Pith Number

pith:W3F362HZ

pith:2026:W3F362HZIVDX63ZZZJ7OUJEEB4

not attested not anchored not stored refs resolved

A Rigid Category of DNA Secondary Structures

Andr\'es Ortiz-Mu\~noz

DNA sequences form objects and non-pseudoknotted secondary structures form morphisms in a strict pivotal monoidal category.

arxiv:2605.12740 v1 · 2026-05-12 · math.CT · cs.ET

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one line summary

A rigid monoidal category is constructed with DNA sequences as objects and non-pseudoknotted secondary structures as morphisms via planar matchings.

References

21 extracted · 21 resolved · 1 Pith anchors

[1] Mathematical foundations for a compositional distributional model of meaning 2010 · arXiv:1003.4394

[2] 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 1992

[3] 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 1994 · doi:10.1016/s0092-8240(05)80205-8

[4] 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 1996

[5] 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 2083 · doi:10.1103/physreve.47.2083

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:49.102228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6cbbf68f945477f6f39ca7eea24840f397dbadb8ec796ee4fd22b9064633e32

Aliases

arxiv: 2605.12740 · arxiv_version: 2605.12740v1 · doi: 10.48550/arxiv.2605.12740 · pith_short_12: W3F362HZIVDX · pith_short_16: W3F362HZIVDX63ZZ · pith_short_8: W3F362HZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W3F362HZIVDX63ZZZJ7OUJEEB4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b6cbbf68f945477f6f39ca7eea24840f397dbadb8ec796ee4fd22b9064633e32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd7257531f178cd6e3a40cae1b2e5c9dbe049661b272fd08bee0e9b8e69ea565",
    "cross_cats_sorted": [
      "cs.ET"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-05-12T20:45:00Z",
    "title_canon_sha256": "2140f6eef5793a1ef8d4ccbd0af6ae5670aef1842ce37d4cbb77da1c6bdbefe2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12740",
    "kind": "arxiv",
    "version": 1
  }
}