{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:YKRNLQ6E6W6B2SL2YNXIRMNNBY","short_pith_number":"pith:YKRNLQ6E","schema_version":"1.0","canonical_sha256":"c2a2d5c3c4f5bc1d497ac36e88b1ad0e091f5bf03686cfbeabe4238ab3efd876","source":{"kind":"arxiv","id":"2408.02328","version":1},"attestation_state":"computed","paper":{"title":"Past and future of the cap set problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ernie Croot, P\\'eter P\\'al Pach, Vsevolod F. Lev","submitted_at":"2024-08-05T09:11:52Z","abstract_excerpt":"We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore."},"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":"2408.02328","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2024-08-05T09:11:52Z","cross_cats_sorted":[],"title_canon_sha256":"7a400d1a742006dea0b0b239d03f574169a862132e37e8b394dcfe6891c6a981","abstract_canon_sha256":"dca735d73adb1952b3960313253f28f2e64427a08d08296335620ff3b2cd18ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:52:11.366927Z","signature_b64":"qiKJvLRmQnH+vLU/2Z6YrKriqOSpRTcy1xKJiNWVRY67rJ1WA0J2iEivyrRA1p5jRZMuf4BxEf/L0bnnHujsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2a2d5c3c4f5bc1d497ac36e88b1ad0e091f5bf03686cfbeabe4238ab3efd876","last_reissued_at":"2026-07-05T08:52:11.366419Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:52:11.366419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Past and future of the cap set problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ernie Croot, P\\'eter P\\'al Pach, Vsevolod F. Lev","submitted_at":"2024-08-05T09:11:52Z","abstract_excerpt":"We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.02328","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/2408.02328/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":"2408.02328","created_at":"2026-07-05T08:52:11.366487+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.02328v1","created_at":"2026-07-05T08:52:11.366487+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.02328","created_at":"2026-07-05T08:52:11.366487+00:00"},{"alias_kind":"pith_short_12","alias_value":"YKRNLQ6E6W6B","created_at":"2026-07-05T08:52:11.366487+00:00"},{"alias_kind":"pith_short_16","alias_value":"YKRNLQ6E6W6B2SL2","created_at":"2026-07-05T08:52:11.366487+00:00"},{"alias_kind":"pith_short_8","alias_value":"YKRNLQ6E","created_at":"2026-07-05T08:52:11.366487+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.11057","citing_title":"STRCMP: Integrating Graph Structural Priors with Language Models for Combinatorial Optimization","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY","json":"https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY.json","graph_json":"https://pith.science/api/pith-number/YKRNLQ6E6W6B2SL2YNXIRMNNBY/graph.json","events_json":"https://pith.science/api/pith-number/YKRNLQ6E6W6B2SL2YNXIRMNNBY/events.json","paper":"https://pith.science/paper/YKRNLQ6E"},"agent_actions":{"view_html":"https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY","download_json":"https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY.json","view_paper":"https://pith.science/paper/YKRNLQ6E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.02328&json=true","fetch_graph":"https://pith.science/api/pith-number/YKRNLQ6E6W6B2SL2YNXIRMNNBY/graph.json","fetch_events":"https://pith.science/api/pith-number/YKRNLQ6E6W6B2SL2YNXIRMNNBY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY/action/storage_attestation","attest_author":"https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY/action/author_attestation","sign_citation":"https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY/action/citation_signature","submit_replication":"https://pith.science/pith/YKRNLQ6E6W6B2SL2YNXIRMNNBY/action/replication_record"}},"created_at":"2026-07-05T08:52:11.366487+00:00","updated_at":"2026-07-05T08:52:11.366487+00:00"}