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pith:IDCMOTKX

pith:2026:IDCMOTKXHNFVE67MGXE4EX7AUT

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Viability Space Decomposition: A geometric partition of survival outcomes in single- and multi-agent systems

Connor McShaffrey, Randall D. Beer

Viability space decomposition partitions state space into regions of qualitatively similar survival outcomes using mortality, ordering, and collapse manifolds.

arxiv:2605.16753 v1 · 2026-05-16 · q-bio.QM · math.DS

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Claims

C1strongest claim

Viability space decomposition reveals how several new classes of manifolds (mortality, ordering, and collapse) permit a complete decomposition of state space into regions of qualitatively similar survival outcomes: a viability portrait.

C2weakest assumption

That the introduced manifolds can be identified and used to achieve a complete decomposition for the class of viability-constrained ODE models without model-specific limitations that would leave some survival outcomes unclassified.

C3one line summary

Viability space decomposition decomposes state space in viability-constrained dynamical systems into qualitatively similar survival regions via mortality, ordering, and collapse manifolds, demonstrated on subcellular, cellular, and coupled-cell models.

References

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[1] This makes the set of molecules autocatalytic

[2] Numerical exploration To approximate the possible existential outcomes in the single-cell physiology, we uniformly sample a million initial conditions in the range [Mi] ∈ [0, 20]. We then numerically

[3] The complement of the viability region V α, colored black, corresponds to where the total survival time is zero because the agent cannot exist beyond its viability region

[4] Viability portrait A phase portrait analysis within the cell’s viability region reveals two equilibrium points: a saddle node EPS = (4 .008, 2.407) (light green point) and a sta- ble equilibrium point

[5] gives an ordering manifold O shown as a purple con- tour that separates T ′ 1 and T ′ 2 (Fig. 5(c)). Zooming in closer around o and sampling another 160,000 initial con- ditions for improved resolutio

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Receipt and verification

First computed	2026-05-20T00:03:19.847409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40c4c74d573b4b527bec35c9c25fe0a4c2dc6019721614228e32a0b26ef54fcf

Aliases

arxiv: 2605.16753 · arxiv_version: 2605.16753v1 · doi: 10.48550/arxiv.2605.16753 · pith_short_12: IDCMOTKXHNFV · pith_short_16: IDCMOTKXHNFVE67M · pith_short_8: IDCMOTKX

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/IDCMOTKXHNFVE67MGXE4EX7AUT \
  | 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: 40c4c74d573b4b527bec35c9c25fe0a4c2dc6019721614228e32a0b26ef54fcf

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "60023d5988fcfd695f6f23e05140ec542a3b032a0b4baad5071f1d18e2c8bdd7",
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      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-bio.QM",
    "submitted_at": "2026-05-16T02:09:14Z",
    "title_canon_sha256": "b574791e9c866136e32f1fac19d3bce1476ff2ca66c77ef4c37dec970cad1de8"
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  "source": {
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    "kind": "arxiv",
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