{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UUWKYLLHEBDF72KCOR4P5YXVT2","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":"ac9da30c8c616c02d913d5cedf3724ddaa9065ca53f52aba3f8dcda8427d10d5","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.ET","submitted_at":"2018-07-12T21:28:40Z","title_canon_sha256":"c4661ed9ea702bbce77b9edc3a1cd4d6bbd9e9f43ffc7ad20e39cb229b00d993"},"schema_version":"1.0","source":{"id":"1807.04831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04831","created_at":"2026-05-18T00:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04831v2","created_at":"2026-05-18T00:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04831","created_at":"2026-05-18T00:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"UUWKYLLHEBDF","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UUWKYLLHEBDF72KC","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UUWKYLLH","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:4ab0b6b5bf406786413ee8c363e26df4b896d1089bedd896f5e7c1fed678c8b5","target":"graph","created_at":"2026-05-18T00:10:36Z","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":"In this paper, we prove that in the abstract Tile Assembly Model (aTAM), an accretion-based model which only allows for a single tile to attach to a growing assembly at each step, there are no tile assembly systems capable of self-assembling the discrete self-similar fractals known as the \"H\" and \"U\" fractals. We then show that in a related model which allows for hierarchical self-assembly, the 2-Handed Assembly Model (2HAM), there does exist a tile assembly systems which self-assembles the \"U\" fractal and conjecture that the same holds for the \"H\" fractal. This is the first example of discret","authors_text":"Jacob Hendricks, Joseph Opseth, Matthew Patitz, Scott Summers","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.ET","submitted_at":"2018-07-12T21:28:40Z","title":"Hierarchical Growth is Necessary and (Sometimes) Sufficient to Self-Assemble Discrete Self-Similar Fractals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04831","kind":"arxiv","version":2},"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:ec5c78ff8d2291138e2d2f3dba60d8b2c776d9d23d5cc1a2989c3023bf9573bc","target":"record","created_at":"2026-05-18T00:10:36Z","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":"ac9da30c8c616c02d913d5cedf3724ddaa9065ca53f52aba3f8dcda8427d10d5","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.ET","submitted_at":"2018-07-12T21:28:40Z","title_canon_sha256":"c4661ed9ea702bbce77b9edc3a1cd4d6bbd9e9f43ffc7ad20e39cb229b00d993"},"schema_version":"1.0","source":{"id":"1807.04831","kind":"arxiv","version":2}},"canonical_sha256":"a52cac2d6720465fe9427478fee2f59e8f1e8b0b8e35d84efbc783be36751a9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a52cac2d6720465fe9427478fee2f59e8f1e8b0b8e35d84efbc783be36751a9d","first_computed_at":"2026-05-18T00:10:36.624666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:36.624666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VO13/2SBEis9taRRGp23p0bXOFHg6c6qxdzCNWtpP4cYyLODLIk4VzfUU3RCXdJhZa0EG8Qdx09pn8y4Em5QCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:36.625299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec5c78ff8d2291138e2d2f3dba60d8b2c776d9d23d5cc1a2989c3023bf9573bc","sha256:4ab0b6b5bf406786413ee8c363e26df4b896d1089bedd896f5e7c1fed678c8b5"],"state_sha256":"f7f83a338312369b2170c9d6f93db1bd0bc425574402cda95e78831591189d17"}