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In particular, in the principal case $m=\\binom{t}{r}$ their conjecture states that every $H\\subseteq \\mathbb{N}^{(r)}$ of size $\\binom{t}{r}$ satisfies \\begin{align*} \\max \\{\\sum_{A \\in H}\\prod_{i\\in A} y_i \\ \\colon \\ y_1,y_2,\\ldots \\geq 0; \\sum_{i\\in \\mathbb{N}} y_i=1 \\}&\\leq \\frac{1}{t^r}\\binom{t}{r}. \\end{align*}\n  We prove the above statement for all $r\\geq 4$ and large values of $t$ (the case $r=3$ was settled"},"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":"1703.04273","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-13T07:25:58Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"05fefdc76767b0e904eec97c10b9a11cdb1fb12260ac5d086d8b9730233d3893","abstract_canon_sha256":"4e45cbed8b8bb4418c75d1e00bc362f7f524a437a9225e452b0cec36ba2f104a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:10.546725Z","signature_b64":"3guiA4NahRrVATykXa/9wltqg/VTroyJn/AP7fyFcvDp28fZjt4gGUJJZBkYSA6LjUhw5GL5cpyJhZt8itUUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c9235fa3f1b63530190f4e85c9204ce59224961f3165b235de72c93b53b5b22","last_reissued_at":"2026-05-18T00:33:10.545991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:10.545991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lagrangians of hypergraphs: The Frankl-F\\\"uredi conjecture holds almost everywhere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Mykhaylo Tyomkyn","submitted_at":"2017-03-13T07:25:58Z","abstract_excerpt":"Frankl and F\\\"uredi conjectured in 1989 that the maximum Lagrangian of all $r$-uniform hypergraphs of fixed size $m$ is realised by the initial segment of the colexicographic order. In particular, in the principal case $m=\\binom{t}{r}$ their conjecture states that every $H\\subseteq \\mathbb{N}^{(r)}$ of size $\\binom{t}{r}$ satisfies \\begin{align*} \\max \\{\\sum_{A \\in H}\\prod_{i\\in A} y_i \\ \\colon \\ y_1,y_2,\\ldots \\geq 0; \\sum_{i\\in \\mathbb{N}} y_i=1 \\}&\\leq \\frac{1}{t^r}\\binom{t}{r}. \\end{align*}\n  We prove the above statement for all $r\\geq 4$ and large values of $t$ (the case $r=3$ was settled"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04273","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":""},"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":"1703.04273","created_at":"2026-05-18T00:33:10.546109+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.04273v1","created_at":"2026-05-18T00:33:10.546109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04273","created_at":"2026-05-18T00:33:10.546109+00:00"},{"alias_kind":"pith_short_12","alias_value":"FSJDL6R7DNRV","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FSJDL6R7DNRVGAMQ","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FSJDL6R7","created_at":"2026-05-18T12:31:15.632608+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/FSJDL6R7DNRVGAMQ6TUFZEQEZZ","json":"https://pith.science/pith/FSJDL6R7DNRVGAMQ6TUFZEQEZZ.json","graph_json":"https://pith.science/api/pith-number/FSJDL6R7DNRVGAMQ6TUFZEQEZZ/graph.json","events_json":"https://pith.science/api/pith-number/FSJDL6R7DNRVGAMQ6TUFZEQEZZ/events.json","paper":"https://pith.science/paper/FSJDL6R7"},"agent_actions":{"view_html":"https://pith.science/pith/FSJDL6R7DNRVGAMQ6TUFZEQEZZ","download_json":"https://pith.science/pith/FSJDL6R7DNRVGAMQ6TUFZEQEZZ.json","view_paper":"https://pith.science/paper/FSJDL6R7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.04273&json=true","fetch_graph":"https://pith.science/api/pith-number/FSJDL6R7DNRVGAMQ6TUFZEQEZZ/graph.json","fetch_events":"https://pith.science/api/pith-number/FSJDL6R7DNRVGAMQ6TUFZEQEZZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FSJDL6R7DNRVGAMQ6TUFZEQEZZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FSJDL6R7DNRVGAMQ6TUFZEQEZZ/action/storage_attestation","attest_author":"https://pith.science/pith/FSJDL6R7DNRVGAMQ6TUFZEQEZZ/action/author_attestation","sign_citation":"https://pith.science/pith/FSJDL6R7DNRVGAMQ6TUFZEQEZZ/action/citation_signature","submit_replication":"https://pith.science/pith/FSJDL6R7DNRVGAMQ6TUFZEQEZZ/action/replication_record"}},"created_at":"2026-05-18T00:33:10.546109+00:00","updated_at":"2026-05-18T00:33:10.546109+00:00"}