{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KESER2LRLC4FO5V6NYAQFEGY6B","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":"89b6d84482d5ee954640cd2c81d5b0954dc4600355325909e174394cdb572968","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-20T17:27:53Z","title_canon_sha256":"1d5294511fed61773f45849c86b500ab53f9c55305692b65d11f6492214f8625"},"schema_version":"1.0","source":{"id":"2505.14641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.14641","created_at":"2026-07-05T11:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"2505.14641v1","created_at":"2026-07-05T11:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.14641","created_at":"2026-07-05T11:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"KESER2LRLC4F","created_at":"2026-07-05T11:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"KESER2LRLC4FO5V6","created_at":"2026-07-05T11:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"KESER2LR","created_at":"2026-07-05T11:06:16Z"}],"graph_snapshots":[{"event_id":"sha256:98f998640ba71dd5888c1a32226b40d6a37ce7d1ef77c22032037a594da1429a","target":"graph","created_at":"2026-07-05T11:06:16Z","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/2505.14641/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Following recent work on the VC-dimension of subsets of various pseudorandom graphs, we study the VC-dimension of Hamming graphs, which have proved somewhat resistant to the standard techniques in the literature. Our methods are elementary, and agree with or improve upon previously known results. In particular, for $H(2,q)$ we show tight bounds on the size of a subset of vertices to guarantee VC-dimension 2 or 3. We also prove an assortment of results for other parameters, with many of these being tight as well.","authors_text":"Christopher Housholder, Layna Mangiapanello, Steven Senger","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-20T17:27:53Z","title":"VC-dimension of subsets of Hamming graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14641","kind":"arxiv","version":1},"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":"sha256:5fff4f731c17e4c536891c68ffe867d9d8e16dff9db72a5190f71dccf002b17c","target":"record","created_at":"2026-07-05T11:06:16Z","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":"89b6d84482d5ee954640cd2c81d5b0954dc4600355325909e174394cdb572968","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-20T17:27:53Z","title_canon_sha256":"1d5294511fed61773f45849c86b500ab53f9c55305692b65d11f6492214f8625"},"schema_version":"1.0","source":{"id":"2505.14641","kind":"arxiv","version":1}},"canonical_sha256":"512448e97158b85776be6e010290d8f06515e4a801a12ab95d6c1077b34fbfc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"512448e97158b85776be6e010290d8f06515e4a801a12ab95d6c1077b34fbfc8","first_computed_at":"2026-07-05T11:06:16.921414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:06:16.921414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5V7cWIjGXggLopt1xUKqhengoe1IIPOzahvCMz3WPEZs6/Iqn17VR6yIXW4+4LejHeBNzwN2009VF5K2hajNCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:06:16.921970Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.14641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fff4f731c17e4c536891c68ffe867d9d8e16dff9db72a5190f71dccf002b17c","sha256:98f998640ba71dd5888c1a32226b40d6a37ce7d1ef77c22032037a594da1429a"],"state_sha256":"9103f2471b5fc2e902078261990d1d07ebeb752dcd78148415c46dfdfb195a28"}