NeuroCore™: Mathematical Formalization
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2026
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| _version_ | 1866901137198678016 |
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| author | Nicoletti, Davide Luca |
| author_facet | Nicoletti, Davide Luca |
| contents | <div> <div> <div> <h1>Emergent Dynamical Regimes Architecture</h1> </div> </div> </div> <div> <p><br>First public theoretical disclosure.<br>This release formalizes the 7-layer multilayer conceptual structure for high-entropy flux analysis. It establishes the mathematical basis for regime identification (Layer 3) and state space partitioning (Layer 4), providing the empirical stability threshold (Kc ≈ 1.441).</p> <div> Emergent Dynamical Regimes in High-Entropy Flux. </div> <p>Layer Description</p> <p>Layer O Configuration space </p> <p>Layer 1 Flow / map : → </p> <p>Layer 2 State evolution ( ) = ( 0 )</p> <p>Layer 3 Basins / Regimes = { ( )}</p> <p>Layer 4 Partition of space = ∪ </p> <p>Layer 5, Layer 6, Layer 7, Local dynamics (interactions within subspaces) Basins / regimes (conceptual diagrams).</p> <p>Measurable observables , , </p> <div> <h2>System Flow</h2> </div> <p>The system evolves according to a dynamical operator:</p> <p>Φ : X → X</p> <div> <h2>State Evolution</h2> </div> <p>x(t) = Φ(x0) where</p> <p>x0 ∈ X</p> <div> <h2>Regime / Basin Definition</h2> </div> <p>Γ = { x(t) }</p> <p>The trajectory forms basins of attraction representing emergent regimes.</p> <div> <h2>Partition of State Space</h2> </div> <p>The state space can be partitioned into regime subsets:</p> <p>X = U ∪ XK</p> <p>where</p> <ul> <li><strong>U</strong> represents stable attractor regions</li> <li><strong>XK</strong> represents critical or transition regions</li> </ul> <div> <h2>Observables</h2> </div> <p>The system dynamics can be described through measurable observables:</p> <p>n, J, R</p> <p>representing system-dependent measurable quantities extracted from the flux dynamics.</p> <div> <h1>Multilayer Conceptual Architecture</h1> </div> <table> <tbody><tr> <th>Layer</th> <th>Description</th> </tr> </tbody><tbody> <tr> <td>Layer 0</td> <td>Configuration Space X</td> </tr> <tr> <td>Layer 1</td> <td>Dynamical Flow Φ : X → X</td> </tr> <tr> <td>Layer 2</td> <td>State Evolution x(t) = Φ(x0)</td> </tr> <tr> <td>Layer 3</td> <td>Basins / Regimes Γ</td> </tr> <tr> <td>Layer 4</td> <td>Partition of Space X = U ∪ XK</td> </tr> <tr> <td>Layer 5</td> <td>Local dynamics within subspaces</td> </tr> <tr> <td>Layer 6</td> <td>Regime diagrams / attractor structure</td> </tr> <tr> <td>Layer 7</td> <td>Measurable observables n, J, R</td> </tr> </tbody> </table> <p> </p> <div>References</div> <p>Strogatz, S. – <em>Nonlinear Dynamics and Chaos</em><br>Friston, K. – <em>The Free Energy Principle</em><br>Shannon, C. – <em>A Mathematical Theory of Communication</em></p> <p> </p> <p>Authenticity & Intellectual Property.<br>Statement: "This ecosystem is protected by a deterministic digital signature."</p> <p>Current build SHA-256: [6d59bd8d8f4c89ffb4d140f5b89c664798701b4cac8ae373aaaa71540a459116].</p> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18905519 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | NeuroCore™: Mathematical Formalization Nicoletti, Davide Luca <div> <div> <div> <h1>Emergent Dynamical Regimes Architecture</h1> </div> </div> </div> <div> <p><br>First public theoretical disclosure.<br>This release formalizes the 7-layer multilayer conceptual structure for high-entropy flux analysis. It establishes the mathematical basis for regime identification (Layer 3) and state space partitioning (Layer 4), providing the empirical stability threshold (Kc ≈ 1.441).</p> <div> Emergent Dynamical Regimes in High-Entropy Flux. </div> <p>Layer Description</p> <p>Layer O Configuration space </p> <p>Layer 1 Flow / map : → </p> <p>Layer 2 State evolution ( ) = ( 0 )</p> <p>Layer 3 Basins / Regimes = { ( )}</p> <p>Layer 4 Partition of space = ∪ </p> <p>Layer 5, Layer 6, Layer 7, Local dynamics (interactions within subspaces) Basins / regimes (conceptual diagrams).</p> <p>Measurable observables , , </p> <div> <h2>System Flow</h2> </div> <p>The system evolves according to a dynamical operator:</p> <p>Φ : X → X</p> <div> <h2>State Evolution</h2> </div> <p>x(t) = Φ(x0) where</p> <p>x0 ∈ X</p> <div> <h2>Regime / Basin Definition</h2> </div> <p>Γ = { x(t) }</p> <p>The trajectory forms basins of attraction representing emergent regimes.</p> <div> <h2>Partition of State Space</h2> </div> <p>The state space can be partitioned into regime subsets:</p> <p>X = U ∪ XK</p> <p>where</p> <ul> <li><strong>U</strong> represents stable attractor regions</li> <li><strong>XK</strong> represents critical or transition regions</li> </ul> <div> <h2>Observables</h2> </div> <p>The system dynamics can be described through measurable observables:</p> <p>n, J, R</p> <p>representing system-dependent measurable quantities extracted from the flux dynamics.</p> <div> <h1>Multilayer Conceptual Architecture</h1> </div> <table> <tbody><tr> <th>Layer</th> <th>Description</th> </tr> </tbody><tbody> <tr> <td>Layer 0</td> <td>Configuration Space X</td> </tr> <tr> <td>Layer 1</td> <td>Dynamical Flow Φ : X → X</td> </tr> <tr> <td>Layer 2</td> <td>State Evolution x(t) = Φ(x0)</td> </tr> <tr> <td>Layer 3</td> <td>Basins / Regimes Γ</td> </tr> <tr> <td>Layer 4</td> <td>Partition of Space X = U ∪ XK</td> </tr> <tr> <td>Layer 5</td> <td>Local dynamics within subspaces</td> </tr> <tr> <td>Layer 6</td> <td>Regime diagrams / attractor structure</td> </tr> <tr> <td>Layer 7</td> <td>Measurable observables n, J, R</td> </tr> </tbody> </table> <p> </p> <div>References</div> <p>Strogatz, S. – <em>Nonlinear Dynamics and Chaos</em><br>Friston, K. – <em>The Free Energy Principle</em><br>Shannon, C. – <em>A Mathematical Theory of Communication</em></p> <p> </p> <p>Authenticity & Intellectual Property.<br>Statement: "This ecosystem is protected by a deterministic digital signature."</p> <p>Current build SHA-256: [6d59bd8d8f4c89ffb4d140f5b89c664798701b4cac8ae373aaaa71540a459116].</p> </div> |
| title | NeuroCore™: Mathematical Formalization |
| url | https://doi.org/10.5281/zenodo.18905519 |