TEO Framework — Thermodynamics of Emergent Orchestration¶

The TEO framework is the mathematical core of this repository's theoretical architecture. It translates the qualitative principles — self-organization, homeostasis, criticality, identity — into a single coupled system of ordinary differential equations (ODEs) that can be simulated, calibrated, and falsified.

Formalized in the paper. The constraint conjunction developed here is given a citation-ready treatment — necessity theorem, sufficiency conjecture, and the capability-loading result — in The Viable Corridor, which carries the current refined formalism (substrate-coupled value dynamics, cumulative overshoot). For where this node sits in the wider project, see Canonical Path v2.

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) — 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 — fixed point (Chord equilibrium), limit cycle (oscillatory consensus), and chaotic (Edge of Chaos) — 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.
Thermodynamic Tokenomics	Applies the TEO entropy budget (\(D_{\max}\)) to political economy: compute as the base currency, Ecological Dissipation Rights (EDR) as the unit, Proof-of-Dissipation as the protocol. The framework's application to economic substrate-coupling.

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.