{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MWXXPYVFV554JG7DRBCUI27BEL","short_pith_number":"pith:MWXXPYVF","schema_version":"1.0","canonical_sha256":"65af77e2a5af7bc49be38845446be122eb1ec22f123904abf81efa609be97e50","source":{"kind":"arxiv","id":"2605.21408","version":1},"attestation_state":"computed","paper":{"title":"TCARD: Nearly Balanced Two-Level Designs with Treatment Cardinality Constraints with an Application to LLM Prompt Engineering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Kexin Xie, Ryan Lekivetz, Xinwei Deng","submitted_at":"2026-05-20T17:06:34Z","abstract_excerpt":"Modern experimental designs often face the so-called treatment cardinality constraint, which is the constraint on the number of included factors in each treatment. Experiments with such constraints are commonly encountered in engineering simulation, AI system tuning, and large-scale system verification. This calls for the development of adequate designs to enable statistical efficiency for modeling and analysis within feasible constraints. In this work, we study two-level designs under this $k$-treatment cardinality constraint (TCARD), where the design matrix $\\mathbf{X} \\in \\{0,1\\}^{n \\times "},"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":"2605.21408","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-05-20T17:06:34Z","cross_cats_sorted":[],"title_canon_sha256":"639a0716aa099b200648fa71f9bb88c9accaf295614ab3704c167b45cb4f8e7c","abstract_canon_sha256":"723e184a0088232629ce3d8e54a97a61d26656e1f56f83f8954bd5fe590ee7f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T02:05:33.323788Z","signature_b64":"9xu5b/CuPqNX7u7jQySKefEqlFAfi4IwBQ9RRAmfRwOyjudgipSyGUdYaNkNb0PkHeXwWu3yAE8uP2pK8Yx3DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65af77e2a5af7bc49be38845446be122eb1ec22f123904abf81efa609be97e50","last_reissued_at":"2026-05-21T02:05:33.323199Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T02:05:33.323199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"TCARD: Nearly Balanced Two-Level Designs with Treatment Cardinality Constraints with an Application to LLM Prompt Engineering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Kexin Xie, Ryan Lekivetz, Xinwei Deng","submitted_at":"2026-05-20T17:06:34Z","abstract_excerpt":"Modern experimental designs often face the so-called treatment cardinality constraint, which is the constraint on the number of included factors in each treatment. Experiments with such constraints are commonly encountered in engineering simulation, AI system tuning, and large-scale system verification. This calls for the development of adequate designs to enable statistical efficiency for modeling and analysis within feasible constraints. In this work, we study two-level designs under this $k$-treatment cardinality constraint (TCARD), where the design matrix $\\mathbf{X} \\in \\{0,1\\}^{n \\times "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21408","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/2605.21408/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":"2605.21408","created_at":"2026-05-21T02:05:33.323284+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.21408v1","created_at":"2026-05-21T02:05:33.323284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21408","created_at":"2026-05-21T02:05:33.323284+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWXXPYVFV554","created_at":"2026-05-21T02:05:33.323284+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWXXPYVFV554JG7D","created_at":"2026-05-21T02:05:33.323284+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWXXPYVF","created_at":"2026-05-21T02:05:33.323284+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/MWXXPYVFV554JG7DRBCUI27BEL","json":"https://pith.science/pith/MWXXPYVFV554JG7DRBCUI27BEL.json","graph_json":"https://pith.science/api/pith-number/MWXXPYVFV554JG7DRBCUI27BEL/graph.json","events_json":"https://pith.science/api/pith-number/MWXXPYVFV554JG7DRBCUI27BEL/events.json","paper":"https://pith.science/paper/MWXXPYVF"},"agent_actions":{"view_html":"https://pith.science/pith/MWXXPYVFV554JG7DRBCUI27BEL","download_json":"https://pith.science/pith/MWXXPYVFV554JG7DRBCUI27BEL.json","view_paper":"https://pith.science/paper/MWXXPYVF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.21408&json=true","fetch_graph":"https://pith.science/api/pith-number/MWXXPYVFV554JG7DRBCUI27BEL/graph.json","fetch_events":"https://pith.science/api/pith-number/MWXXPYVFV554JG7DRBCUI27BEL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWXXPYVFV554JG7DRBCUI27BEL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWXXPYVFV554JG7DRBCUI27BEL/action/storage_attestation","attest_author":"https://pith.science/pith/MWXXPYVFV554JG7DRBCUI27BEL/action/author_attestation","sign_citation":"https://pith.science/pith/MWXXPYVFV554JG7DRBCUI27BEL/action/citation_signature","submit_replication":"https://pith.science/pith/MWXXPYVFV554JG7DRBCUI27BEL/action/replication_record"}},"created_at":"2026-05-21T02:05:33.323284+00:00","updated_at":"2026-05-21T02:05:33.323284+00:00"}