{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3O2GKEFSH6GY4AA7VWCTZM3BRG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a953d4265397744be1894e086e707d320ae29fdf759b365c0e22f6bc3aac764b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-03T17:32:08Z","title_canon_sha256":"08c1bb8ec44a85f371a2091dafa888902c4f8f234d10b1113929a5a823b52760"},"schema_version":"1.0","source":{"id":"2007.01827","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.01827","created_at":"2026-07-05T01:16:57Z"},{"alias_kind":"arxiv_version","alias_value":"2007.01827v2","created_at":"2026-07-05T01:16:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.01827","created_at":"2026-07-05T01:16:57Z"},{"alias_kind":"pith_short_12","alias_value":"3O2GKEFSH6GY","created_at":"2026-07-05T01:16:57Z"},{"alias_kind":"pith_short_16","alias_value":"3O2GKEFSH6GY4AA7","created_at":"2026-07-05T01:16:57Z"},{"alias_kind":"pith_short_8","alias_value":"3O2GKEFS","created_at":"2026-07-05T01:16:57Z"}],"graph_snapshots":[{"event_id":"sha256:8cf91c73329f11fcd2ce28594ac17507b1d2db500517855ef23a4f1d130a5acd","target":"graph","created_at":"2026-07-05T01:16:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.01827/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $H$ and $F$ be hypergraphs. We say $H$ contains $F$ as a trace if there exists some set $S \\subseteq V(H)$ such that $H|_S:=\\{E\\cap S: E \\in E(H)\\}$ contains a subhypergraph isomorphic to $F$. In this paper we give an upper bound on the number of edges in a $3$-uniform hypergraph that does not contain $K_{2,t}$ as a trace when $t$ is large. In particular, we show that $ \\lim_{t\\to \\infty}\\lim_{n\\to \\infty} \\frac{\\mathrm{ex}(n, \\mathrm{Tr}_3(K_{2,t}))}{t^{3/2}n^{3/2}} = \\frac{1}{6}.$\n  Moreover, we show $\\frac{1}{2} n^{3/2} + o(n^{3/2}) \\leq \\mathrm{ex}(n, \\mathrm{Tr}_3(C_4)) \\leq \\frac{5}{","authors_text":"Ruth Luo, Sam Spiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-03T17:32:08Z","title":"Forbidding $K_{2,t}$ traces in triple systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.01827","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ab1580b53e539d2c8c1dbddf4979b2441295b95dbab8867350ec3cec7b21f660","target":"record","created_at":"2026-07-05T01:16:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a953d4265397744be1894e086e707d320ae29fdf759b365c0e22f6bc3aac764b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-07-03T17:32:08Z","title_canon_sha256":"08c1bb8ec44a85f371a2091dafa888902c4f8f234d10b1113929a5a823b52760"},"schema_version":"1.0","source":{"id":"2007.01827","kind":"arxiv","version":2}},"canonical_sha256":"dbb46510b23f8d8e001fad853cb36189a0afb8932e17e8989b65868686956a4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbb46510b23f8d8e001fad853cb36189a0afb8932e17e8989b65868686956a4c","first_computed_at":"2026-07-05T01:16:57.387824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:16:57.387824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eJxODo52YRvoHSWBRfDmZ9UDgWJEW0W/aFvst2A99cFvFfUSTHsE3XWfRUnQ/Ran6DfHIxfN8hmNYdk9xVqtBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:16:57.388165Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.01827","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab1580b53e539d2c8c1dbddf4979b2441295b95dbab8867350ec3cec7b21f660","sha256:8cf91c73329f11fcd2ce28594ac17507b1d2db500517855ef23a4f1d130a5acd"],"state_sha256":"596ed19a1cfb13746cc3a1697ce6a8b6f8fc57ece068bc03a74a9192d13760c8"}