{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GS2ABZCTJSLVZ56DQKMNC2H5FZ","short_pith_number":"pith:GS2ABZCT","schema_version":"1.0","canonical_sha256":"34b400e4534c975cf7c38298d168fd2e44d603d297923478207000cfeeee3829","source":{"kind":"arxiv","id":"2606.07946","version":1},"attestation_state":"computed","paper":{"title":"Stolarsky-Type Inequalities in a Max-Convolution Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johannes Hosle","submitted_at":"2026-06-06T02:33:58Z","abstract_excerpt":"For $m \\in \\mathbb{N}$, let $q_m := \\frac{\\log(2m+1)}{2\\log(m+1)}$. The max-convolution inequality \\begin{align*}\n  \\sum_{k=0}^{2m}\\left(\\max_{i+j=k} x_i y_j \\right)^{q_m} &\\ge \\left(\\sum_{i=0}^{m} x_i\\right)^{q_m} \\left(\\sum_{j=0}^{m} y_j\\right)^{q_m} \\end{align*}for arbitrary sequences $x_0 \\ge x_1 \\ge ... \\ge x_m \\ge 0, y_0 \\ge y_1 \\ge ... \\ge y_m \\ge 0$ implies an affirmative answer to a question of Bourgain, Dilworth, Ford, Konyagin, and Kutzarova \\cite{BDFKK} on the sizes of sumsets in product sets. This inequality was proven for $m = 2$ by Becker, Ivanisvili, Krachun, and Madrid \\cite{B"},"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":"2606.07946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-06T02:33:58Z","cross_cats_sorted":[],"title_canon_sha256":"3269c2eb4de5f7558174d0b050512269bdb0c9f11e6884d05b8c3e5b358e6f70","abstract_canon_sha256":"caf7b09972834173bd52c6cb5d1b01f69d76ec0ba879cf294d2a6e28229c3ec4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:04:56.110447Z","signature_b64":"QtDGZuCWuLC50QhNh24DIbYHc6T6CV9T83Tx40RVu5pZVX8Nr065hZ0hv7Iey+t2VMyyee5fEc/ZF7h2yq25AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34b400e4534c975cf7c38298d168fd2e44d603d297923478207000cfeeee3829","last_reissued_at":"2026-06-09T01:04:56.110060Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:04:56.110060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stolarsky-Type Inequalities in a Max-Convolution Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johannes Hosle","submitted_at":"2026-06-06T02:33:58Z","abstract_excerpt":"For $m \\in \\mathbb{N}$, let $q_m := \\frac{\\log(2m+1)}{2\\log(m+1)}$. The max-convolution inequality \\begin{align*}\n  \\sum_{k=0}^{2m}\\left(\\max_{i+j=k} x_i y_j \\right)^{q_m} &\\ge \\left(\\sum_{i=0}^{m} x_i\\right)^{q_m} \\left(\\sum_{j=0}^{m} y_j\\right)^{q_m} \\end{align*}for arbitrary sequences $x_0 \\ge x_1 \\ge ... \\ge x_m \\ge 0, y_0 \\ge y_1 \\ge ... \\ge y_m \\ge 0$ implies an affirmative answer to a question of Bourgain, Dilworth, Ford, Konyagin, and Kutzarova \\cite{BDFKK} on the sizes of sumsets in product sets. This inequality was proven for $m = 2$ by Becker, Ivanisvili, Krachun, and Madrid \\cite{B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07946","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/2606.07946/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":"2606.07946","created_at":"2026-06-09T01:04:56.110123+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.07946v1","created_at":"2026-06-09T01:04:56.110123+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07946","created_at":"2026-06-09T01:04:56.110123+00:00"},{"alias_kind":"pith_short_12","alias_value":"GS2ABZCTJSLV","created_at":"2026-06-09T01:04:56.110123+00:00"},{"alias_kind":"pith_short_16","alias_value":"GS2ABZCTJSLVZ56D","created_at":"2026-06-09T01:04:56.110123+00:00"},{"alias_kind":"pith_short_8","alias_value":"GS2ABZCT","created_at":"2026-06-09T01:04:56.110123+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.25350","citing_title":"Geometric Block Exponents and a Uniform Mixed-Alphabet Sumset Inequality","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GS2ABZCTJSLVZ56DQKMNC2H5FZ","json":"https://pith.science/pith/GS2ABZCTJSLVZ56DQKMNC2H5FZ.json","graph_json":"https://pith.science/api/pith-number/GS2ABZCTJSLVZ56DQKMNC2H5FZ/graph.json","events_json":"https://pith.science/api/pith-number/GS2ABZCTJSLVZ56DQKMNC2H5FZ/events.json","paper":"https://pith.science/paper/GS2ABZCT"},"agent_actions":{"view_html":"https://pith.science/pith/GS2ABZCTJSLVZ56DQKMNC2H5FZ","download_json":"https://pith.science/pith/GS2ABZCTJSLVZ56DQKMNC2H5FZ.json","view_paper":"https://pith.science/paper/GS2ABZCT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.07946&json=true","fetch_graph":"https://pith.science/api/pith-number/GS2ABZCTJSLVZ56DQKMNC2H5FZ/graph.json","fetch_events":"https://pith.science/api/pith-number/GS2ABZCTJSLVZ56DQKMNC2H5FZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GS2ABZCTJSLVZ56DQKMNC2H5FZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GS2ABZCTJSLVZ56DQKMNC2H5FZ/action/storage_attestation","attest_author":"https://pith.science/pith/GS2ABZCTJSLVZ56DQKMNC2H5FZ/action/author_attestation","sign_citation":"https://pith.science/pith/GS2ABZCTJSLVZ56DQKMNC2H5FZ/action/citation_signature","submit_replication":"https://pith.science/pith/GS2ABZCTJSLVZ56DQKMNC2H5FZ/action/replication_record"}},"created_at":"2026-06-09T01:04:56.110123+00:00","updated_at":"2026-06-09T01:04:56.110123+00:00"}