{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:CLHWSAQHG3KLTJGCCDJ3QVRIGS","short_pith_number":"pith:CLHWSAQH","canonical_record":{"source":{"id":"2006.15661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-28T17:33:25Z","cross_cats_sorted":[],"title_canon_sha256":"0126e5ea3ea982ce7ab496cce06ab70a48d05cd1029c230442643ca73bb452d4","abstract_canon_sha256":"7e1df8dfe78b48158cbb811760267e0372e945ad223c1e2d224fb85c7e3dc475"},"schema_version":"1.0"},"canonical_sha256":"12cf69020736d4b9a4c210d3b8562834b6ca7fe7325ec8d00683422d115bea1f","source":{"kind":"arxiv","id":"2006.15661","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.15661","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"2006.15661v1","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.15661","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"CLHWSAQHG3KL","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"pith_short_16","alias_value":"CLHWSAQHG3KLTJGC","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"pith_short_8","alias_value":"CLHWSAQH","created_at":"2026-07-05T01:14:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:CLHWSAQHG3KLTJGCCDJ3QVRIGS","target":"record","payload":{"canonical_record":{"source":{"id":"2006.15661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-28T17:33:25Z","cross_cats_sorted":[],"title_canon_sha256":"0126e5ea3ea982ce7ab496cce06ab70a48d05cd1029c230442643ca73bb452d4","abstract_canon_sha256":"7e1df8dfe78b48158cbb811760267e0372e945ad223c1e2d224fb85c7e3dc475"},"schema_version":"1.0"},"canonical_sha256":"12cf69020736d4b9a4c210d3b8562834b6ca7fe7325ec8d00683422d115bea1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:14:07.835666Z","signature_b64":"7PEaJWwhSkthzqZLXy4BhvB8NOFWJ4EA/7b1q9fk8i+r9WNoubm8ni9R4FZEi3beuwT9ro1ovqsWHXB/fXq+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12cf69020736d4b9a4c210d3b8562834b6ca7fe7325ec8d00683422d115bea1f","last_reissued_at":"2026-07-05T01:14:07.835120Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:14:07.835120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.15661","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":"2026-07-05T01:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HJfz8hP0/6tv30+mgEhSrZcIP6kvHWIRk0Ec+Hz4VgRxaYgOL3APWf6ast4IuNXAE/ciZUNxKn6cFrbQeWJ9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:32:53.902204Z"},"content_sha256":"4d32a22b626a0dafa3ed7a47910af8408c8d9ae9a62c27ef6e675f8a38b05883","schema_version":"1.0","event_id":"sha256:4d32a22b626a0dafa3ed7a47910af8408c8d9ae9a62c27ef6e675f8a38b05883"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:CLHWSAQHG3KLTJGCCDJ3QVRIGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-vanishing for cubic $L$--functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandra Florea, Chantal David, Matilde Lalin","submitted_at":"2020-06-28T17:33:25Z","abstract_excerpt":"We prove that there is a positive proportion of $L$-functions associated to cubic characters over $\\mathbb{F}_q[T]$ that do not vanish at the critical point $s=1/2$. This is achieved by computing the first mollified moment using techniques previously developed by the authors in their work on the first moment of cubic $L$-functions, and by obtaining a sharp upper bound for the second mollified moment, building on work of Lester-Radziwill, which in turn develops further ideas from the work of Soundararajan, Harper, and Radziwill-Soundararajan. We work in the non-Kummer setting when $q \\equiv 2\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.15661","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/2006.15661/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":"2026-07-05T01:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hAf4ps+vxmUdTbkQsyVp/4YLpGMLNAG/M2KU5ra0Ln/doCN/7NcrrANguyRhnt92rYKjgOV4dVsLbjC4XixUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:32:53.902709Z"},"content_sha256":"c77effe42d561d49456eeb8b2e2a73e1d836e8cc4a4868985100bb7269d5346b","schema_version":"1.0","event_id":"sha256:c77effe42d561d49456eeb8b2e2a73e1d836e8cc4a4868985100bb7269d5346b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CLHWSAQHG3KLTJGCCDJ3QVRIGS/bundle.json","state_url":"https://pith.science