{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BWDVCKKU6HNS4HOALDDSJCMFSK","short_pith_number":"pith:BWDVCKKU","schema_version":"1.0","canonical_sha256":"0d87512954f1db2e1dc058c724898592b973c05de3bf8c1c2a5d8b4de3f82f42","source":{"kind":"arxiv","id":"2511.21061","version":3},"attestation_state":"computed","paper":{"title":"Density of rainbow triangles and properly colored $K_4$'s","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernard Lidick\\'y, J\\'ozsef Balogh, Peter Bradshaw, Ramon I. Garcia","submitted_at":"2025-11-26T05:00:45Z","abstract_excerpt":"We establish a sharp upper bound on the number of properly $3$-edge-colored $K_4$'s in graphs with $R$ red, $G$ green and $B$ blue edges. We give a computer-free flag-algebra proof of this bound, and we also convert our proof into a classical counting proof and an entropy proof.\n  Additionally, for every $k\\ge 4$, for a fixed rainbow coloring $F$ of a complete graph $K_k$, we give a sharp upper bound on the number copies of $F$ in a $\\binom{k}{2}$-edge-colored graph. Our proof of this result relies on a new flag-algebra version of H\\\"older's inequality.\n  We also give a computer-free flag-alge"},"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":"2511.21061","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-11-26T05:00:45Z","cross_cats_sorted":[],"title_canon_sha256":"a842f256ed6e1c35ac8808402b46a535f7ea87cc3f6b8025b5efe6da598ac7de","abstract_canon_sha256":"dd978422a4937bb59212c1c54c2f2e57c9ea2f22c4517f181a6c660a91f8a186"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:18.963720Z","signature_b64":"NLbSUCBVYctgLopiQWK8er7/uDpfqVM12QenuFIhsSyZURGwhiieClnL603zPjrp+7ZrWVWmvCBS7IBBUEVSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d87512954f1db2e1dc058c724898592b973c05de3bf8c1c2a5d8b4de3f82f42","last_reissued_at":"2026-06-23T02:13:18.963130Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:18.963130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Density of rainbow triangles and properly colored $K_4$'s","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernard Lidick\\'y, J\\'ozsef Balogh, Peter Bradshaw, Ramon I. Garcia","submitted_at":"2025-11-26T05:00:45Z","abstract_excerpt":"We establish a sharp upper bound on the number of properly $3$-edge-colored $K_4$'s in graphs with $R$ red, $G$ green and $B$ blue edges. We give a computer-free flag-algebra proof of this bound, and we also convert our proof into a classical counting proof and an entropy proof.\n  Additionally, for every $k\\ge 4$, for a fixed rainbow coloring $F$ of a complete graph $K_k$, we give a sharp upper bound on the number copies of $F$ in a $\\binom{k}{2}$-edge-colored graph. Our proof of this result relies on a new flag-algebra version of H\\\"older's inequality.\n  We also give a computer-free flag-alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.21061","kind":"arxiv","version":3},"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/2511.21061/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":"2511.21061","created_at":"2026-06-23T02:13:18.963196+00:00"},{"alias_kind":"arxiv_version","alias_value":"2511.21061v3","created_at":"2026-06-23T02:13:18.963196+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.21061","created_at":"2026-06-23T02:13:18.963196+00:00"},{"alias_kind":"pith_short_12","alias_value":"BWDVCKKU6HNS","created_at":"2026-06-23T02:13:18.963196+00:00"},{"alias_kind":"pith_short_16","alias_value":"BWDVCKKU6HNS4HOA","created_at":"2026-06-23T02:13:18.963196+00:00"},{"alias_kind":"pith_short_8","alias_value":"BWDVCKKU","created_at":"2026-06-23T02:13:18.963196+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/BWDVCKKU6HNS4HOALDDSJCMFSK","json":"https://pith.science/pith/BWDVCKKU6HNS4HOALDDSJCMFSK.json","graph_json":"https://pith.science/api/pith-number/BWDVCKKU6HNS4HOALDDSJCMFSK/graph.json","events_json":"https://pith.science/api/pith-number/BWDVCKKU6HNS4HOALDDSJCMFSK/events.json","paper":"https://pith.science/paper/BWDVCKKU"},"agent_actions":{"view_html":"https://pith.science/pith/BWDVCKKU6HNS4HOALDDSJCMFSK","download_json":"https://pith.science/pith/BWDVCKKU6HNS4HOALDDSJCMFSK.json","view_paper":"https://pith.science/paper/BWDVCKKU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2511.21061&json=true","fetch_graph":"https://pith.science/api/pith-number/BWDVCKKU6HNS4HOALDDSJCMFSK/graph.json","fetch_events":"https://pith.science/api/pith-number/BWDVCKKU6HNS4HOALDDSJCMFSK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BWDVCKKU6HNS4HOALDDSJCMFSK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BWDVCKKU6HNS4HOALDDSJCMFSK/action/storage_attestation","attest_author":"https://pith.science/pith/BWDVCKKU6HNS4HOALDDSJCMFSK/action/author_attestation","sign_citation":"https://pith.science/pith/BWDVCKKU6HNS4HOALDDSJCMFSK/action/citation_signature","submit_replication":"https://pith.science/pith/BWDVCKKU6HNS4HOALDDSJCMFSK/action/replication_record"}},"created_at":"2026-06-23T02:13:18.963196+00:00","updated_at":"2026-06-23T02:13:18.963196+00:00"}