Radial Interaction Tomography: Recognizing Non-Transitive Evolutionary Games from One Range-Expansion Image

• URL: http://arxiv.org/abs/2607.00378v1
• Date: Wed, 01 Jul 2026 03:23:47 GMT
• Title: Radial Interaction Tomography: Recognizing Non-Transitive Evolutionary Games from One Range-Expansion Image
• Abstract summary: We formulate a computer-vision inverse problem: from one endpoint image of an accretive multi-type expansion, recover the radius-indexed pairwise boundary-flow field.<n>The observable is a geometric signal extracted from sector-boundary curves in log-polar coordinates.
• Score: 0.2864713389096699
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Colored sectors in a microbial range expansion encode more than lineage survival counts. We formulate a computer-vision inverse problem: from one endpoint image of an accretive multi-type expansion, recover the radius-indexed pairwise boundary-flow field and test whether the visual pattern is compatible with a transitive scalar fitness hierarchy. The observable is a geometric signal extracted from sector-boundary curves in log-polar coordinates. We prove endpoint observability and stability for frozen fronts, weighted transitive/cyclic decomposition, contact-complete circular design, physical-clock and mechanism non-identifiability, exact Gaussian cyclicity testing, and Bonferroni-valid interval scanning. The benchmark is deterministic: analytic endpoint images, blurred/noisy pixel round trips, scalar-null stress tests, public-image tracing, multi-resolution mechanistic endpoints, and a non-learning frozen-front simulator. The implementation recovers pairwise edge-flow histories from endpoint images, detects cyclic residuals in a mechanistic four-type expansion, and uses those residuals as forcing signals for a dimensionless active design-control layer covering reaction-diffusion control, phenotype-frontier optimization, protocol synthesis, Monte Carlo robustness, and a downstream population-state bridge.

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