{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Z3HFC2WEORTARO4ZWG2PHFJEQP","short_pith_number":"pith:Z3HFC2WE","schema_version":"1.0","canonical_sha256":"cece516ac4746608bb99b1b4f3952483d66c841b7130e5b7d1abbfd280c830fa","source":{"kind":"arxiv","id":"1505.08015","version":1},"attestation_state":"computed","paper":{"title":"The second Dirichlet coefficient starts out negative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David W. Farmer, Sally Koutsoliotas","submitted_at":"2015-05-29T12:28:14Z","abstract_excerpt":"Classical modular forms of small weight and low level are likely to have a negative second Fourier coefficient. Similarly, the labeling scheme for elliptic curves tends to give smaller labels to the higher-rank curves. These observations are easily made when browsing the L-functions and Modular Forms Database, available at http://www.LMFDB.org/. An explanation lies in the L-functions associated to these objects."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.08015","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-29T12:28:14Z","cross_cats_sorted":[],"title_canon_sha256":"107c9e226a5acdb304f7d17fbbbd136694426975ab7be1ea5d7018d83d638470","abstract_canon_sha256":"9e0e4536b0a0c29be29b17baefbdc1ece62714aa3447352d4df366d370c5d62c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:00.035601Z","signature_b64":"a5BkJttAdYWbjpvZgdyLRtZBrtGAgaLs8gT+lNjtXUQPC8oT4EOr6Qz+dlu2bjY2rtBCaisauZMbQc0tZDOaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cece516ac4746608bb99b1b4f3952483d66c841b7130e5b7d1abbfd280c830fa","last_reissued_at":"2026-05-18T02:00:00.034957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:00.034957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The second Dirichlet coefficient starts out negative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David W. Farmer, Sally Koutsoliotas","submitted_at":"2015-05-29T12:28:14Z","abstract_excerpt":"Classical modular forms of small weight and low level are likely to have a negative second Fourier coefficient. Similarly, the labeling scheme for elliptic curves tends to give smaller labels to the higher-rank curves. These observations are easily made when browsing the L-functions and Modular Forms Database, available at http://www.LMFDB.org/. An explanation lies in the L-functions associated to these objects."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08015","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.08015","created_at":"2026-05-18T02:00:00.035061+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.08015v1","created_at":"2026-05-18T02:00:00.035061+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.08015","created_at":"2026-05-18T02:00:00.035061+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z3HFC2WEORTA","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z3HFC2WEORTARO4Z","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z3HFC2WE","created_at":"2026-05-18T12:29:52.810259+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z3HFC2WEORTARO4ZWG2PHFJEQP","json":"https://pith.science/pith/Z3HFC2WEORTARO4ZWG2PHFJEQP.json","graph_json":"https://pith.science/api/pith-number/Z3HFC2WEORTARO4ZWG2PHFJEQP/graph.json","events_json":"https://pith.science/api/pith-number/Z3HFC2WEORTARO4ZWG2PHFJEQP/events.json","paper":"https://pith.science/paper/Z3HFC2WE"},"agent_actions":{"view_html":"https://pith.science/pith/Z3HFC2WEORTARO4ZWG2PHFJEQP","download_json":"https://pith.science/pith/Z3HFC2WEORTARO4ZWG2PHFJEQP.json","view_paper":"https://pith.science/paper/Z3HFC2WE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.08015&json=true","fetch_graph":"https://pith.science/api/pith-number/Z3HFC2WEORTARO4ZWG2PHFJEQP/graph.json","fetch_events":"https://pith.science/api/pith-number/Z3HFC2WEORTARO4ZWG2PHFJEQP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z3HFC2WEORTARO4ZWG2PHFJEQP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z3HFC2WEORTARO4ZWG2PHFJEQP/action/storage_attestation","attest_author":"https://pith.science/pith/Z3HFC2WEORTARO4ZWG2PHFJEQP/action/author_attestation","sign_citation":"https://pith.science/pith/Z3HFC2WEORTARO4ZWG2PHFJEQP/action/citation_signature","submit_replication":"https://pith.science/pith/Z3HFC2WEORTARO4ZWG2PHFJEQP/action/replication_record"}},"created_at":"2026-05-18T02:00:00.035061+00:00","updated_at":"2026-05-18T02:00:00.035061+00:00"}