{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PP5YXECOIN3PIEBVG5ODA2OXYI","short_pith_number":"pith:PP5YXECO","schema_version":"1.0","canonical_sha256":"7bfb8b904e4376f41035375c3069d7c223a1358aaeeebc4b494b6709f163cd38","source":{"kind":"arxiv","id":"2606.23018","version":1},"attestation_state":"computed","paper":{"title":"Sidorenko Inequalities for Two-Sided Group Correlation Kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yuqi Zhao","submitted_at":"2026-06-22T08:30:05Z","abstract_excerpt":"Sidorenko's conjecture asserts that every bipartite graph has at least the expected homomorphism density in every graph of a given edge density. Motivated by Cayley-type formulations of Sidorenko-type inequalities, we study a two-sided correlation construction on finite groups.\n  Let $\\Gamma$ be a finite group and let $f:\\Gamma\\to\\mathbb{R}$ be a real-valued function. We define a directed kernel on $\\Gamma$ by $$\\mathcal C_f(x,y)=|\\Gamma|^{-1}\\sum_{a_1,a_2\\in\\Gamma:\\, xa_1=a_2y} f(a_1)f(a_2)=\\mathbb{E}_{z\\in\\Gamma} f(x^{-1}z)f(zy^{-1}).$$ When $f=\\mathbf{1}_A$, this is the normalized size of t"},"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":"2606.23018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-22T08:30:05Z","cross_cats_sorted":[],"title_canon_sha256":"03695b649595e704a1fdb6fe6561da8b8d431b27b05fa840371810053942a88d","abstract_canon_sha256":"6756519355f17bb8c809f03659fb2966d613900a8dfb4db28fc06192c9c4c873"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:06.882031Z","signature_b64":"1EP4pe8wrPt/cghEUdWnQDuO14w3NhAsP11OoCkZhQVIW2YCyULGJk4Yg4QA6yDWa9jNoR7/hn6OUjstwUcmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bfb8b904e4376f41035375c3069d7c223a1358aaeeebc4b494b6709f163cd38","last_reissued_at":"2026-06-23T03:14:06.881604Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:06.881604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sidorenko Inequalities for Two-Sided Group Correlation Kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yuqi Zhao","submitted_at":"2026-06-22T08:30:05Z","abstract_excerpt":"Sidorenko's conjecture asserts that every bipartite graph has at least the expected homomorphism density in every graph of a given edge density. Motivated by Cayley-type formulations of Sidorenko-type inequalities, we study a two-sided correlation construction on finite groups.\n  Let $\\Gamma$ be a finite group and let $f:\\Gamma\\to\\mathbb{R}$ be a real-valued function. We define a directed kernel on $\\Gamma$ by $$\\mathcal C_f(x,y)=|\\Gamma|^{-1}\\sum_{a_1,a_2\\in\\Gamma:\\, xa_1=a_2y} f(a_1)f(a_2)=\\mathbb{E}_{z\\in\\Gamma} f(x^{-1}z)f(zy^{-1}).$$ When $f=\\mathbf{1}_A$, this is the normalized size of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23018","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/2606.23018/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":"2606.23018","created_at":"2026-06-23T03:14:06.881662+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.23018v1","created_at":"2026-06-23T03:14:06.881662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23018","created_at":"2026-06-23T03:14:06.881662+00:00"},{"alias_kind":"pith_short_12","alias_value":"PP5YXECOIN3P","created_at":"2026-06-23T03:14:06.881662+00:00"},{"alias_kind":"pith_short_16","alias_value":"PP5YXECOIN3PIEBV","created_at":"2026-06-23T03:14:06.881662+00:00"},{"alias_kind":"pith_short_8","alias_value":"PP5YXECO","created_at":"2026-06-23T03:14:06.881662+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/PP5YXECOIN3PIEBVG5ODA2OXYI","json":"https://pith.science/pith/PP5YXECOIN3PIEBVG5ODA2OXYI.json","graph_json":"https://pith.science/api/pith-number/PP5YXECOIN3PIEBVG5ODA2OXYI/graph.json","events_json":"https://pith.science/api/pith-number/PP5YXECOIN3PIEBVG5ODA2OXYI/events.json","paper":"https://pith.science/paper/PP5YXECO"},"agent_actions":{"view_html":"https://pith.science/pith/PP5YXECOIN3PIEBVG5ODA2OXYI","download_json":"https://pith.science/pith/PP5YXECOIN3PIEBVG5ODA2OXYI.json","view_paper":"https://pith.science/paper/PP5YXECO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.23018&json=true","fetch_graph":"https://pith.science/api/pith-number/PP5YXECOIN3PIEBVG5ODA2OXYI/graph.json","fetch_events":"https://pith.science/api/pith-number/PP5YXECOIN3PIEBVG5ODA2OXYI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PP5YXECOIN3PIEBVG5ODA2OXYI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PP5YXECOIN3PIEBVG5ODA2OXYI/action/storage_attestation","attest_author":"https://pith.science/pith/PP5YXECOIN3PIEBVG5ODA2OXYI/action/author_attestation","sign_citation":"https://pith.science/pith/PP5YXECOIN3PIEBVG5ODA2OXYI/action/citation_signature","submit_replication":"https://pith.science/pith/PP5YXECOIN3PIEBVG5ODA2OXYI/action/replication_record"}},"created_at":"2026-06-23T03:14:06.881662+00:00","updated_at":"2026-06-23T03:14:06.881662+00:00"}