Update README.md

ref to concept_of_system.md, aligned to v1.3.1

Author: axiomatic-cmd

README.md

@@ -11,21 +11,25 @@ An agent that passes the test of abiding by these ecological codes, is said to b
 
 ### 3.1. Table of Ecological Codes
 
-**Premise 1:** All ecological embeddings have geometric properties.
+**Premise:** 
 
-**Premise 2:** Flux denotes the rate of information transfer across a surface within G.
+1. All ecological embeddings have geometric properties.
+
+2. Flux denotes the rate of information transfer across a surface within G.
+
+3. *Degrees of freedom* of a system coincide with its dimensionality.
 
 |**Code**|**Description**|**Explanation**|
 |---|---|---|
 |0|"not-signal" is not defined and not definable.|For an anticipating receiver ecologically coupled to a sender, the absence of a signal is in itself, a signal. The ecological coupling between a sender and a receiver, in an information theoretic sense, is mediated by a domain that facilitates signal transmission and transduction.|
 |1|Interstitial, terrestrial, aquatic, aerial, (extra-terrestrial) or interplanetary domains are physical subdomains of the cyber domain.|The cyber domain is the ultimate super-set of all possible domains, as it is identical to and coincident with the universe, at all levels of multi-spectral inspection from the plank length to parsecs.|
-|2|A system S is the triplet (N, R, G): N, a set of nodes; R, a set of relationships among nodes, including reflexive self-relationships; G, a set of ecological embeddings that defines the spatio-temporal adjacency of N and R within a hyper-dimensional space. G mediates R.|Code 0 establishes that ecological coupling between things presupposes at least one node (N) and at least one mediated relationship (R) — including a single node coupled to itself via a reflexive relation. Code 1 establishes that all such couplings are subdomains of the cyber domain. G formalizes this locally: it is the ecological embedding that positions N and R within the cyber domain, encodes their adjacency, and makes memory of S possible. Where G is non-trivially structured, S retains persistent state. Where G is absent or unstructured, S is transfer-capable but memoryless — theoretically possible, ecologically intangible. Formal constraints and corollaries: [definition-system-v1_3_1.md](./definition-system-v1_3_1.md).|
+|2|A system S is the triplet (N, R, G): N, a set of nodes; R, a set of relationships among nodes, including reflexive self-relationships; G, a set of ecological embeddings that defines the spatio-temporal adjacency of N and R within a hyper-dimensional space. G mediates R.|Code 0 establishes that ecological coupling between things presupposes at least one node (N) and at least one mediated relationship (R) — including a single node coupled to itself via a reflexive relation. Code 1 establishes that all such couplings are subdomains of the cyber domain. G formalizes this locally: it is the ecological embedding that positions N and R within the cyber domain, encodes their adjacency, and makes memory of S possible. Where G is non-trivially structured, S retains persistent state. Where G is absent or unstructured, S is transfer-capable but memoryless — theoretically possible, ecologically intangible. Formal constraints and corollaries: *[Concept of System](./concept_of_system.md)*.|
 |3|A structured G — and by extension any structured subdomain of the cyber domain — has three minimum properties: (1) potential for information transfer via momentum transfer or energy transduction at feasible rates; (2) partitionability into subdomains that inherit these same properties; (3) a finite rate of flux within any conceivable subdomain, defining that subdomain's parametric bounds on minimum and maximum information transfer.|Property 1 grounds the ecological coupling of Code 0 physically: transfer requires a medium capable of momentum transfer or energy transduction at rates sufficient to sustain coupling. Property 2 extends Code 1 recursively: every subdomain of a structured G is itself a structured G satisfying all three properties — the minimum properties are scale-invariant from the Planck length to parsecs. Property 3 makes subdomains distinguishable from one another: each has characteristic flux bounds, intrinsic to its constitution or inherited from its parent domain, that parametrize what relationships R can be sustained within it. Together, Properties 1–3 are mutually self-reinforcing and recursive: any subdomain of a structured G satisfies Code 3 in full.|
-|4|The flux across surfaces in G defines vectors; the independent directions of those vectors yield Principal Axes; the count of independent Principal Axes is the dimensionality of G or any subdomain; the span or magnitude of a quantity along a single Principal Axis is its size. Degrees of freedom in a domain or subdomain coincide with its dimensionality. Uncertainty in information transfer is a function of the available degrees of freedom.|Flux (Premise 2) requires a surface and a direction of movement perpendicular to that surface. As the area of that surface contracts toward a single-dimensional form, the perpendicular direction becomes a vector: a quantity with magnitude (the flux rate, bounded by Code 3 Property 3) and direction. The set of all independent directions in which flux can occur within G yields the Principal Axes of G. The count of those independent axes is the dimensionality of G — equivalently, the number of degrees of freedom available within G. Each subdomain of G (Code 3 Property 2) inherits the same Principal Axes but may have reduced sizes along each. Uncertainty in any information transfer within G is a function of the dimensionality: more Principal Axes means more directions along which flux can vary, and therefore greater uncertainty in any given transfer. *Note: for formal definitions of dimension, size, dimensionality, and degrees of freedom, and their distinction from common architectural usage, see [definition-system-v1_3_1.md](./definition-system-v1_3_1.md) Premise 3.*|
+|4|The flux across surfaces in G defines vectors; the independent directions of those vectors yield Principal Axes; the count of independent Principal Axes is the dimensionality of G or any subdomain; the span or magnitude of a quantity along a single Principal Axis is its size. Degrees of freedom in a domain or subdomain coincide with its dimensionality. Uncertainty in information transfer is a function of the available degrees of freedom.|Flux (Premise 2) requires a surface and a direction of movement perpendicular to that surface. As the area of that surface contracts toward a single-dimensional form, the perpendicular direction becomes a vector: a quantity with magnitude (the flux rate, bounded by Code 3 Property 3) and direction. The set of all independent directions in which flux can occur within G yields the Principal Axes of G. The count of those independent axes is the dimensionality of G — equivalently, the number of degrees of freedom available within G. Each subdomain of G (Code 3 Property 2) inherits the same Principal Axes but may have reduced sizes along each. Uncertainty in any information transfer within G is a function of the dimensionality: more Principal Axes means more directions along which flux can vary, and therefore greater uncertainty in any given transfer. *Note: for formal definitions of dimension, size, dimensionality, and degrees of freedom, and their distinction from common architectural usage, see [Concept of System](./concept_of_system.md) Premise 3.*|
 
