{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:STQSJ3K4YKLKWMS4NPE65ORTC2","short_pith_number":"pith:STQSJ3K4","schema_version":"1.0","canonical_sha256":"94e124ed5cc296ab325c6bc9eeba3316b6afb715b9257ad61cab348d1f4413d4","source":{"kind":"arxiv","id":"2309.05046","version":2},"attestation_state":"computed","paper":{"title":"Product Sets of Arithmetic Progressions in Function Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lior Bary-Soroker, Noam Goldgraber","submitted_at":"2023-09-10T14:49:26Z","abstract_excerpt":"We study product sets of finite arithmetic progressions of polynomials over a finite field. We prove a lower bound for the size of the product set, uniform in a wide range of parameters. We apply our results to resolve the function field variants of Erd\\H{o}s' multiplication table problem."},"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":"2309.05046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-09-10T14:49:26Z","cross_cats_sorted":[],"title_canon_sha256":"15e52dc99d30a65609e29a0a2ea30014cdb9dbd0ade965f99ed1f6e48980c64a","abstract_canon_sha256":"4b5e45c01fd3635dad216bb1cb42a2c2f11f4c67b04dcd1868e094807d74ff73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:51:29.434324Z","signature_b64":"8K9vW1ScXiDukskLpmlVALLzcTXubzuO3vS/CHHyOZy4K4h5+hQxXMx+Xhr+r6q4vRMeKW0bCTqmIJzdfBu2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e124ed5cc296ab325c6bc9eeba3316b6afb715b9257ad61cab348d1f4413d4","last_reissued_at":"2026-07-05T06:51:29.433900Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:51:29.433900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Product Sets of Arithmetic Progressions in Function Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lior Bary-Soroker, Noam Goldgraber","submitted_at":"2023-09-10T14:49:26Z","abstract_excerpt":"We study product sets of finite arithmetic progressions of polynomials over a finite field. We prove a lower bound for the size of the product set, uniform in a wide range of parameters. We apply our results to resolve the function field variants of Erd\\H{o}s' multiplication table problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05046","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/2309.05046/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2309.05046","created_at":"2026-07-05T06:51:29.433954+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.05046v2","created_at":"2026-07-05T06:51:29.433954+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.05046","created_at":"2026-07-05T06:51:29.433954+00:00"},{"alias_kind":"pith_short_12","alias_value":"STQSJ3K4YKLK","created_at":"2026-07-05T06:51:29.433954+00:00"},{"alias_kind":"pith_short_16","alias_value":"STQSJ3K4YKLKWMS4","created_at":"2026-07-05T06:51:29.433954+00:00"},{"alias_kind":"pith_short_8","alias_value":"STQSJ3K4","created_at":"2026-07-05T06:51:29.433954+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/STQSJ3K4YKLKWMS4NPE65ORTC2","json":"https://pith.science/pith/STQSJ3K4YKLKWMS4NPE65ORTC2.json","graph_json":"https://pith.science/api/pith-number/STQSJ3K4YKLKWMS4NPE65ORTC2/graph.json","events_json":"https://pith.science/api/pith-number/STQSJ3K4YKLKWMS4NPE65ORTC2/events.json","paper":"https://pith.science/paper/STQSJ3K4"},"agent_actions":{"view_html":"https://pith.science/pith/STQSJ3K4YKLKWMS4NPE65ORTC2","download_json":"https://pith.science/pith/STQSJ3K4YKLKWMS4NPE65ORTC2.json","view_paper":"https://pith.science/paper/STQSJ3K4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.05046&json=true","fetch_graph":"https://pith.science/api/pith-number/STQSJ3K4YKLKWMS4NPE65ORTC2/graph.json","fetch_events":"https://pith.science/api/pith-number/STQSJ3K4YKLKWMS4NPE65ORTC2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/STQSJ3K4YKLKWMS4NPE65ORTC2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/STQSJ3K4YKLKWMS4NPE65ORTC2/action/storage_attestation","attest_author":"https://pith.science/pith/STQSJ3K4YKLKWMS4NPE65ORTC2/action/author_attestation","sign_citation":"https://pith.science/pith/STQSJ3K4YKLKWMS4NPE65ORTC2/action/citation_signature","submit_replication":"https://pith.science/pith/STQSJ3K4YKLKWMS4NPE65ORTC2/action/replication_record"}},"created_at":"2026-07-05T06:51:29.433954+00:00","updated_at":"2026-07-05T06:51:29.433954+00:00"}