{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TSWYJZRJKHQFLSUC6ZG5KPI44X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4e061d46365ba3bfd691bab8b4d35ad8e6fd9f748573a2d988db3943ba925753","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-26T06:51:18Z","title_canon_sha256":"6da7e1b0751538f6ae7b1860051a121d7b13d1b6511d4a747b69c66cd5ccd951"},"schema_version":"1.0","source":{"id":"2605.26614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26614","created_at":"2026-05-27T01:06:02Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26614v1","created_at":"2026-05-27T01:06:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26614","created_at":"2026-05-27T01:06:02Z"},{"alias_kind":"pith_short_12","alias_value":"TSWYJZRJKHQF","created_at":"2026-05-27T01:06:02Z"},{"alias_kind":"pith_short_16","alias_value":"TSWYJZRJKHQFLSUC","created_at":"2026-05-27T01:06:02Z"},{"alias_kind":"pith_short_8","alias_value":"TSWYJZRJ","created_at":"2026-05-27T01:06:02Z"}],"graph_snapshots":[{"event_id":"sha256:9b2dc92a9dafa737967116d859da6221404770b177cff1319d00048e6a6919cf","target":"graph","created_at":"2026-05-27T01:06:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.26614/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a spectral approach to Sidorenko-type inequalities and apply it to establish sharp edge-spectral supersaturation results. Let $H$ be a bipartite graph with $v$ vertices and $e$ edges, where $v\\le e$, and write $M(G)=2e(G)$. We prove that Sidorenko's conjecture is equivalent to a spectral strengthening: \\[\n  \\hom(H,G)\\ge M(G)^e |V(G)|^{v-2e} \\quad \\text{ if and only if }\\quad \\hom(H,G)\\ge \\lambda(G)^{2e-v}M(G)^{v-e}. \\] We also introduce an operator-norm certificate which, via the Riesz--Thorin interpolation, gives direct proofs of the spectral Sidorenko inequality in several cases. ","authors_text":"Hong Liu, Shengtong Zhang, Wilson Lin, Yongtao Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-26T06:51:18Z","title":"Spectral Sidorenko inequalities and edge-spectral supersaturation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26614","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3789a48d9ab0be08c981d2a020b0fa7ef6d6d913d62471d80b659f73c8e903c6","target":"record","created_at":"2026-05-27T01:06:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4e061d46365ba3bfd691bab8b4d35ad8e6fd9f748573a2d988db3943ba925753","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-26T06:51:18Z","title_canon_sha256":"6da7e1b0751538f6ae7b1860051a121d7b13d1b6511d4a747b69c66cd5ccd951"},"schema_version":"1.0","source":{"id":"2605.26614","kind":"arxiv","version":1}},"canonical_sha256":"9cad84e62951e055ca82f64dd53d1ce5f27b318f56a085d9c41e7010aa23ee3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cad84e62951e055ca82f64dd53d1ce5f27b318f56a085d9c41e7010aa23ee3f","first_computed_at":"2026-05-27T01:06:02.223873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:06:02.223873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gZ+8cWP+t2s3BFX2DuNaLoH+IEYQ5ab+puaZU5qcfxb0jaCon/yF61NFEao7H9zRu2LNhXpb7A3lquCOc6TpBg==","signature_status":"signed_v1","signed_at":"2026-05-27T01:06:02.224847Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3789a48d9ab0be08c981d2a020b0fa7ef6d6d913d62471d80b659f73c8e903c6","sha256:9b2dc92a9dafa737967116d859da6221404770b177cff1319d00048e6a6919cf"],"state_sha256":"d6cd551b89712f42347df3e76bc39342bb2fc4ba2ed3db05629bf67656d613e7"}