Crossing the Functional Desert: Cascade-Driven Assembly and Feasibility Transitions in Early Life
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909999635103744 |
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| author | Wilkerson, Galen J. |
| author_facet | Wilkerson, Galen J. |
| contents | The origin of life poses a problem of combinatorial feasibility: How can temporally supported functional organization arise in exponentially branching assembly spaces when unguided exploration behaves as a memoryless random walk? We show that nonlinear threshold-cascade dynamics in connected interaction networks provide a minimal, substrate-agnostic mechanism that can soften this obstruction. Below a critical connectivity threshold, cascades die out locally and structured input-output response mappings remain sparse and transient-a "functional desert" in which accumulation is dynamically unsupported. Near the critical percolation threshold, system-spanning cascades emerge, enabling discriminative functional responses. We illustrate this transition using a minimal toy model and generalize the argument to arbitrary networked systems. Also near criticality, cascades introduce finite-timescale structural and functional coherence, directional bias, and weak dynamical path-dependence into otherwise memoryless exploration, allowing biased accumulation. This connectivity-driven transition-functional percolation-requires only generic ingredients: interacting units, nonlinear thresholds, influence transmission, and non-zero coherence times. The mechanism does not explain specific biochemical pathways, but it identifies a necessary dynamical regime in which structured functional organization can emerge and be temporarily supported, providing a physical foundation for how combinatorial feasibility barriers can be crossed through network dynamics alone. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_06272 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Crossing the Functional Desert: Cascade-Driven Assembly and Feasibility Transitions in Early Life Wilkerson, Galen J. Physics and Society Adaptation and Self-Organizing Systems Biological Physics Molecular Networks Populations and Evolution 37N25 J.3; J.2; G.2.2; G.3; I.6.5; F.2.2 The origin of life poses a problem of combinatorial feasibility: How can temporally supported functional organization arise in exponentially branching assembly spaces when unguided exploration behaves as a memoryless random walk? We show that nonlinear threshold-cascade dynamics in connected interaction networks provide a minimal, substrate-agnostic mechanism that can soften this obstruction. Below a critical connectivity threshold, cascades die out locally and structured input-output response mappings remain sparse and transient-a "functional desert" in which accumulation is dynamically unsupported. Near the critical percolation threshold, system-spanning cascades emerge, enabling discriminative functional responses. We illustrate this transition using a minimal toy model and generalize the argument to arbitrary networked systems. Also near criticality, cascades introduce finite-timescale structural and functional coherence, directional bias, and weak dynamical path-dependence into otherwise memoryless exploration, allowing biased accumulation. This connectivity-driven transition-functional percolation-requires only generic ingredients: interacting units, nonlinear thresholds, influence transmission, and non-zero coherence times. The mechanism does not explain specific biochemical pathways, but it identifies a necessary dynamical regime in which structured functional organization can emerge and be temporarily supported, providing a physical foundation for how combinatorial feasibility barriers can be crossed through network dynamics alone. |
| title | Crossing the Functional Desert: Cascade-Driven Assembly and Feasibility Transitions in Early Life |
| topic | Physics and Society Adaptation and Self-Organizing Systems Biological Physics Molecular Networks Populations and Evolution 37N25 J.3; J.2; G.2.2; G.3; I.6.5; F.2.2 |
| url | https://arxiv.org/abs/2601.06272 |