{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LOI5CEKNUQZY5EXMK4PHM2R27D","short_pith_number":"pith:LOI5CEKN","schema_version":"1.0","canonical_sha256":"5b91d1114da4338e92ec571e766a3af8fddad5639f4a86730e9cea9d7b33c540","source":{"kind":"arxiv","id":"1404.2962","version":1},"attestation_state":"computed","paper":{"title":"Computing Minimum Tile Sets to Self-Assemble Colors Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Aleck C. Johnsen, Ming-Yang Kao, Shinnosuke Seki","submitted_at":"2014-04-10T22:48:39Z","abstract_excerpt":"Patterned self-assembly tile set synthesis (PATS) aims at finding a minimum tile set to uniquely self-assemble a given rectangular color pattern. For $k \\ge 1$, $k$-PATS is a variant of PATS that restricts input patterns to those with at most $k$ colors. We prove the {\\bf NP}-hardness of 29-PATS, where the best known is that of 60-PATS."},"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":"1404.2962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-04-10T22:48:39Z","cross_cats_sorted":[],"title_canon_sha256":"012ac14a38847267156acc0c9d8417774b9f26b00052236175bf919b1f3755bb","abstract_canon_sha256":"b114c7d5e61277351324324c658daeb1938aa296923cf6d321996258d452955a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:22.789308Z","signature_b64":"lkijOXTpr86Pp25Gzakjn00o3JGKXow+AYY1AnL9NhIn1qkD7yQ1okZftVVLOh5Sj+tEH+aEt7YFNrOmpR5KDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b91d1114da4338e92ec571e766a3af8fddad5639f4a86730e9cea9d7b33c540","last_reissued_at":"2026-05-18T02:54:22.788889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:22.788889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing Minimum Tile Sets to Self-Assemble Colors Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Aleck C. Johnsen, Ming-Yang Kao, Shinnosuke Seki","submitted_at":"2014-04-10T22:48:39Z","abstract_excerpt":"Patterned self-assembly tile set synthesis (PATS) aims at finding a minimum tile set to uniquely self-assemble a given rectangular color pattern. For $k \\ge 1$, $k$-PATS is a variant of PATS that restricts input patterns to those with at most $k$ colors. We prove the {\\bf NP}-hardness of 29-PATS, where the best known is that of 60-PATS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2962","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":"1404.2962","created_at":"2026-05-18T02:54:22.788948+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2962v1","created_at":"2026-05-18T02:54:22.788948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2962","created_at":"2026-05-18T02:54:22.788948+00:00"},{"alias_kind":"pith_short_12","alias_value":"LOI5CEKNUQZY","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LOI5CEKNUQZY5EXM","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LOI5CEKN","created_at":"2026-05-18T12:28:38.356838+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/LOI5CEKNUQZY5EXMK4PHM2R27D","json":"https://pith.science/pith/LOI5CEKNUQZY5EXMK4PHM2R27D.json","graph_json":"https://pith.science/api/pith-number/LOI5CEKNUQZY5EXMK4PHM2R27D/graph.json","events_json":"https://pith.science/api/pith-number/LOI5CEKNUQZY5EXMK4PHM2R27D/events.json","paper":"https://pith.science/paper/LOI5CEKN"},"agent_actions":{"view_html":"https://pith.science/pith/LOI5CEKNUQZY5EXMK4PHM2R27D","download_json":"https://pith.science/pith/LOI5CEKNUQZY5EXMK4PHM2R27D.json","view_paper":"https://pith.science/paper/LOI5CEKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2962&json=true","fetch_graph":"https://pith.science/api/pith-number/LOI5CEKNUQZY5EXMK4PHM2R27D/graph.json","fetch_events":"https://pith.science/api/pith-number/LOI5CEKNUQZY5EXMK4PHM2R27D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LOI5CEKNUQZY5EXMK4PHM2R27D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LOI5CEKNUQZY5EXMK4PHM2R27D/action/storage_attestation","attest_author":"https://pith.science/pith/LOI5CEKNUQZY5EXMK4PHM2R27D/action/author_attestation","sign_citation":"https://pith.science/pith/LOI5CEKNUQZY5EXMK4PHM2R27D/action/citation_signature","submit_replication":"https://pith.science/pith/LOI5CEKNUQZY5EXMK4PHM2R27D/action/replication_record"}},"created_at":"2026-05-18T02:54:22.788948+00:00","updated_at":"2026-05-18T02:54:22.788948+00:00"}