{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IYCXKDPKLDWRLZDIEB46JARKHQ","short_pith_number":"pith:IYCXKDPK","schema_version":"1.0","canonical_sha256":"4605750dea58ed15e4682079e4822a3c0288251b41c3bb0ba5d8a5d16ea3bf24","source":{"kind":"arxiv","id":"2607.16854","version":1},"attestation_state":"computed","paper":{"title":"Linear Tur\\'an Numbers of Uniform Hypertrees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Pragya Verma, Rajat Adak","submitted_at":"2026-07-18T15:32:12Z","abstract_excerpt":"A hypergraph is \\emph{linear} if every pair of vertices is contained in at most one hyperedge. For a family $\\mathcal{F}$ of $r$-uniform hypergraphs, the linear Tur'an number $ex^{\\mathrm{lin}}_r(n,\\mathcal{F})$ is the maximum number of hyperedges in an $n$-vertex $\\mathcal{F}$-free linear $r$-uniform hypergraph. Extending the work of Gy'arf'as, Ruszink'o, and S'ark\"ozy on $3$-uniform linear hypertrees, we study linear Tur'an numbers for higher uniformity.\n  We determine the linear Tur'an number of the $r$-uniform linear star $S_k^r$, proving [ex^{\\mathrm{lin}}_r(n,S_k^r)\\le \\frac{n(k-1)}{r},]"},"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":"2607.16854","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-18T15:32:12Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"fd5bc5907a3b2e65322438e9684d6f49fa28721a220e8a389fb0c682685ec70b","abstract_canon_sha256":"07320fc075d585e997a5f02d1389bc65cc52fd8659dd20a672f59e72d84d7788"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T01:21:02.394020Z","signature_b64":"A8DBq4fduCijqwA5/Mrt3Yvx7tgwK1Y22YMS6+Yw+Sdt4ZrMLsUvoHpvW9owZHfTu5f2i/5tD2lvXEbDx4UDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4605750dea58ed15e4682079e4822a3c0288251b41c3bb0ba5d8a5d16ea3bf24","last_reissued_at":"2026-07-21T01:21:02.393123Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T01:21:02.393123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear Tur\\'an Numbers of Uniform Hypertrees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Pragya Verma, Rajat Adak","submitted_at":"2026-07-18T15:32:12Z","abstract_excerpt":"A hypergraph is \\emph{linear} if every pair of vertices is contained in at most one hyperedge. For a family $\\mathcal{F}$ of $r$-uniform hypergraphs, the linear Tur'an number $ex^{\\mathrm{lin}}_r(n,\\mathcal{F})$ is the maximum number of hyperedges in an $n$-vertex $\\mathcal{F}$-free linear $r$-uniform hypergraph. Extending the work of Gy'arf'as, Ruszink'o, and S'ark\"ozy on $3$-uniform linear hypertrees, we study linear Tur'an numbers for higher uniformity.\n  We determine the linear Tur'an number of the $r$-uniform linear star $S_k^r$, proving [ex^{\\mathrm{lin}}_r(n,S_k^r)\\le \\frac{n(k-1)}{r},]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16854","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/2607.16854/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":"2607.16854","created_at":"2026-07-21T01:21:02.393591+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.16854v1","created_at":"2026-07-21T01:21:02.393591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16854","created_at":"2026-07-21T01:21:02.393591+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYCXKDPKLDWR","created_at":"2026-07-21T01:21:02.393591+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYCXKDPKLDWRLZDI","created_at":"2026-07-21T01:21:02.393591+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYCXKDPK","created_at":"2026-07-21T01:21:02.393591+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/IYCXKDPKLDWRLZDIEB46JARKHQ","json":"https://pith.science/pith/IYCXKDPKLDWRLZDIEB46JARKHQ.json","graph_json":"https://pith.science/api/pith-number/IYCXKDPKLDWRLZDIEB46JARKHQ/graph.json","events_json":"https://pith.science/api/pith-number/IYCXKDPKLDWRLZDIEB46JARKHQ/events.json","paper":"https://pith.science/paper/IYCXKDPK"},"agent_actions":{"view_html":"https://pith.science/pith/IYCXKDPKLDWRLZDIEB46JARKHQ","download_json":"https://pith.science/pith/IYCXKDPKLDWRLZDIEB46JARKHQ.json","view_paper":"https://pith.science/paper/IYCXKDPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.16854&json=true","fetch_graph":"https://pith.science/api/pith-number/IYCXKDPKLDWRLZDIEB46JARKHQ/graph.json","fetch_events":"https://pith.science/api/pith-number/IYCXKDPKLDWRLZDIEB46JARKHQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYCXKDPKLDWRLZDIEB46JARKHQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYCXKDPKLDWRLZDIEB46JARKHQ/action/storage_attestation","attest_author":"https://pith.science/pith/IYCXKDPKLDWRLZDIEB46JARKHQ/action/author_attestation","sign_citation":"https://pith.science/pith/IYCXKDPKLDWRLZDIEB46JARKHQ/action/citation_signature","submit_replication":"https://pith.science/pith/IYCXKDPKLDWRLZDIEB46JARKHQ/action/replication_record"}},"created_at":"2026-07-21T01:21:02.393591+00:00","updated_at":"2026-07-21T01:21:02.393591+00:00"}