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2025
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| Acceso en liña: | https://doi.org/10.5281/zenodo.17855921 |
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| author | Atkinson, James |
| author_facet | Atkinson, James |
| contents | <p>Project website: https://www.integrodynamics.org/</p> <p>This paper develops a formal theory of symmetry as a governing constraint in allocation, governance, and algorithmic decision systems. Rather than treating fairness as a declared norm or external corrective, the framework treats symmetry as a structural property that must be preserved dynamically under stochastic stress. When a system is subjected to symmetric perturbation, sustained deviation from its declared proportions constitutes measurable evidence of imbalance, hidden asymmetry, or motivated drift.</p> <p>At its core, the model treats every allocation as an experiment in structural balance. Under entropy-certified randomness and bounded rational updating, a system that genuinely instantiates symmetric rules must converge toward its declared proportions without external correction. Failure of convergence is not interpreted as implementation error but as evidential exposure of asymmetry embedded in the system’s internal geometry.</p> <p>The framework integrates stochastic kernel design, adaptive weighting, and conservation-style procedural constraints to ensure that symmetry is not assumed but enforced through outcome dynamics. In this formulation, symmetry becomes both a generative principle and an audit signal: it governs behaviour while simultaneously measuring its own violation.</p> <p>This paper establishes symmetry as the procedural axis of a broader mathematical programme of integrity. Preceded by the formalisation of contradiction as an epistemic diagnostic and followed by institutional-scale sentinel architectures, the theory situates symmetry as the bridge between reasoning and governance — the mechanism by which declared fairness either proves itself in motion or collapses under stress.</p> <p><strong>Keywords:</strong> symmetry; procedural integrity; stochastic governance; evidential fairness; entropy-certified randomness; proportional drift; bounded rational dynamics; procedural audit; algorithmic accountability; convergence testing; integrity verification; epistemic symmetry; governance design; adversarial calibration; procedural neutrality; information entropy; fairness-by-construction; systemic balance.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17855921 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | Part II - SYMMETRY: invariance, entropy and the conservation of integrity Atkinson, James mathematics of integrity symmetric convergence procedural integrity stochastic governance evidential fairness entropy-certified randomness proportional drift bounded rational dynamics procedural audit algorithmic accountability fairness diagnostics convergence testing integrity verification epistemic symmetry governance design adversarial calibration procedural neutrality information entropy fairness-by-construction systemic balance <p>Project website: https://www.integrodynamics.org/</p> <p>This paper develops a formal theory of symmetry as a governing constraint in allocation, governance, and algorithmic decision systems. Rather than treating fairness as a declared norm or external corrective, the framework treats symmetry as a structural property that must be preserved dynamically under stochastic stress. When a system is subjected to symmetric perturbation, sustained deviation from its declared proportions constitutes measurable evidence of imbalance, hidden asymmetry, or motivated drift.</p> <p>At its core, the model treats every allocation as an experiment in structural balance. Under entropy-certified randomness and bounded rational updating, a system that genuinely instantiates symmetric rules must converge toward its declared proportions without external correction. Failure of convergence is not interpreted as implementation error but as evidential exposure of asymmetry embedded in the system’s internal geometry.</p> <p>The framework integrates stochastic kernel design, adaptive weighting, and conservation-style procedural constraints to ensure that symmetry is not assumed but enforced through outcome dynamics. In this formulation, symmetry becomes both a generative principle and an audit signal: it governs behaviour while simultaneously measuring its own violation.</p> <p>This paper establishes symmetry as the procedural axis of a broader mathematical programme of integrity. Preceded by the formalisation of contradiction as an epistemic diagnostic and followed by institutional-scale sentinel architectures, the theory situates symmetry as the bridge between reasoning and governance — the mechanism by which declared fairness either proves itself in motion or collapses under stress.</p> <p><strong>Keywords:</strong> symmetry; procedural integrity; stochastic governance; evidential fairness; entropy-certified randomness; proportional drift; bounded rational dynamics; procedural audit; algorithmic accountability; convergence testing; integrity verification; epistemic symmetry; governance design; adversarial calibration; procedural neutrality; information entropy; fairness-by-construction; systemic balance.</p> |
| title | Part II - SYMMETRY: invariance, entropy and the conservation of integrity |
| topic | mathematics of integrity symmetric convergence procedural integrity stochastic governance evidential fairness entropy-certified randomness proportional drift bounded rational dynamics procedural audit algorithmic accountability fairness diagnostics convergence testing integrity verification epistemic symmetry governance design adversarial calibration procedural neutrality information entropy fairness-by-construction systemic balance |
| url | https://doi.org/10.5281/zenodo.17855921 |