{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3BPE6L24HERPVSA2G7CKXQRVTS","short_pith_number":"pith:3BPE6L24","schema_version":"1.0","canonical_sha256":"d85e4f2f5c3922fac81a37c4abc2359c9716a1e64952fb87c233af77f7c89e8d","source":{"kind":"arxiv","id":"2508.20132","version":1},"attestation_state":"computed","paper":{"title":"Delta-system method: a survey","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii","submitted_at":"2025-08-26T15:49:20Z","abstract_excerpt":"In 1960 Erd\\H os and Rado published a paper that, in retrospect, became one of the most influential papers in extremal set theory. They proved a result of Ramsey theoretic flavour, stating that in any sufficiently large family of sets of bounded size there is a homogeneous substructure, called a $\\Delta$-system (also known under the name of a sunflower). For many qualitative results in Discrete Mathematics and Theoretical Computer Science, this has become a very powerful tool to analyze complex set families. Extremal set theory flourished in the 1970's--80's, and many exciting developments hap"},"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":"2508.20132","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-26T15:49:20Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"363db27e96ecd36cb24a5fcd6018d7ce58586e185ca6bb0ce4edc1102a88860c","abstract_canon_sha256":"86b9e5651de1fc6cf0145bb92cf7f55e8dc260b89a39c4072dae3caffcae85cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:00:30.048596Z","signature_b64":"ctY72cj7NuHt4kbQmdBZrD5bysa2E2aeSiTf1keR1PJ6oE7ubU8HWhewp0/Y1Nd5hurbTKJSotqlLStXN5TFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d85e4f2f5c3922fac81a37c4abc2359c9716a1e64952fb87c233af77f7c89e8d","last_reissued_at":"2026-07-05T12:00:30.048093Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:00:30.048093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Delta-system method: a survey","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii","submitted_at":"2025-08-26T15:49:20Z","abstract_excerpt":"In 1960 Erd\\H os and Rado published a paper that, in retrospect, became one of the most influential papers in extremal set theory. They proved a result of Ramsey theoretic flavour, stating that in any sufficiently large family of sets of bounded size there is a homogeneous substructure, called a $\\Delta$-system (also known under the name of a sunflower). For many qualitative results in Discrete Mathematics and Theoretical Computer Science, this has become a very powerful tool to analyze complex set families. Extremal set theory flourished in the 1970's--80's, and many exciting developments hap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.20132","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/2508.20132/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":"2508.20132","created_at":"2026-07-05T12:00:30.048158+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.20132v1","created_at":"2026-07-05T12:00:30.048158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.20132","created_at":"2026-07-05T12:00:30.048158+00:00"},{"alias_kind":"pith_short_12","alias_value":"3BPE6L24HERP","created_at":"2026-07-05T12:00:30.048158+00:00"},{"alias_kind":"pith_short_16","alias_value":"3BPE6L24HERPVSA2","created_at":"2026-07-05T12:00:30.048158+00:00"},{"alias_kind":"pith_short_8","alias_value":"3BPE6L24","created_at":"2026-07-05T12:00:30.048158+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.12178","citing_title":"On the maximum number of vectors in $\\{0,\\pm1\\}^n$ with forbidden inner products","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2607.00318","citing_title":"A Complete Intersection Theorem for Large Permutation Groups","ref_index":32,"is_internal_anchor":false},{"citing_arxiv_id":"2605.30092","citing_title":"Short proofs of three combinatorial results in the Johnson scheme","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02698","citing_title":"Structure of $t$-Intersecting Families of Vector Spaces","ref_index":29,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3BPE6L24HERPVSA2G7CKXQRVTS","json":"https://pith.science/pith/3BPE6L24HERPVSA2G7CKXQRVTS.json","graph_json":"https://pith.science/api/pith-number/3BPE6L24HERPVSA2G7CKXQRVTS/graph.json","events_json":"https://pith.science/api/pith-number/3BPE6L24HERPVSA2G7CKXQRVTS/events.json","paper":"https://pith.science/paper/3BPE6L24"},"agent_actions":{"view_html":"https://pith.science/pith/3BPE6L24HERPVSA2G7CKXQRVTS","download_json":"https://pith.science/pith/3BPE6L24HERPVSA2G7CKXQRVTS.json","view_paper":"https://pith.science/paper/3BPE6L24","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.20132&json=true","fetch_graph":"https://pith.science/api/pith-number/3BPE6L24HERPVSA2G7CKXQRVTS/graph.json","fetch_events":"https://pith.science/api/pith-number/3BPE6L24HERPVSA2G7CKXQRVTS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3BPE6L24HERPVSA2G7CKXQRVTS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3BPE6L24HERPVSA2G7CKXQRVTS/action/storage_attestation","attest_author":"https://pith.science/pith/3BPE6L24HERPVSA2G7CKXQRVTS/action/author_attestation","sign_citation":"https://pith.science/pith/3BPE6L24HERPVSA2G7CKXQRVTS/action/citation_signature","submit_replication":"https://pith.science/pith/3BPE6L24HERPVSA2G7CKXQRVTS/action/replication_record"}},"created_at":"2026-07-05T12:00:30.048158+00:00","updated_at":"2026-07-05T12:00:30.048158+00:00"}