{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TD46HEU7NCAMKPKP32TIK5EUZP","short_pith_number":"pith:TD46HEU7","schema_version":"1.0","canonical_sha256":"98f9e3929f6880c53d4fdea6857494cbccddf0d576ec00329a4d5d4aef3cb23b","source":{"kind":"arxiv","id":"1411.2314","version":2},"attestation_state":"computed","paper":{"title":"A characterization of functions with vanishing averages over products of disjoint sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Hamed Hatami, Pooya Hatami, Yaqiao Li","submitted_at":"2014-11-10T02:45:00Z","abstract_excerpt":"Given $\\alpha_1,...,\\alpha_m \\in (0,1)$, we characterize all integrable functions $f:[0,1]^m \\to \\mathbb{C}$ satisfying $\\int_{A_1 \\times ...\\times A_m} f =0$ for any collection of disjoint sets $A_1,...,A_m \\subseteq [0,1]$ of respective measures $\\alpha_1,...,\\alpha_m$. We use this characterization to settle some of the conjectures in [S. Janson and V. S\\'os, More on quasi-random graphs, subgraph counts and graph limits, arXiv:1405.6808]."},"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":"1411.2314","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-10T02:45:00Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"1d7513d3b7b9330522eb966e0f9f657d61a96e95495aabdf95479a662367bd6d","abstract_canon_sha256":"7d41190ee2650ddae96d19983d2e0bd36e5c850584fafb18d74c46c43836de8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:17.179865Z","signature_b64":"GI/S3RP7hrh2mowpHiED0IsTa3T5aABQv25sWmP7Mi4kGmjQylUsLXoIpvlz9MfcZIAX0H4Eqpru1l+rqIRYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98f9e3929f6880c53d4fdea6857494cbccddf0d576ec00329a4d5d4aef3cb23b","last_reissued_at":"2026-05-18T02:29:17.179404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:17.179404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of functions with vanishing averages over products of disjoint sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Hamed Hatami, Pooya Hatami, Yaqiao Li","submitted_at":"2014-11-10T02:45:00Z","abstract_excerpt":"Given $\\alpha_1,...,\\alpha_m \\in (0,1)$, we characterize all integrable functions $f:[0,1]^m \\to \\mathbb{C}$ satisfying $\\int_{A_1 \\times ...\\times A_m} f =0$ for any collection of disjoint sets $A_1,...,A_m \\subseteq [0,1]$ of respective measures $\\alpha_1,...,\\alpha_m$. We use this characterization to settle some of the conjectures in [S. Janson and V. S\\'os, More on quasi-random graphs, subgraph counts and graph limits, arXiv:1405.6808]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2314","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":"1411.2314","created_at":"2026-05-18T02:29:17.179471+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.2314v2","created_at":"2026-05-18T02:29:17.179471+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2314","created_at":"2026-05-18T02:29:17.179471+00:00"},{"alias_kind":"pith_short_12","alias_value":"TD46HEU7NCAM","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"TD46HEU7NCAMKPKP","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"TD46HEU7","created_at":"2026-05-18T12:28:49.207871+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/TD46HEU7NCAMKPKP32TIK5EUZP","json":"https://pith.science/pith/TD46HEU7NCAMKPKP32TIK5EUZP.json","graph_json":"https://pith.science/api/pith-number/TD46HEU7NCAMKPKP32TIK5EUZP/graph.json","events_json":"https://pith.science/api/pith-number/TD46HEU7NCAMKPKP32TIK5EUZP/events.json","paper":"https://pith.science/paper/TD46HEU7"},"agent_actions":{"view_html":"https://pith.science/pith/TD46HEU7NCAMKPKP32TIK5EUZP","download_json":"https://pith.science/pith/TD46HEU7NCAMKPKP32TIK5EUZP.json","view_paper":"https://pith.science/paper/TD46HEU7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.2314&json=true","fetch_graph":"https://pith.science/api/pith-number/TD46HEU7NCAMKPKP32TIK5EUZP/graph.json","fetch_events":"https://pith.science/api/pith-number/TD46HEU7NCAMKPKP32TIK5EUZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TD46HEU7NCAMKPKP32TIK5EUZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TD46HEU7NCAMKPKP32TIK5EUZP/action/storage_attestation","attest_author":"https://pith.science/pith/TD46HEU7NCAMKPKP32TIK5EUZP/action/author_attestation","sign_citation":"https://pith.science/pith/TD46HEU7NCAMKPKP32TIK5EUZP/action/citation_signature","submit_replication":"https://pith.science/pith/TD46HEU7NCAMKPKP32TIK5EUZP/action/replication_record"}},"created_at":"2026-05-18T02:29:17.179471+00:00","updated_at":"2026-05-18T02:29:17.179471+00:00"}