{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LU3LTSMBQ3YRIMIMMUZJIGNBMW","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":"3d7455e523fdeadce71d6be1e78517aa927010b858b567b022ce1b756a97b77b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-01-02T02:50:43Z","title_canon_sha256":"78aded5692f438f712b4f2b8df22e17b2bbe74c8362ea30ef55dbc8bb2cfeeaf"},"schema_version":"1.0","source":{"id":"1401.0359","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0359","created_at":"2026-05-18T01:28:44Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0359v5","created_at":"2026-05-18T01:28:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0359","created_at":"2026-05-18T01:28:44Z"},{"alias_kind":"pith_short_12","alias_value":"LU3LTSMBQ3YR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LU3LTSMBQ3YRIMIM","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LU3LTSMB","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:f310b4360c284762c4d7eaf06e891a023fabbad08710523fbffc4c908fe068b0","target":"graph","created_at":"2026-05-18T01:28:44Z","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 prove two tight bounds on the behavior of a model of self-assembling particles introduced by Dabby and Chen (SODA 2013), called insertion systems, where monomers insert themselves into the middle of a growing linear polymer. First, we prove that the expressive power of these systems is equal to context-free grammars, answering a question posed by Dabby and Chen. Second, we prove that systems of $k$ monomer types can deterministically construct polymers of length $n = 2^{\\Theta(k^{3/2})}$ in $O(\\log^{5/3}(n))$ expected time, and that this is optimal in both the number of monomer types and ex","authors_text":"Andrew Winslow, Benjamin Hescott, Caleb Malchik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-01-02T02:50:43Z","title":"Tight Bounds for Active Self-Assembly Using an Insertion Primitive"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0359","kind":"arxiv","version":5},"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":"sha256:48709428ee4a9b9fab044e8d36ac25058fe1d8f9b592060fd18e8361b18b9e1d","target":"record","created_at":"2026-05-18T01:28:44Z","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":"3d7455e523fdeadce71d6be1e78517aa927010b858b567b022ce1b756a97b77b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-01-02T02:50:43Z","title_canon_sha256":"78aded5692f438f712b4f2b8df22e17b2bbe74c8362ea30ef55dbc8bb2cfeeaf"},"schema_version":"1.0","source":{"id":"1401.0359","kind":"arxiv","version":5}},"canonical_sha256":"5d36b9c98186f114310c65329419a165a477080e19960b26a0324fe340f69920","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d36b9c98186f114310c65329419a165a477080e19960b26a0324fe340f69920","first_computed_at":"2026-05-18T01:28:44.692349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:44.692349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H7UJLK08mZTmi3/KI5KSjF87sD/fvUluaPMeFnwB3Y7RHazJm3MFlPrIuXLinIpFwyIf8zKeNjCy1yWZvZfOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:44.692837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0359","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48709428ee4a9b9fab044e8d36ac25058fe1d8f9b592060fd18e8361b18b9e1d","sha256:f310b4360c284762c4d7eaf06e891a023fabbad08710523fbffc4c908fe068b0"],"state_sha256":"1191fb84291c5e618ce25239fb4386e59e72d2a24d36f246cebd0233d5632648"}