{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FSEHR3BI77CFTXNRATAYRVBSA4","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":"b7d4a72ed367847ce4ddf0c7c5f8a4d46379c28172be088915d47150fb7b11e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-10T18:56:09Z","title_canon_sha256":"23fa9ac97bf709dc20b0255a4a18ae8873d4673dc1e6a3f850967a4d7731dd31"},"schema_version":"1.0","source":{"id":"1703.03799","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03799","created_at":"2026-05-18T00:48:14Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03799v2","created_at":"2026-05-18T00:48:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03799","created_at":"2026-05-18T00:48:14Z"},{"alias_kind":"pith_short_12","alias_value":"FSEHR3BI77CF","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FSEHR3BI77CFTXNR","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FSEHR3BI","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:21d11d71b4acaa3315027f6eaed37d8f87d024211e89303b3f12905ddf595e9b","target":"graph","created_at":"2026-05-18T00:48:14Z","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":"Motivated by the problem of determining unknotted routes for the scaffolding strand in DNA origami self-assembly, we examine existence and knottedness of A-trails in graphs embedded on the torus. We show that any A-trail in a checkerboard-colorable torus graph is unknotted and characterize the existence of A-trails in checkerboard-colorable torus graphs in terms of pairs of quasitrees in associated embeddings. Surface meshes are frequent targets for DNA nanostructure self-assembly, and so we study both triangular and rectangular torus grids. We show that, aside from one exceptional family, a t","authors_text":"Ada Morse, Brenna Smith, David Perry, Greta Pangborn, Jessica Greene, Jo Ellis-Monaghan, William Adkisson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-10T18:56:09Z","title":"DNA Origami and Unknotted A-trails in Torus Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03799","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":"sha256:63a4be2b94202a26b498215a81f416a49126254ce93543c51f4372f28c00d326","target":"record","created_at":"2026-05-18T00:48:14Z","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":"b7d4a72ed367847ce4ddf0c7c5f8a4d46379c28172be088915d47150fb7b11e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-10T18:56:09Z","title_canon_sha256":"23fa9ac97bf709dc20b0255a4a18ae8873d4673dc1e6a3f850967a4d7731dd31"},"schema_version":"1.0","source":{"id":"1703.03799","kind":"arxiv","version":2}},"canonical_sha256":"2c8878ec28ffc459ddb104c188d43207337447aaff9046496c09c802184ec696","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c8878ec28ffc459ddb104c188d43207337447aaff9046496c09c802184ec696","first_computed_at":"2026-05-18T00:48:14.197979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:14.197979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o5dNVktjzKgSQicX7vkVoe+oCqGWk6FkyNmNoPvxKPBXmWS/JZq22BYckF1ATcDT+uK+vwB75AMHqB19+mXuAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:14.198528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.03799","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63a4be2b94202a26b498215a81f416a49126254ce93543c51f4372f28c00d326","sha256:21d11d71b4acaa3315027f6eaed37d8f87d024211e89303b3f12905ddf595e9b"],"state_sha256":"b16203e049f49afcff0d74b834e001f2e1b91fbaa38d7fab656a75caf1984c62"}