{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JLM5VALRAIFWKLR625CM7XONWQ","short_pith_number":"pith:JLM5VALR","schema_version":"1.0","canonical_sha256":"4ad9da8171020b652e3ed744cfddcdb422a16549ba2e4b7a5c55b50bb7aed22d","source":{"kind":"arxiv","id":"1405.2293","version":2},"attestation_state":"computed","paper":{"title":"A study in sums of products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"\\'E. Fouvry, E. Kowalski, Ph. Michel","submitted_at":"2014-05-09T17:19:09Z","abstract_excerpt":"We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic number theory."},"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":"1405.2293","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-05-09T17:19:09Z","cross_cats_sorted":[],"title_canon_sha256":"b073f2d751cee38db1bf92cc9296bd392860589ab2b410d1db76e8f37e34023b","abstract_canon_sha256":"910edb907f6f2f79fdc786449910a8325a690af22abf1552a9e4d4f6d95200c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:12.284589Z","signature_b64":"p94wDodPx34ZugAWrKrABVHTQW2OxGyrLNuwbpOF2tlsFKD8yZohbsjQVi8jiTsIgOWQ+FlEIjjmhXiJvuOEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ad9da8171020b652e3ed744cfddcdb422a16549ba2e4b7a5c55b50bb7aed22d","last_reissued_at":"2026-05-18T01:35:12.283912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:12.283912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A study in sums of products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"\\'E. Fouvry, E. Kowalski, Ph. Michel","submitted_at":"2014-05-09T17:19:09Z","abstract_excerpt":"We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic number theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2293","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":""},"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":"1405.2293","created_at":"2026-05-18T01:35:12.284030+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.2293v2","created_at":"2026-05-18T01:35:12.284030+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2293","created_at":"2026-05-18T01:35:12.284030+00:00"},{"alias_kind":"pith_short_12","alias_value":"JLM5VALRAIFW","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"JLM5VALRAIFWKLR6","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"JLM5VALR","created_at":"2026-05-18T12:28:33.132498+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/JLM5VALRAIFWKLR625CM7XONWQ","json":"https://pith.science/pith/JLM5VALRAIFWKLR625CM7XONWQ.json","graph_json":"https://pith.science/api/pith-number/JLM5VALRAIFWKLR625CM7XONWQ/graph.json","events_json":"https://pith.science/api/pith-number/JLM5VALRAIFWKLR625CM7XONWQ/events.json","paper":"https://pith.science/paper/JLM5VALR"},"agent_actions":{"view_html":"https://pith.science/pith/JLM5VALRAIFWKLR625CM7XONWQ","download_json":"https://pith.science/pith/JLM5VALRAIFWKLR625CM7XONWQ.json","view_paper":"https://pith.science/paper/JLM5VALR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.2293&json=true","fetch_graph":"https://pith.science/api/pith-number/JLM5VALRAIFWKLR625CM7XONWQ/graph.json","fetch_events":"https://pith.science/api/pith-number/JLM5VALRAIFWKLR625CM7XONWQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JLM5VALRAIFWKLR625CM7XONWQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JLM5VALRAIFWKLR625CM7XONWQ/action/storage_attestation","attest_author":"https://pith.science/pith/JLM5VALRAIFWKLR625CM7XONWQ/action/author_attestation","sign_citation":"https://pith.science/pith/JLM5VALRAIFWKLR625CM7XONWQ/action/citation_signature","submit_replication":"https://pith.science/pith/JLM5VALRAIFWKLR625CM7XONWQ/action/replication_record"}},"created_at":"2026-05-18T01:35:12.284030+00:00","updated_at":"2026-05-18T01:35:12.284030+00:00"}