{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:P6XSJ35KUA2SNB6STPO2I665WR","short_pith_number":"pith:P6XSJ35K","schema_version":"1.0","canonical_sha256":"7faf24efaaa0352687d29bdda47bddb44f08e521535e9a2ff47f0c73c5468c03","source":{"kind":"arxiv","id":"1707.01930","version":2},"attestation_state":"computed","paper":{"title":"A tale of stars and cliques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Reiher, Joanna Polcyn, Tomasz {\\L}uczak","submitted_at":"2017-07-06T18:28:15Z","abstract_excerpt":"We show that for an infinitely many natural numbers $k$ there are $k$-uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\\mathcal{A}(k,I, n)$ denote the class of $k$-graphs on $n$ vertices in which the sizes of all pairwise intersections of edges belong to a set $I$. We show that if $k=rt^2$ for some $r\\ge 1$ and $t\\ge 2$, and~$I$ is chosen in some special way, the densest graphs in $\\mathcal{A}(rt^2,I, n)$ are either dominated by stars of large degree, or basically, they are `$t$-thick' $rt^2$-graphs in which vertices are partitioned into groups"},"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":"1707.01930","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-06T18:28:15Z","cross_cats_sorted":[],"title_canon_sha256":"965cdb4f46c5f036bf8ec1f394cdeb08960dd9118e92fc00a15133167a008eba","abstract_canon_sha256":"f7f45093bed9ea89ef65233777ca1f8acb6e761e0021606184b552401e39c62c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:23.803480Z","signature_b64":"0Vnup74KQzi3w06Ps9IPZ4VFQmUzORnAiCB0+7Pfapa4geDydhUEdvysqxda86iHwmFAHsqq2oTwjqtF2gzzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7faf24efaaa0352687d29bdda47bddb44f08e521535e9a2ff47f0c73c5468c03","last_reissued_at":"2026-05-18T00:11:23.802847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:23.802847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A tale of stars and cliques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Reiher, Joanna Polcyn, Tomasz {\\L}uczak","submitted_at":"2017-07-06T18:28:15Z","abstract_excerpt":"We show that for an infinitely many natural numbers $k$ there are $k$-uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\\mathcal{A}(k,I, n)$ denote the class of $k$-graphs on $n$ vertices in which the sizes of all pairwise intersections of edges belong to a set $I$. We show that if $k=rt^2$ for some $r\\ge 1$ and $t\\ge 2$, and~$I$ is chosen in some special way, the densest graphs in $\\mathcal{A}(rt^2,I, n)$ are either dominated by stars of large degree, or basically, they are `$t$-thick' $rt^2$-graphs in which vertices are partitioned into groups"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01930","kind":"arxiv","version":2},"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":"1707.01930","created_at":"2026-05-18T00:11:23.802946+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.01930v2","created_at":"2026-05-18T00:11:23.802946+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01930","created_at":"2026-05-18T00:11:23.802946+00:00"},{"alias_kind":"pith_short_12","alias_value":"P6XSJ35KUA2S","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"P6XSJ35KUA2SNB6S","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"P6XSJ35K","created_at":"2026-05-18T12:31:37.085036+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/P6XSJ35KUA2SNB6STPO2I665WR","json":"https://pith.science/pith/P6XSJ35KUA2SNB6STPO2I665WR.json","graph_json":"https://pith.science/api/pith-number/P6XSJ35KUA2SNB6STPO2I665WR/graph.json","events_json":"https://pith.science/api/pith-number/P6XSJ35KUA2SNB6STPO2I665WR/events.json","paper":"https://pith.science/paper/P6XSJ35K"},"agent_actions":{"view_html":"https://pith.science/pith/P6XSJ35KUA2SNB6STPO2I665WR","download_json":"https://pith.science/pith/P6XSJ35KUA2SNB6STPO2I665WR.json","view_paper":"https://pith.science/paper/P6XSJ35K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.01930&json=true","fetch_graph":"https://pith.science/api/pith-number/P6XSJ35KUA2SNB6STPO2I665WR/graph.json","fetch_events":"https://pith.science/api/pith-number/P6XSJ35KUA2SNB6STPO2I665WR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P6XSJ35KUA2SNB6STPO2I665WR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P6XSJ35KUA2SNB6STPO2I665WR/action/storage_attestation","attest_author":"https://pith.science/pith/P6XSJ35KUA2SNB6STPO2I665WR/action/author_attestation","sign_citation":"https://pith.science/pith/P6XSJ35KUA2SNB6STPO2I665WR/action/citation_signature","submit_replication":"https://pith.science/pith/P6XSJ35KUA2SNB6STPO2I665WR/action/replication_record"}},"created_at":"2026-05-18T00:11:23.802946+00:00","updated_at":"2026-05-18T00:11:23.802946+00:00"}