{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UUWKYLLHEBDF72KCOR4P5YXVT2","short_pith_number":"pith:UUWKYLLH","schema_version":"1.0","canonical_sha256":"a52cac2d6720465fe9427478fee2f59e8f1e8b0b8e35d84efbc783be36751a9d","source":{"kind":"arxiv","id":"1807.04831","version":2},"attestation_state":"computed","paper":{"title":"Hierarchical Growth is Necessary and (Sometimes) Sufficient to Self-Assemble Discrete Self-Similar Fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.ET","authors_text":"Jacob Hendricks, Joseph Opseth, Matthew Patitz, Scott Summers","submitted_at":"2018-07-12T21:28:40Z","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"},"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":"1807.04831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.ET","submitted_at":"2018-07-12T21:28:40Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"c4661ed9ea702bbce77b9edc3a1cd4d6bbd9e9f43ffc7ad20e39cb229b00d993","abstract_canon_sha256":"ac9da30c8c616c02d913d5cedf3724ddaa9065ca53f52aba3f8dcda8427d10d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:36.625299Z","signature_b64":"VO13/2SBEis9taRRGp23p0bXOFHg6c6qxdzCNWtpP4cYyLODLIk4VzfUU3RCXdJhZa0EG8Qdx09pn8y4Em5QCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a52cac2d6720465fe9427478fee2f59e8f1e8b0b8e35d84efbc783be36751a9d","last_reissued_at":"2026-05-18T00:10:36.624666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:36.624666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchical Growth is Necessary and (Sometimes) Sufficient to Self-Assemble Discrete Self-Similar Fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.ET","authors_text":"Jacob Hendricks, Joseph Opseth, Matthew Patitz, Scott Summers","submitted_at":"2018-07-12T21:28:40Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04831","kind":"arxiv","version":2},"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":"1807.04831","created_at":"2026-05-18T00:10:36.624750+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.04831v2","created_at":"2026-05-18T00:10:36.624750+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04831","created_at":"2026-05-18T00:10:36.624750+00:00"},{"alias_kind":"pith_short_12","alias_value":"UUWKYLLHEBDF","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UUWKYLLHEBDF72KC","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UUWKYLLH","created_at":"2026-05-18T12:32:56.356000+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/UUWKYLLHEBDF72KCOR4P5YXVT2","json":"https://pith.science/pith/UUWKYLLHEBDF72KCOR4P5YXVT2.json","graph_json":"https://pith.science/api/pith-number/UUWKYLLHEBDF72KCOR4P5YXVT2/graph.json","events_json":"https://pith.science/api/pith-number/UUWKYLLHEBDF72KCOR4P5YXVT2/events.json","paper":"https://pith.science/paper/UUWKYLLH"},"agent_actions":{"view_html":"https://pith.science/pith/UUWKYLLHEBDF72KCOR4P5YXVT2","download_json":"https://pith.science/pith/UUWKYLLHEBDF72KCOR4P5YXVT2.json","view_paper":"https://pith.science/paper/UUWKYLLH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.04831&json=true","fetch_graph":"https://pith.science/api/pith-number/UUWKYLLHEBDF72KCOR4P5YXVT2/graph.json","fetch_events":"https://pith.science/api/pith-number/UUWKYLLHEBDF72KCOR4P5YXVT2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UUWKYLLHEBDF72KCOR4P5YXVT2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UUWKYLLHEBDF72KCOR4P5YXVT2/action/storage_attestation","attest_author":"https://pith.science/pith/UUWKYLLHEBDF72KCOR4P5YXVT2/action/author_attestation","sign_citation":"https://pith.science/pith/UUWKYLLHEBDF72KCOR4P5YXVT2/action/citation_signature","submit_replication":"https://pith.science/pith/UUWKYLLHEBDF72KCOR4P5YXVT2/action/replication_record"}},"created_at":"2026-05-18T00:10:36.624750+00:00","updated_at":"2026-05-18T00:10:36.624750+00:00"}