS2M76B4W4GVS","short_pith_number":"pith:32KUAUPB","canonical_record":{"source":{"id":"1909.00854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-09-02T20:30:02Z","cross_cats_sorted":[],"title_canon_sha256":"5a93b2b2d7a027926cd81596c3b140467155e56cd11199b93be9f93ee03f89c3","abstract_canon_sha256":"4320e1c3107650ac33f7ba1192832c0a63962b91564b34a08ce05d318b264186"},"schema_version":"1.0"},"canonical_sha256":"de954051e10aba4c3a5a67fc1e5b86aca2a24f911f9f7ac315ce22a57fb0d8df","source":{"kind":"arxiv","id":"1909.00854","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.00854","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"arxiv_version","alias_value":"1909.00854v1","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.00854","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"pith_short_12","alias_value":"32KUAUPBBK5E","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"pith_short_16","alias_value":"32KUAUPBBK5EYOS2","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"pith_short_8","alias_value":"32KUAUPB","created_at":"2026-07-05T00:01:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:32KUAUPBBK5EYOS2M76B4W4GVS","target":"record","payload":{"canonical_record":{"source":{"id":"1909.00854","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-09-02T20:30:02Z","cross_cats_sorted":[],"title_canon_sha256":"5a93b2b2d7a027926cd81596c3b140467155e56cd11199b93be9f93ee03f89c3","abstract_canon_sha256":"4320e1c3107650ac33f7ba1192832c0a63962b91564b34a08ce05d318b264186"},"schema_version":"1.0"},"canonical_sha256":"de954051e10aba4c3a5a67fc1e5b86aca2a24f911f9f7ac315ce22a57fb0d8df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:01:13.371644Z","signature_b64":"qiYW73zL9kBW0dIHU/4le9dR9bgj/IZcnmEXzeo4fydKsiLqOX5ZcVetMrwbMr/DDHTtgOhgYcS3gH+Z63XDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de954051e10aba4c3a5a67fc1e5b86aca2a24f911f9f7ac315ce22a57fb0d8df","last_reissued_at":"2026-07-05T00:01:13.371234Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:01:13.371234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.00854","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":"2026-07-05T00:01:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3lwHm2RouzZ1bgrN/nCbzwTejxZ6sVAYSj4zAqiuC7Wx4J0ZLjuMxI5v6+Q22zAZ1qRPXHb6yoq/GFDuqETnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T08:10:51.159878Z"},"content_sha256":"7a0cb5d5ebb9f04e8236ed5d66a4566d892a00a568421d56d8cc4b2e1f93c9d8","schema_version":"1.0","event_id":"sha256:7a0cb5d5ebb9f04e8236ed5d66a4566d892a00a568421d56d8cc4b2e1f93c9d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:32KUAUPBBK5EYOS2M76B4W4GVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moments of Dirichlet $L$-functions with prime conductors over function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandra Florea, Hung M. Bui","submitted_at":"2019-09-02T20:30:02Z","abstract_excerpt":"We compute the second moment in the family of quadratic Dirichlet $L$-functions with prime conductors over $\\mathbb{F}_q[x]$ when the degree of the discriminant goes to infinity, obtaining one of the lower order terms. We also obtain an asymptotic formula with the leading order term for the mean value of the derivatives of $L$-functions associated to quadratic twists of a fixed elliptic curve over $\\mathbb{F}_q(t)$ by monic irreducible polynomials, which allows us to show that there exists a monic irreducible polynomial such that the analytic rank of the corresponding twisted elliptic curve is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00854","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.00854/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":"2026-07-05T00:01:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HlrQVUTNOQd+KkJYe/gS5Gjf5MJFUNfy/AUdVeSBLUvF//TsM+mBJDvp6/zehwv4qDeRdRFmViVwQjB5BLLRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T08:10:51.160497Z"},"content_sha256":"42edebeeb40f9459b1e0f3dcd287f60c5da1403965df9586bf6cbf8c867e1666","schema_version":"1.0","event_id":"sha256:42edebeeb40f9459b1e0f3dcd287f60c5da1403965df9586bf6cbf8c867e1666"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/32KUAUPBBK5EYOS2M76B4W4GVS/bundle.json","state_url":"https://pith.science/pith/32KUAUPBBK5EYOS2M76B4W4GVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/32KUAUPBBK5EYOS2M76B4W4GVS/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":"2026-08-20T08:10:51Z","links":{"resolver":"https://pith.science/pith/32KUAUPBBK5EYOS2M76B4W4GVS","bundle":"https://pith.science/pith/32KUAUPBBK5EYOS2M76B4W4GVS/bundle.json","state":"https://pith.science/pith/32KUAUPBBK5EYOS2M76B4W4GVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/32KUAUPBBK5EYOS2M76B4W4GVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:32KUAUPBBK5EYOS2M76B4W4GVS","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":"4320e1c3107650ac33f7ba1192832c0a63962b91564b34a08ce05d318b264186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-09-02T20:30:02Z","title_canon_sha256":"5a93b2b2d7a027926cd81596c3b140467155e56cd11199b93be9f93ee03f89c3"},"schema_version":"1.0","source":{"id":"1909.00854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.00854","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"arxiv_version","alias_value":"1909.00854v1","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.00854","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"pith_short_12","alias_value":"32KUAUPBBK5E","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"pith_short_16","alias_value":"32KUAUPBBK5EYOS2","created_at":"2026-07-05T00:01:13Z"},{"alias_kind":"pith_short_8","alias_value":"32KUAUPB","created_at":"2026-07-05T00:01:13Z"}],"graph_snapshots":[{"event_id":"sha256:42edebeeb40f9459b1e0f3dcd287f60c5da1403965df9586bf6cbf8c867e1666","target":"graph","created_at":"2026-07-05T00:01:13Z","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/1909.00854/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compute the second moment in the family of quadratic Dirichlet $L$-functions with prime conductors over $\\mathbb{F}_q[x]$ when the degree of the discriminant goes to infinity, obtaining one of the lower order terms. We also obtain an asymptotic formula with the leading order term for the mean value of the derivatives of $L$-functions associated to quadratic twists of a fixed elliptic curve over $\\mathbb{F}_q(t)$ by monic irreducible polynomials, which allows us to show that there exists a monic irreducible polynomial such that the analytic rank of the corresponding twisted elliptic curve is","authors_text":"Alexandra Florea, Hung M. Bui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-09-02T20:30:02Z","title":"Moments of Dirichlet $L$-functions with prime conductors over function fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00854","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":"sha256:7a0cb5d5ebb9f04e8236ed5d66a4566d892a00a568421d56d8cc4b2e1f93c9d8","target":"record","created_at":"2026-07-05T00:01:13Z","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":"4320e1c3107650ac33f7ba1192832c0a63962b91564b34a08ce05d318b264186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-09-02T20:30:02Z","title_canon_sha256":"5a93b2b2d7a027926cd81596c3b140467155e56cd11199b93be9f93ee03f89c3"},"schema_version":"1.0","source":{"id":"1909.00854","kind":"arxiv","version":1}},"canonical_sha256":"de954051e10aba4c3a5a67fc1e5b86aca2a24f911f9f7ac315ce22a57fb0d8df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de954051e10aba4c3a5a67fc1e5b86aca2a24f911f9f7ac315ce22a57fb0d8df","first_computed_at":"2026-07-05T00:01:13.371234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:01:13.371234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qiYW73zL9kBW0dIHU/4le9dR9bgj/IZcnmEXzeo4fydKsiLqOX5ZcVetMrwbMr/DDHTtgOhgYcS3gH+Z63XDCw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:01:13.371644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.00854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a0cb5d5ebb9f04e8236ed5d66a4566d892a00a568421d56d8cc4b2e1f93c9d8","sha256:42edebeeb40f9459b1e0f3dcd287f60c5da1403965df9586bf6cbf8c867e1666"],"state_sha256":"c22bbc8b0333137da19c8f639ed5c6e888013700c44c9578999b7166a707b9e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DB/blLumTAYt72ju87o1BPuuG/s060F5xzidrL58h2sZcYHkvneVkDDKzbh/Y/1t6jYi2sxOdXZMrtAdQl3CCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T08:10:51.166221Z","bundle_sha256":"41c0077a42f9b0841c767df60055dd643537c60a0ff93980f0158d4dd9f0ec97"}}