/pith/CLHWSAQHG3KLTJGCCDJ3QVRIGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CLHWSAQHG3KLTJGCCDJ3QVRIGS/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":"2026-08-06T10:32:53Z","links":{"resolver":"https://pith.science/pith/CLHWSAQHG3KLTJGCCDJ3QVRIGS","bundle":"https://pith.science/pith/CLHWSAQHG3KLTJGCCDJ3QVRIGS/bundle.json","state":"https://pith.science/pith/CLHWSAQHG3KLTJGCCDJ3QVRIGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CLHWSAQHG3KLTJGCCDJ3QVRIGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:CLHWSAQHG3KLTJGCCDJ3QVRIGS","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":"7e1df8dfe78b48158cbb811760267e0372e945ad223c1e2d224fb85c7e3dc475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-28T17:33:25Z","title_canon_sha256":"0126e5ea3ea982ce7ab496cce06ab70a48d05cd1029c230442643ca73bb452d4"},"schema_version":"1.0","source":{"id":"2006.15661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.15661","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"2006.15661v1","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.15661","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"CLHWSAQHG3KL","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"pith_short_16","alias_value":"CLHWSAQHG3KLTJGC","created_at":"2026-07-05T01:14:07Z"},{"alias_kind":"pith_short_8","alias_value":"CLHWSAQH","created_at":"2026-07-05T01:14:07Z"}],"graph_snapshots":[{"event_id":"sha256:c77effe42d561d49456eeb8b2e2a73e1d836e8cc4a4868985100bb7269d5346b","target":"graph","created_at":"2026-07-05T01:14:07Z","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/2006.15661/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that there is a positive proportion of $L$-functions associated to cubic characters over $\\mathbb{F}_q[T]$ that do not vanish at the critical point $s=1/2$. This is achieved by computing the first mollified moment using techniques previously developed by the authors in their work on the first moment of cubic $L$-functions, and by obtaining a sharp upper bound for the second mollified moment, building on work of Lester-Radziwill, which in turn develops further ideas from the work of Soundararajan, Harper, and Radziwill-Soundararajan. We work in the non-Kummer setting when $q \\equiv 2\\p","authors_text":"Alexandra Florea, Chantal David, Matilde Lalin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-28T17:33:25Z","title":"Non-vanishing for cubic $L$--functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.15661","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":"sha256:4d32a22b626a0dafa3ed7a47910af8408c8d9ae9a62c27ef6e675f8a38b05883","target":"record","created_at":"2026-07-05T01:14:07Z","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":"7e1df8dfe78b48158cbb811760267e0372e945ad223c1e2d224fb85c7e3dc475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-28T17:33:25Z","title_canon_sha256":"0126e5ea3ea982ce7ab496cce06ab70a48d05cd1029c230442643ca73bb452d4"},"schema_version":"1.0","source":{"id":"2006.15661","kind":"arxiv","version":1}},"canonical_sha256":"12cf69020736d4b9a4c210d3b8562834b6ca7fe7325ec8d00683422d115bea1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12cf69020736d4b9a4c210d3b8562834b6ca7fe7325ec8d00683422d115bea1f","first_computed_at":"2026-07-05T01:14:07.835120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:14:07.835120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7PEaJWwhSkthzqZLXy4BhvB8NOFWJ4EA/7b1q9fk8i+r9WNoubm8ni9R4FZEi3beuwT9ro1ovqsWHXB/fXq+Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:14:07.835666Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.15661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d32a22b626a0dafa3ed7a47910af8408c8d9ae9a62c27ef6e675f8a38b05883","sha256:c77effe42d561d49456eeb8b2e2a73e1d836e8cc4a4868985100bb7269d5346b"],"state_sha256":"756088a6ed4f9319817c7ed4f225c01626404caa155e409a2c5ccad5b56d7e6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opNt9ADdTw9LCTBn2hIR2X0OE4dPo6wLO0jXX7t9vsLibo955nOL5MAukuJq7OKXlzpQT9A69E5CQ+z/1pNqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T10:32:53.909788Z","bundle_sha256":"a731e1d6b5ced5652cf680932595b725d955fd5e8a4bffce87952f0f04fc4ce7"}}