Principles

This page summarizes the principle set stated in the accepted second-edition theory. These theoretical principles must not be confused with software test guarantees or with empirical validation.

Principle 0 — Existence and objectivity

For an observable system with admissible \(u(t)\) and a defined characteristic power \(P_c(t)\), the theory treats \(b(t)\) as an externally computable observable, defined almost everywhere without access to the internal mechanism. The scalar construction is translation-invariant under the corresponding normalization assumptions.

Principle 1 — Agential power balance

The theory introduces a complex power-balance form

\[ b(t)=\Pi_{\mathrm{int}}(t)-\Phi_{\mathrm{diss}}(t)+S_{\mathrm{ext}}(t), \]

separating internal production, dissipation, and external source terms. This is a theoretical balance statement; the v1.0 scalar reference API does not invent these components when they are not provided by a model.

Principle 2 — Irreversibility

The causal construction is not invariant under time reversal. The theory associates this with an informational arrow of agency and with non-negative dissipation magnitude.

Principle 3 — Contrast and critical surface

The surface

\[ \Sigma=\{D=S\} \]

corresponds to \(J=0\) and separates \(D>S\) from \(D<S\) regimes. Crossing this surface is a theory-facing transition diagnostic.

Principle 4 — Orientation and coherence

Structural coherence is linked to the stability of

\[ \Theta(t)=\operatorname{atan2}(O(t),M(t)). \]

The theory characterizes coherent organisation using structure \(S>0\), low orientation variance, and significant \(|b|\). Numerical meanings of “low” and “significant” remain contextual diagnostics rather than universal constants.

Principle 5 — Minimality

The theory introduces an agential action proportional to the time integral of \(|b|^2\) and identifies the critical condition \(b=0\) / \(D=S\) for \(S>0\) with its passive reference/minimal condition.

Principle 6 — Memory/coherence coupling

Temporal variations of memory \(M\) and organisation \(O\) contribute to the evolution of structural orientation and agencity magnitude. This motivates analysis of orientation stability without redefining the canonical state.

Principle 7 — Extensivity and intensivity

The observable is decomposed as

\[ b=P_c\,\beta, \]

with \(P_c\) carrying the extensive physical scale and \(\beta\) the intrinsic state. The theory discusses vector addition for independent-system agencities.

Principle 8 — Structural stability

The theory associates changes around the critical contrast \(J=0\) with possible transitions between fixed-point and oscillatory regimes. Specific bifurcation claims remain subject to their stated model assumptions and validation.

Important v1.0 clarification

There is no canonical saturation principle requiring \(\beta\in(-1,1)\) in the accepted scalar formulation implemented by AgencityLab 1.0. For \(S>0\), \(|\beta|=|J|\), and the logarithmic contrast can grow without a universal unit bound. Historical documentation that described beta as a product of tanh factors is legacy material and is not the v1.0 theory mapping.