{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CKYZANY6TWRF33W5FLTZA7T66G","short_pith_number":"pith:CKYZANY6","schema_version":"1.0","canonical_sha256":"12b190371e9da25deedd2ae7907e7ef1ac7a3659d26ce8b341cf667b3b59393d","source":{"kind":"arxiv","id":"1409.1619","version":1},"attestation_state":"computed","paper":{"title":"A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tile set synthesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Aleck Johnsen, Ming-Yang Kao, Shinnosuke Seki","submitted_at":"2014-09-04T21:29:02Z","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 >= 1, k-PATS is a variant of PATS that restricts input patterns to those with at most $k$ colors. A computer-assisted proof has been recently proposed for 2-PATS by Kari et al. [arXiv:1404.0967 (2014)]. In contrast, the best known manually-checkable proof is for the NP-hardness of 29-PATS by Johnsen, Kao, and Seki [ISAAC 2013, LNCS 8283, pp.~699-710]. We propose a manually-checkable proof for the NP-hardness of 11-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":"1409.1619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-09-04T21:29:02Z","cross_cats_sorted":[],"title_canon_sha256":"59c3ad125c0d0a3d5ecd61e76f86ca3e38c9af54ec539eef90df34faf218a0fb","abstract_canon_sha256":"a9979f468f2290403700b10d8d1268e63c67ac2bafa4dc85a5238fdbb1bc2b07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:25.653727Z","signature_b64":"j1IDU4gngxynoBmIPuoBqAHtMf2efH8AmdT5yUU7ynBZfgzsUYnxrj9l3jX4urcJlEtHW4t/oaUNfY66gUkXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12b190371e9da25deedd2ae7907e7ef1ac7a3659d26ce8b341cf667b3b59393d","last_reissued_at":"2026-05-18T02:43:25.653001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:25.653001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tile set synthesis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Aleck Johnsen, Ming-Yang Kao, Shinnosuke Seki","submitted_at":"2014-09-04T21:29:02Z","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 >= 1, k-PATS is a variant of PATS that restricts input patterns to those with at most $k$ colors. A computer-assisted proof has been recently proposed for 2-PATS by Kari et al. [arXiv:1404.0967 (2014)]. In contrast, the best known manually-checkable proof is for the NP-hardness of 29-PATS by Johnsen, Kao, and Seki [ISAAC 2013, LNCS 8283, pp.~699-710]. We propose a manually-checkable proof for the NP-hardness of 11-PATS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1619","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":"1409.1619","created_at":"2026-05-18T02:43:25.653122+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1619v1","created_at":"2026-05-18T02:43:25.653122+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1619","created_at":"2026-05-18T02:43:25.653122+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKYZANY6TWRF","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKYZANY6TWRF33W5","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKYZANY6","created_at":"2026-05-18T12:28:22.404517+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/CKYZANY6TWRF33W5FLTZA7T66G","json":"https://pith.science/pith/CKYZANY6TWRF33W5FLTZA7T66G.json","graph_json":"https://pith.science/api/pith-number/CKYZANY6TWRF33W5FLTZA7T66G/graph.json","events_json":"https://pith.science/api/pith-number/CKYZANY6TWRF33W5FLTZA7T66G/events.json","paper":"https://pith.science/paper/CKYZANY6"},"agent_actions":{"view_html":"https://pith.science/pith/CKYZANY6TWRF33W5FLTZA7T66G","download_json":"https://pith.science/pith/CKYZANY6TWRF33W5FLTZA7T66G.json","view_paper":"https://pith.science/paper/CKYZANY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1619&json=true","fetch_graph":"https://pith.science/api/pith-number/CKYZANY6TWRF33W5FLTZA7T66G/graph.json","fetch_events":"https://pith.science/api/pith-number/CKYZANY6TWRF33W5FLTZA7T66G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKYZANY6TWRF33W5FLTZA7T66G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKYZANY6TWRF33W5FLTZA7T66G/action/storage_attestation","attest_author":"https://pith.science/pith/CKYZANY6TWRF33W5FLTZA7T66G/action/author_attestation","sign_citation":"https://pith.science/pith/CKYZANY6TWRF33W5FLTZA7T66G/action/citation_signature","submit_replication":"https://pith.science/pith/CKYZANY6TWRF33W5FLTZA7T66G/action/replication_record"}},"created_at":"2026-05-18T02:43:25.653122+00:00","updated_at":"2026-05-18T02:43:25.653122+00:00"}