{"paper":{"title":"A Rigid Category of DNA Secondary Structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"DNA sequences form objects and non-pseudoknotted secondary structures form morphisms in a strict pivotal monoidal category.","cross_cats":["cs.ET"],"primary_cat":"math.CT","authors_text":"Andr\\'es Ortiz-Mu\\~noz","submitted_at":"2026-05-12T20:45:00Z","abstract_excerpt":"We construct a strict pivotal monoidal category $\\mathcal{D}_{\\mathrm{DNA}}$ whose objects are DNA sequences (words over $\\{A,C,G,T\\}$) and whose morphisms are isotopy classes of typed noncrossing planar matchings, composed of through-strands and Watson-Crick-typed arcs, in a rectangle with source and target boundaries. The dual of a sequence is its reverse complement, evaluation and coevaluation are canonical duplex pairings, and the snake identities hold by planar isotopy. A bending correspondence identifies each morphism $x \\to y$ with a secondary structure on the combined word $x{}^{\\vee} "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We construct a strict pivotal monoidal category D_DNA whose objects are DNA sequences (words over {A,C,G,T}) and whose morphisms are isotopy classes of typed noncrossing planar matchings... the generalized elements ε → w are exactly the non-pseudoknotted secondary structures on w.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That every morphism x → y corresponds exactly to a secondary structure on the combined word x^∨ y via the bending correspondence, and that composition reduces to a zip-and-transfer operation without introducing pseudoknots or crossings.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A rigid monoidal category is constructed with DNA sequences as objects and non-pseudoknotted secondary structures as morphisms via planar matchings.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"DNA sequences form objects and non-pseudoknotted secondary structures form morphisms in a strict pivotal monoidal category.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c8e498c27315fab250a42fa951ad89dc38146f7a745b2e4383cde5acbf31fe57"},"source":{"id":"2605.12740","kind":"arxiv","version":1},"verdict":{"id":"b986f907-1aae-4ad2-84ec-f389f7eb35cd","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:41:17.200553Z","strongest_claim":"We construct a strict pivotal monoidal category D_DNA whose objects are DNA sequences (words over {A,C,G,T}) and whose morphisms are isotopy classes of typed noncrossing planar matchings... the generalized elements ε → w are exactly the non-pseudoknotted secondary structures on w.","one_line_summary":"A rigid monoidal category is constructed with DNA sequences as objects and non-pseudoknotted secondary structures as morphisms via planar matchings.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That every morphism x → y corresponds exactly to a secondary structure on the combined word x^∨ y via the bending correspondence, and that composition reduces to a zip-and-transfer operation without introducing pseudoknots or crossings.","pith_extraction_headline":"DNA sequences form objects and non-pseudoknotted secondary structures form morphisms in a strict pivotal monoidal category."},"references":{"count":21,"sample":[{"doi":"","year":2010,"title":"Mathematical foundations for a compositional distributional model of meaning","work_id":"fb62d8c5-e6b1-49dd-9c02-97e57b74e187","ref_index":1,"cited_arxiv_id":"1003.4394","is_internal_anchor":true},{"doi":"","year":1992,"title":"W. Fontana. Algorithmic chemistry: A model for functional self-organization. In C. G. Langton, C. Taylor, J. D. Farmer, and S. Rasmussen, editors,Artificial Life II. Addison-Wesley, 1992","work_id":"f67d1ea5-0172-44ab-b0db-18baa849a1f8","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/s0092-8240(05)80205-8","year":1994,"title":"W. Fontana and L. W. Buss. The arrival of the fittest: Toward a theory of biological organization.Bulletin of Mathematical Biology, 56:1–64, 1994.doi:10.1016/S0092-8240(05)80205-8","work_id":"96b9c67e-2151-4a82-af4d-e4624376afee","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1996,"title":"W. Fontana and L. W. Buss. The barrier of objects: From dynamical systems to bounded organizations. In J. Casti and A. Karlqvist, editors,Boundaries and Barriers, pages 56–116. Addison-Wesley, 1996","work_id":"7a3e3131-c13e-4538-9d44-0d01bf74fa09","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1103/physreve.47.2083","year":2083,"title":"W. Fontana, P. F. Stadler, E. G. Bornberg-Bauer, T. Griesmacher, I. L. Hofacker, M. Tacker, P. Tarazona, E. D. Weinberger, and P. Schuster. RNA folding and combinatory landscapes.Physical Review E, 47","work_id":"02240035-e54d-4ae1-85f3-c580a72ba2c7","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":21,"snapshot_sha256":"3435078af02269e33d13c94297cd9801cc894b03ce9895803a739b9e07492535","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"b9f5bd0c04fb5cc7bf03f3809c18e731cec1d8ef50cb6b69c630d70bde63c52b"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}