{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7J74TJQ425DPABW66XKEBTYLUK","short_pith_number":"pith:7J74TJQ4","schema_version":"1.0","canonical_sha256":"fa7fc9a61cd746f006def5d440cf0ba2af965f257cbfac3b1700b37f4547aa20","source":{"kind":"arxiv","id":"2607.25023","version":1},"attestation_state":"computed","paper":{"title":"Schrijver Number Quasi-Tensorization and Multicolor Ramsey Bounds via Robust OR Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ijay Narang, Yukai Tang","submitted_at":"2026-07-27T19:32:34Z","abstract_excerpt":"We introduce a robust OR polynomial framework for composing positive semidefinite certificates across OR constraints. We demonstrate the power of this method in two applications.\n  The first is on acute-free families. A set $\\mathcal F=\\{(x_i^{(1)},\\ldots,x_i^{(r)})\\}_{i=1}^M \\subseteq (S^{n-1})^r$ is $r$-way acute-free if, for every $i\\neq j$, there is a coordinate $t\\in[r]$ such that $\\langle x_i^{(t)},x_j^{(t)}\\rangle\\leq 0$. We write $M_r(n)$ for the maximum size of such a set, and $M_r^{\\pm}(n)$ for the hypercube restriction. On the hypercube, $r$-way acute-free sets are independent sets "},"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":"2607.25023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-27T19:32:34Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"77925e68887964498e8554e08dd3eef5807c8fd351d52ed93bffdd260a97bf85","abstract_canon_sha256":"2e3c17cdfb32be66a30c0125de1809831d65089a354e55c5d13010ccb9e9b42f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T00:24:58.167311Z","signature_b64":"6Bp0n1xoZxlhcnbJ+lbeUkQWHwi6fchjZilPIU4GEqvJnAjzIZUbwAzrF75ej2bteddh/ov7d0gL3MQboTX+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa7fc9a61cd746f006def5d440cf0ba2af965f257cbfac3b1700b37f4547aa20","last_reissued_at":"2026-07-29T00:24:58.166503Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T00:24:58.166503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schrijver Number Quasi-Tensorization and Multicolor Ramsey Bounds via Robust OR Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ijay Narang, Yukai Tang","submitted_at":"2026-07-27T19:32:34Z","abstract_excerpt":"We introduce a robust OR polynomial framework for composing positive semidefinite certificates across OR constraints. We demonstrate the power of this method in two applications.\n  The first is on acute-free families. A set $\\mathcal F=\\{(x_i^{(1)},\\ldots,x_i^{(r)})\\}_{i=1}^M \\subseteq (S^{n-1})^r$ is $r$-way acute-free if, for every $i\\neq j$, there is a coordinate $t\\in[r]$ such that $\\langle x_i^{(t)},x_j^{(t)}\\rangle\\leq 0$. We write $M_r(n)$ for the maximum size of such a set, and $M_r^{\\pm}(n)$ for the hypercube restriction. On the hypercube, $r$-way acute-free sets are independent sets "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25023","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/2607.25023/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":"2607.25023","created_at":"2026-07-29T00:24:58.166913+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.25023v1","created_at":"2026-07-29T00:24:58.166913+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25023","created_at":"2026-07-29T00:24:58.166913+00:00"},{"alias_kind":"pith_short_12","alias_value":"7J74TJQ425DP","created_at":"2026-07-29T00:24:58.166913+00:00"},{"alias_kind":"pith_short_16","alias_value":"7J74TJQ425DPABW6","created_at":"2026-07-29T00:24:58.166913+00:00"},{"alias_kind":"pith_short_8","alias_value":"7J74TJQ4","created_at":"2026-07-29T00:24:58.166913+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.01962","citing_title":"New upper bound for multicolor Ramsey numbers","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7J74TJQ425DPABW66XKEBTYLUK","json":"https://pith.science/pith/7J74TJQ425DPABW66XKEBTYLUK.json","graph_json":"https://pith.science/api/pith-number/7J74TJQ425DPABW66XKEBTYLUK/graph.json","events_json":"https://pith.science/api/pith-number/7J74TJQ425DPABW66XKEBTYLUK/events.json","paper":"https://pith.science/paper/7J74TJQ4"},"agent_actions":{"view_html":"https://pith.science/pith/7J74TJQ425DPABW66XKEBTYLUK","download_json":"https://pith.science/pith/7J74TJQ425DPABW66XKEBTYLUK.json","view_paper":"https://pith.science/paper/7J74TJQ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.25023&json=true","fetch_graph":"https://pith.science/api/pith-number/7J74TJQ425DPABW66XKEBTYLUK/graph.json","fetch_events":"https://pith.science/api/pith-number/7J74TJQ425DPABW66XKEBTYLUK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7J74TJQ425DPABW66XKEBTYLUK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7J74TJQ425DPABW66XKEBTYLUK/action/storage_attestation","attest_author":"https://pith.science/pith/7J74TJQ425DPABW66XKEBTYLUK/action/author_attestation","sign_citation":"https://pith.science/pith/7J74TJQ425DPABW66XKEBTYLUK/action/citation_signature","submit_replication":"https://pith.science/pith/7J74TJQ425DPABW66XKEBTYLUK/action/replication_record"}},"created_at":"2026-07-29T00:24:58.166913+00:00","updated_at":"2026-07-29T00:24:58.166913+00:00"}