{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YBFZ5ZGWTBZLFU4OY73ZZTNR6V","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":"c81ff26ec55cac4bec3f657ace60c3a206c6730a6095f05e77ccac0f4c7e5c69","cross_cats_sorted":["cs.ET"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-10-13T22:40:53Z","title_canon_sha256":"0e3796fdebd3c0e0c798cc61f91dd7081df26b4a5f238f25e5013ae63eb0645f"},"schema_version":"1.0","source":{"id":"1510.03919","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03919","created_at":"2026-05-18T01:04:45Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03919v3","created_at":"2026-05-18T01:04:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03919","created_at":"2026-05-18T01:04:45Z"},{"alias_kind":"pith_short_12","alias_value":"YBFZ5ZGWTBZL","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YBFZ5ZGWTBZLFU4O","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YBFZ5ZGW","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:fa53505206129791e25c077714e91985908311347a1440a159f72981b7b74670","target":"graph","created_at":"2026-05-18T01:04:45Z","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"},"paper":{"abstract_excerpt":"We analyze the number of tile types $t$, bins $b$, and stages necessary to assemble $n \\times n$ squares and scaled shapes in the staged tile assembly model. For $n \\times n$ squares, we prove $\\mathcal{O}(\\frac{\\log{n} - tb - t\\log t}{b^2} + \\frac{\\log \\log b}{\\log t})$ stages suffice and $\\Omega(\\frac{\\log{n} - tb - t\\log t}{b^2})$ are necessary for almost all $n$. For shapes $S$ with Kolmogorov complexity $K(S)$, we prove $\\mathcal{O}(\\frac{K(S) - tb - t\\log t}{b^2} + \\frac{\\log \\log b}{\\log t})$ stages suffice and $\\Omega(\\frac{K(S) - tb - t\\log t}{b^2})$ are necessary to assemble a scaled","authors_text":"Andrew Winslow, Cameron Chalk, Eric Martinez, Luis Vega, Robert Schweller, Tim Wylie","cross_cats":["cs.ET"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-10-13T22:40:53Z","title":"Optimal Staged Self-Assembly of General Shapes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03919","kind":"arxiv","version":3},"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":"sha256:01106a692dd493b2eb1198f2f27d381061709209fdb4c6b4c2694859671bde21","target":"record","created_at":"2026-05-18T01:04:45Z","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":"c81ff26ec55cac4bec3f657ace60c3a206c6730a6095f05e77ccac0f4c7e5c69","cross_cats_sorted":["cs.ET"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-10-13T22:40:53Z","title_canon_sha256":"0e3796fdebd3c0e0c798cc61f91dd7081df26b4a5f238f25e5013ae63eb0645f"},"schema_version":"1.0","source":{"id":"1510.03919","kind":"arxiv","version":3}},"canonical_sha256":"c04b9ee4d69872b2d38ec7f79ccdb1f56196f9112f60e31229281b7702e83c1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c04b9ee4d69872b2d38ec7f79ccdb1f56196f9112f60e31229281b7702e83c1b","first_computed_at":"2026-05-18T01:04:45.678402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:45.678402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v9hCI7iHrJ0Pm8Rr8w4ec/GtBN1Ia6a/LqGqZmTbhDFxw3FIy6GZxQvtbkq5WWK9eIZD6xSxZsSc2WmCTnWeCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:45.678918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03919","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01106a692dd493b2eb1198f2f27d381061709209fdb4c6b4c2694859671bde21","sha256:fa53505206129791e25c077714e91985908311347a1440a159f72981b7b74670"],"state_sha256":"85f1541204e8f967af9e420f1a2011a2dc670fdc9591c6f2db7326684e7be207"}