{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DU6OHJXITQISWNUURYSXGUPUIQ","short_pith_number":"pith:DU6OHJXI","schema_version":"1.0","canonical_sha256":"1d3ce3a6e89c112b36948e257351f4440f2e66325941b63d34fd064b01c73e2e","source":{"kind":"arxiv","id":"1505.04611","version":1},"attestation_state":"computed","paper":{"title":"A Generalization of Combinatorial Designs Related to Almost Difference Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Baokun Ding, Jerod Michel","submitted_at":"2015-05-18T12:39:40Z","abstract_excerpt":"In this paper we study a certain generalization of combinatorial designs related to almost difference sets, namely the $t$-adesign, which was coined by Cunsheng Ding in 2015. It is clear that $2$-adesigns are a kind of partially balanced incomplete block design which naturally arise in many combinatorial and statistical problems. We discuss some of their basic properties and give several constructions of $2$-adesigns (some of which correspond to new almost difference sets, and others of which correspond to new almost difference families), as well as two constructions of $3$-adesigns. We also d"},"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":"1505.04611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-18T12:39:40Z","cross_cats_sorted":[],"title_canon_sha256":"854a3bb07791c8be81a408369a166b71b6c3919b6ea83b04d5bd373f8fa7a583","abstract_canon_sha256":"2ec4644ff20db68e2b3fcd3c4da698688644ee46c6e4ecb5ca46ca8ab210147d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:25.015251Z","signature_b64":"5nNyVeLIy6dMBvXE0QYhNiMTTtT7dfxGF2YFRzZVXYuXee3d41Qr6QbfuBPJTcG6MqWzBLyJKM/z742/opNUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d3ce3a6e89c112b36948e257351f4440f2e66325941b63d34fd064b01c73e2e","last_reissued_at":"2026-05-18T02:07:25.014894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:25.014894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Generalization of Combinatorial Designs Related to Almost Difference Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Baokun Ding, Jerod Michel","submitted_at":"2015-05-18T12:39:40Z","abstract_excerpt":"In this paper we study a certain generalization of combinatorial designs related to almost difference sets, namely the $t$-adesign, which was coined by Cunsheng Ding in 2015. It is clear that $2$-adesigns are a kind of partially balanced incomplete block design which naturally arise in many combinatorial and statistical problems. We discuss some of their basic properties and give several constructions of $2$-adesigns (some of which correspond to new almost difference sets, and others of which correspond to new almost difference families), as well as two constructions of $3$-adesigns. We also d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04611","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":""},"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":"1505.04611","created_at":"2026-05-18T02:07:25.014952+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.04611v1","created_at":"2026-05-18T02:07:25.014952+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04611","created_at":"2026-05-18T02:07:25.014952+00:00"},{"alias_kind":"pith_short_12","alias_value":"DU6OHJXITQIS","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DU6OHJXITQISWNUU","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DU6OHJXI","created_at":"2026-05-18T12:29:17.054201+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/DU6OHJXITQISWNUURYSXGUPUIQ","json":"https://pith.science/pith/DU6OHJXITQISWNUURYSXGUPUIQ.json","graph_json":"https://pith.science/api/pith-number/DU6OHJXITQISWNUURYSXGUPUIQ/graph.json","events_json":"https://pith.science/api/pith-number/DU6OHJXITQISWNUURYSXGUPUIQ/events.json","paper":"https://pith.science/paper/DU6OHJXI"},"agent_actions":{"view_html":"https://pith.science/pith/DU6OHJXITQISWNUURYSXGUPUIQ","download_json":"https://pith.science/pith/DU6OHJXITQISWNUURYSXGUPUIQ.json","view_paper":"https://pith.science/paper/DU6OHJXI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.04611&json=true","fetch_graph":"https://pith.science/api/pith-number/DU6OHJXITQISWNUURYSXGUPUIQ/graph.json","fetch_events":"https://pith.science/api/pith-number/DU6OHJXITQISWNUURYSXGUPUIQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DU6OHJXITQISWNUURYSXGUPUIQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DU6OHJXITQISWNUURYSXGUPUIQ/action/storage_attestation","attest_author":"https://pith.science/pith/DU6OHJXITQISWNUURYSXGUPUIQ/action/author_attestation","sign_citation":"https://pith.science/pith/DU6OHJXITQISWNUURYSXGUPUIQ/action/citation_signature","submit_replication":"https://pith.science/pith/DU6OHJXITQISWNUURYSXGUPUIQ/action/replication_record"}},"created_at":"2026-05-18T02:07:25.014952+00:00","updated_at":"2026-05-18T02:07:25.014952+00:00"}