TEO Framework — Thermodynamics of Emergent Orchestration¶

The TEO framework is one executable model in the repository's viability branch. It combines selected resource, synchronization, regulation, and substrate variables in a coupled system of ordinary differential equations. Those choices are additions to the reconstructed foundation, not consequences of it.

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 develops or interprets a specific aspect of the framework defined in thermodynamics-of-orchestration.md:

Document	Focus
Lerchner Boundary	An earlier formalization of Identity Persistence (IP) and a proposed Chord/Arpeggio distinction. IP is a selected instrument, not a criterion for a “real” self.
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	An exploratory mapping of developmental-learning ideas onto TEO's selected variables.
Love as Constraint	A normative name for one proposed bundle of viability constraints, with corrected scope for connectivity, substrate budgets, and IP.
A Paperclip Maximizer in TEO	A conditional concentration-and-overshoot trajectory under declared dynamics and controller assumptions.
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 (v0.8 form — value dynamics gated by substrate health \(H\); cumulative substrate budget) is:

\[\frac{dx_i}{dt} = H\,x_i \left( f_i^{(0)}(\mathbf{x}) - \bar{\phi}^{(0)}(\mathbf{x}) \right) + \mathcal{H}_i(\mathbf{x})\]

\[\frac{d\theta_i}{dt} = H\left[\omega_i + \frac{K}{N} \sum_{j=1}^{N} A_{ij} \sin(\theta_j - \theta_i)\right]\]

subject to the cumulative substrate constraint \(\Omega(t) < S_{\max}\), where

\[\Omega(t) = \int_0^t \Big(\sum_i \eta_i\, x_i\, f_i^{(0)} - D_{\max}\Big)_+\, ds, \qquad H = \max\!\Big(0,\ 1 - \tfrac{\Omega}{S_{\max}}\Big)\]

See Thermodynamics of Emergent Orchestration for parameter definitions and simulation results, and The Viable Corridor for the current proof scope and limitations.