{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UKFEWJPXZOROURRDSLQBHWDVWN","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":"ce9ed417afbbe398cae5f5dffe77aa03543b0ca350d3743ec2f2b0f15fc1020f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-18T18:35:00Z","title_canon_sha256":"9851fea96374ff48ee347df1359eb5ed4f4fb2a16375e23413e7b7e8f1cadec6"},"schema_version":"1.0","source":{"id":"1408.4093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4093","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4093v2","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4093","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"UKFEWJPXZORO","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UKFEWJPXZOROURRD","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UKFEWJPX","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:2d6659301892ebba7e5a08a48e522a5c4a92d026e1a6b9bd4b24613a5189ebfb","target":"graph","created_at":"2026-05-18T02:43:08Z","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"},"paper":{"abstract_excerpt":"We prove that for every poset $P$, there is a constant $C$ such that the size of any family of subsets of $[n]$ that does not contain $P$ as an induced subposet is at most $C{\\binom{n}{\\lfloor\\frac{n}{2}\\rfloor}}$, settling a conjecture of Katona, and Lu and Milans. We obtain this bound by establishing a connection to the theory of forbidden submatrices and then applying a higher dimensional variant of the Marcus-Tardos theorem, proved by Klazar and Marcus. We also give a new proof of their result.","authors_text":"Abhishek Methuku, D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-18T18:35:00Z","title":"Forbidden hypermatrices imply general bounds on induced forbidden subposet problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4093","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":"sha256:9788531ef6e2bec98f76499c0b2aae0c0f54f914f58a1cd362b40595ffd21d4c","target":"record","created_at":"2026-05-18T02:43:08Z","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":"ce9ed417afbbe398cae5f5dffe77aa03543b0ca350d3743ec2f2b0f15fc1020f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-18T18:35:00Z","title_canon_sha256":"9851fea96374ff48ee347df1359eb5ed4f4fb2a16375e23413e7b7e8f1cadec6"},"schema_version":"1.0","source":{"id":"1408.4093","kind":"arxiv","version":2}},"canonical_sha256":"a28a4b25f7cba2ea462392e013d875b37b290dad674473d087cff9c61dd6538a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a28a4b25f7cba2ea462392e013d875b37b290dad674473d087cff9c61dd6538a","first_computed_at":"2026-05-18T02:43:08.916145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:08.916145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XTC9j0FOBmBPBCakbHIY7pPZiiPHEkPD+hPOoLsr/G836SFKIqeUy5rsSgtCoudL0hTZObioZ9x4/cbvv6B0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:08.916563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9788531ef6e2bec98f76499c0b2aae0c0f54f914f58a1cd362b40595ffd21d4c","sha256:2d6659301892ebba7e5a08a48e522a5c4a92d026e1a6b9bd4b24613a5189ebfb"],"state_sha256":"a8ecfb3be2979722dc44e99b5d0a275c0790f73baf7e7ee81e0cc50cecfb622b"}