Pith Number

pith:3HYHBVQR

pith:2026:3HYHBVQRIOYSBUYTPTR47AUE66

not attested not anchored not stored refs resolved

How nature discovers rare Turing islands: exploration by common limit cycles

Antonio Matas-Gil, Robert G. Endres, Seyoon Kim

Coupling limit cycles to reaction-diffusion systems lets biology explore rare Turing pattern conditions dynamically.

arxiv:2605.15839 v1 · 2026-05-15 · q-bio.CB · math.DS · physics.bio-ph · q-bio.PE · q-bio.QM

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\usepackage{pith}
\pithnumber{3HYHBVQRIOYSBUYTPTR47AUE66}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

By coupling a reaction-diffusion system to an orbit that modulates some of its parameters, the system can dynamically sweep through Turing-permissive regimes and generate transient spatial patterns.

C2weakest assumption

That biologically plausible coupling exists between common limit cycles and reaction-diffusion parameters such that the modulation sweeps through Turing regimes without preventing pattern formation when conditions are met.

C3one line summary

Coupling limit cycles to reaction-diffusion systems allows dynamic exploration of Turing-permissive regimes, generating transient patterns and improving robustness via an entropy-based Fourier measure.

References

45 extracted · 45 resolved · 0 Pith anchors

[1] The chemical basis of morphogenesis.Philosophical Transactions of the Royal Society of London 1952 · doi:10.1098/rstb.1952.0012

[2] Antonio Matas-Gil and Robert G. Endres. Tuning and toggling turing patterns in gene circuits.Cell Reports Physical Science, 7(1), January 2026. ISSN 2666-3864. doi: 10.1016/ j.xcrp.2025.103056. URLhtt 2026 · doi:10.1016/j.xcrp.2025.103056

[3] Scholes, David Schnoerr, Mark Isalan, and Michael P 2019 · doi:10.1016/j.cels.2019.07.007

[4] W. Driever and C. Nüsslein-Volhard. The bicoid protein determines position in the Drosophila embryo in a concentration-dependent manner.Cell, 54(1):95–104, July 1988. ISSN 0092-8674. doi: 10.1016/0092 1988 · doi:10.1016/0092-8674(88)90183-3

[5] J. Raspopovic, L. Marcon, L. Russo, and J. Sharpe. Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients.Science, 345(6196): 566–570, August 2014. doi: 10.11 2014 · doi:10.1126/science.1252960

Receipt and verification

First computed	2026-05-20T00:01:21.078088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9f070d61143b120d3137ce3cf8284f7b12bca3cda4930d361ee5e18c6e87a11

Aliases

arxiv: 2605.15839 · arxiv_version: 2605.15839v1 · doi: 10.48550/arxiv.2605.15839 · pith_short_12: 3HYHBVQRIOYS · pith_short_16: 3HYHBVQRIOYSBUYT · pith_short_8: 3HYHBVQR

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3HYHBVQRIOYSBUYTPTR47AUE66 \
  | 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: d9f070d61143b120d3137ce3cf8284f7b12bca3cda4930d361ee5e18c6e87a11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ab6b193022ed3631a536238292ecd819879e2d430c29497284cbb337aee52f0",
    "cross_cats_sorted": [
      "math.DS",
      "physics.bio-ph",
      "q-bio.PE",
      "q-bio.QM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "q-bio.CB",
    "submitted_at": "2026-05-15T10:54:01Z",
    "title_canon_sha256": "2ba3a474a0d7e9cc6f74841be3d62408e6f6ee17da257dd4ec24ef291986ae18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15839",
    "kind": "arxiv",
    "version": 1
  }
}