{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:H656OHH4RY65L6UEUHTW36V3MH","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":"0376fb2d643e78ea9b84213f9cf2a65c97ed9cbef47d75afab7c29560b7c552a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-22T11:49:13Z","title_canon_sha256":"53b7e89aa8540d583c003ccf4dcf87d22e191d35d2ec8848fa3f04ff94fad733"},"schema_version":"1.0","source":{"id":"2607.20051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.20051","created_at":"2026-07-23T01:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"2607.20051v1","created_at":"2026-07-23T01:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20051","created_at":"2026-07-23T01:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"H656OHH4RY65","created_at":"2026-07-23T01:24:57Z"},{"alias_kind":"pith_short_16","alias_value":"H656OHH4RY65L6UE","created_at":"2026-07-23T01:24:57Z"},{"alias_kind":"pith_short_8","alias_value":"H656OHH4","created_at":"2026-07-23T01:24:57Z"}],"graph_snapshots":[{"event_id":"sha256:a02ae5e4f3eb63a3616441c8eee20bcd1a2a9f9cd3de6ae84e7886375cd43f83","target":"graph","created_at":"2026-07-23T01:24:57Z","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/2607.20051/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let \\(F\\subseteq\\binom{V}{q}\\) be a \\(q\\)-uniform family on a finite vertex set \\(V\\). Write \\(s_r(F)\\) for the sum of the \\(r\\) largest eigenvalues of its simplicial up-Laplacian and \\(d_F(v)\\) for the degree of \\(v\\in V\\). Then $D_r(F)=\\sum_{v\\in V}\\min\\{d_F(v),r\\}$ is the \\(r\\)-th partial sum of the conjugate degree sequence of \\(F\\). The majorization assertion in the Duval--Reiner conjecture [Trans. Amer. Math. Soc., 2002] states that \\(s_r(F)\\le D_r(F)\\) for every \\(q\\)-uniform family \\(F\\) and every \\(r\\ge1\\). We disprove this assertion in two complementary senses: for every \\(r\\ge5\\), t","authors_text":"Jing Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-22T11:49:13Z","title":"The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20051","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:a0f6ab3f6daab22e566cbb4223f2c86ff39fd642fbcfd7c5e8d0b786dfa38d77","target":"record","created_at":"2026-07-23T01:24:57Z","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":"0376fb2d643e78ea9b84213f9cf2a65c97ed9cbef47d75afab7c29560b7c552a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-22T11:49:13Z","title_canon_sha256":"53b7e89aa8540d583c003ccf4dcf87d22e191d35d2ec8848fa3f04ff94fad733"},"schema_version":"1.0","source":{"id":"2607.20051","kind":"arxiv","version":1}},"canonical_sha256":"3fbbe71cfc8e3dd5fa84a1e76dfabb61c8d3f65c37efcd404cc94de08cb1fb7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fbbe71cfc8e3dd5fa84a1e76dfabb61c8d3f65c37efcd404cc94de08cb1fb7d","first_computed_at":"2026-07-23T01:24:57.426709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-23T01:24:57.426709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8O2MRSWkmXLm8qbvwlrXDwxRBEWLCG3csQu61EZ9N3VUvtbZVkFx3WhlWtn0BkujwIzem1WRWEw1aa5plnU3Bw==","signature_status":"signed_v1","signed_at":"2026-07-23T01:24:57.427570Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.20051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0f6ab3f6daab22e566cbb4223f2c86ff39fd642fbcfd7c5e8d0b786dfa38d77","sha256:a02ae5e4f3eb63a3616441c8eee20bcd1a2a9f9cd3de6ae84e7886375cd43f83"],"state_sha256":"fd13a4538d9bba6d5963fb8e76c4acf4b7f0e711c476ceda9dcaf37cd304917c"}