The Physics of Survival: Fisher Blindness, Rank Collapse, and the Necessity of Basis Rotation in Complex Systems
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2026
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| _version_ | 1866902324129038336 |
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| author | Saurabh, Abhishek |
| author_facet | Saurabh, Abhishek |
| contents | <h3><strong>Description (Abstract)</strong></h3> <p><strong>Abstract</strong></p> <p>We propose a unified <strong>computational framework</strong> linking Non-Equilibrium Thermodynamics, Quantum Error Correction (QEC), and Evolutionary Biology via the geometry of <strong>Structural Time (t_3)</strong>.</p> <p>This monograph establishes an <strong>Effective Field Theory (EFT)</strong> for describing the statistical manifolds of complex adaptive systems. It demonstrates that "Systemic Risk" is not a stochastic anomaly but an invariant topological quantity—termed <strong>Structural Mass</strong>—that accumulates in the macroscopic time dimension (Renormalization Scale z) during standard execution cycles (t_1).</p> <p><strong>Core Theoretical Contributions:</strong></p> <ol> <li> <p><strong>The Fisher-Blindness No-Go Theorem:</strong> We prove that any boundary observer optimizing solely for short-term execution efficiency (Delta X -> 0) becomes statistically blind to structural phase transitions. This is derived strictly from the <strong>Cramér-Rao Bound</strong>, defining a fundamental <strong>Lag Horizon</strong> beyond which risk is mathematically unobservable.</p> </li> <li> <p><strong>Rank Collapse:</strong> We identify the universal failure mode of complex systems as a dimensional reduction of the Covariance Matrix. In Finance, this manifests as a "Liquidity Bomb"; in AI, as "Mode Collapse" (Hallucination); and in Biology, as "Mutational Meltdown."</p> </li> <li> <p><strong>The Stability Governance Limit:</strong> We derive an information-theoretic uncertainty principle, $\Delta X \cdot \Delta P \ge \hbar_{eff}/2$, proving that "Hyper-Stability" (Squeezing) inevitably forces structural risk ($\Delta P$) to diverge.</p> </li> </ol> <p><strong>Biological & Engineering Implications:</strong></p> <p>The framework re-interprets <strong>Sexual Reproduction (Mating)</strong> not as a biological idiosyncrasy, but as a geometric constraint requirement. We demonstrate that mating functions as a <strong>Distributed Error Correction Algorithm</strong> that utilizes <strong>Basis Rotation</strong> to expose and purge hidden structural errors that are invisible to asexual (clonal) lineages.</p> <p>Finally, we propose engineering applications of these principles to solve systemic fragility in synthetic systems:</p> <ul> <li> <p><strong>The Topological Data Analysis (TDA) Engine:</strong> An FPGA-based instrument for detecting "Liquidity Bombs" in financial markets by measuring the topological winding number of the trade manifold.</p> </li> <li> <p><strong>Algorithmic Recombination:</strong> A protocol for AI training to prevent neural mode collapse (hallucination) by periodically rotating the basis vectors of the model weights.</p> </li> </ul> <p><strong>Keywords:</strong> Systemic Risk, Information Geometry, Quantum Error Correction, Evolutionary Dynamics, Fisher Information, Rank Collapse, Econophysics, AI Safety, Topological Data Analysis.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19425437 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Physics of Survival: Fisher Blindness, Rank Collapse, and the Necessity of Basis Rotation in Complex Systems Saurabh, Abhishek Geometric governance, Complex systems, Control theory, Information geometry, Dynamical systems, Risk and stability <h3><strong>Description (Abstract)</strong></h3> <p><strong>Abstract</strong></p> <p>We propose a unified <strong>computational framework</strong> linking Non-Equilibrium Thermodynamics, Quantum Error Correction (QEC), and Evolutionary Biology via the geometry of <strong>Structural Time (t_3)</strong>.</p> <p>This monograph establishes an <strong>Effective Field Theory (EFT)</strong> for describing the statistical manifolds of complex adaptive systems. It demonstrates that "Systemic Risk" is not a stochastic anomaly but an invariant topological quantity—termed <strong>Structural Mass</strong>—that accumulates in the macroscopic time dimension (Renormalization Scale z) during standard execution cycles (t_1).</p> <p><strong>Core Theoretical Contributions:</strong></p> <ol> <li> <p><strong>The Fisher-Blindness No-Go Theorem:</strong> We prove that any boundary observer optimizing solely for short-term execution efficiency (Delta X -> 0) becomes statistically blind to structural phase transitions. This is derived strictly from the <strong>Cramér-Rao Bound</strong>, defining a fundamental <strong>Lag Horizon</strong> beyond which risk is mathematically unobservable.</p> </li> <li> <p><strong>Rank Collapse:</strong> We identify the universal failure mode of complex systems as a dimensional reduction of the Covariance Matrix. In Finance, this manifests as a "Liquidity Bomb"; in AI, as "Mode Collapse" (Hallucination); and in Biology, as "Mutational Meltdown."</p> </li> <li> <p><strong>The Stability Governance Limit:</strong> We derive an information-theoretic uncertainty principle, $\Delta X \cdot \Delta P \ge \hbar_{eff}/2$, proving that "Hyper-Stability" (Squeezing) inevitably forces structural risk ($\Delta P$) to diverge.</p> </li> </ol> <p><strong>Biological & Engineering Implications:</strong></p> <p>The framework re-interprets <strong>Sexual Reproduction (Mating)</strong> not as a biological idiosyncrasy, but as a geometric constraint requirement. We demonstrate that mating functions as a <strong>Distributed Error Correction Algorithm</strong> that utilizes <strong>Basis Rotation</strong> to expose and purge hidden structural errors that are invisible to asexual (clonal) lineages.</p> <p>Finally, we propose engineering applications of these principles to solve systemic fragility in synthetic systems:</p> <ul> <li> <p><strong>The Topological Data Analysis (TDA) Engine:</strong> An FPGA-based instrument for detecting "Liquidity Bombs" in financial markets by measuring the topological winding number of the trade manifold.</p> </li> <li> <p><strong>Algorithmic Recombination:</strong> A protocol for AI training to prevent neural mode collapse (hallucination) by periodically rotating the basis vectors of the model weights.</p> </li> </ul> <p><strong>Keywords:</strong> Systemic Risk, Information Geometry, Quantum Error Correction, Evolutionary Dynamics, Fisher Information, Rank Collapse, Econophysics, AI Safety, Topological Data Analysis.</p> |
| title | The Physics of Survival: Fisher Blindness, Rank Collapse, and the Necessity of Basis Rotation in Complex Systems |
| topic | Geometric governance, Complex systems, Control theory, Information geometry, Dynamical systems, Risk and stability |
| url | https://doi.org/10.5281/zenodo.19425437 |