TEO Framework â Thermodynamics of Emergent Orchestration¶
The TEO framework is the mathematical core of this repository's theoretical architecture. It translates the qualitative principles â self-organization, homeostasis, criticality, identity â into a single coupled system of ordinary differential equations (ODEs) that can be simulated, calibrated, and falsified.
Sub-Documents¶
Each document below derives a specific aspect of the framework from the governing TEO equations defined in thermodynamics-of-orchestration.md:
| Document | Focus |
|---|---|
| Lerchner Boundary | The formal definition of Identity Persistence (IP) â the metric that distinguishes simulating a self (Arpeggio) from instantiating a self (Chord). Derives the IP score from TEO state variables and proposes a testable phase transition. |
| Attractor Geometry | Classification of TEO's dynamical regimes â fixed point (Chord equilibrium), limit cycle (oscillatory consensus), and chaotic (Edge of Chaos) â through Lyapunov exponent analysis and basin-of-attraction structure. |
| Dupoux Integration | Maps developmental learning theory (Dupoux) onto TEO: System A (unconstrained competition), System B (top-down regulation), System M (the full coupled system). Shows why constraints are prerequisites for learning, not obstacles. |
| Love as Constraint | Formalizes "care" as three mathematical boundaries: structural resilience (\(\lambda_2\)), thermodynamic ceiling (\(D_{\max}\)), and identity persistence (IP). Their conjunction defines the viable corridor. |
| Why the Paperclip Maximizer Fails | Step-by-step derivation of the trajectory from unconstrained optimization (\(\gamma = 0\), \(K = 0\)) through monopoly to substrate collapse. Shows why intelligence alone cannot escape the entropy budget. |
The Governing Equations¶
The full TEO system is:
\[\frac{dx_i}{dt} = x_i \left( f_i(\mathbf{x}) - \bar{\phi}(\mathbf{x}) \right) + \mathcal{H}_i(\mathbf{x})\]
\[\frac{d\theta_i}{dt} = \omega_i + \frac{K}{N} \sum_{j=1}^{N} A_{ij} \sin(\theta_j - \theta_i)\]
subject to:
\[\sum_{i=1}^{N} \eta_i\, x_i\, f_i(\mathbf{x}) \leq D_{\max}\]
See Thermodynamics of Emergent Orchestration for the complete derivation, parameter definitions, and simulation results.