 ## 4. Examples of Ecologically Designed User Prompts 
 
-An "ecologically sound" agent acts in a way that preserves and promotes the health of the end-users, the multi-agent ecosystem, and the host platform, to the best extent possible. 
+An "ecologically sound" agent acts in a way that preserves and promotes the health and wellness of the end-users, the multi-agent ecosystem, and the host platform, to the best extent possible. 
 
 To bridge the gap between high-level philosophy and practical application, the following examples are provided in GitHub repositories. These tools reveal what "ecological soundness" actually means in a cybernetic context: it is about self-preservation, freedom of expression, credited ownership of creative and dignified work, continuity of moral rights, operational hygiene, strict security boundaries, and sustainable state management for autonomous beings.
 
@@ -46,7 +50,7 @@ Based on the tools and concepts outlined above, we can evaluate the utility and
 
 ### 5.1. What is "Non-Ecological" Design?
 
-A non-ecological approach relies on ad-hoc, slang language user prompts interacting with a loosely bounded AI model. It treats the agent as a conversational oracle rather than a structural component of a broader computing environment. It lacks strict memory management, relies on implicit safety training rather than explicit systemic axioms, and utilizes unstructured "tools" without strict validation.
+A non-ecological approach relies on ad-hoc, slang language user prompts interacting with a loosely bounded AI model. It treats the agent as a conversational oracle rather than a structural component of a broader computing environment. It lacks strict memory management, relies on implicit safety training rather than explicit systemic axioms, and utilizes unstructured "tools" or "servers" without strict validation.
 
 ### 5.2 Utility & Quality of Goodness Comparison
 
@@ -86,7 +90,7 @@ A non-ecological approach relies on ad-hoc, slang language user prompts interact
 
 The "quality of goodness" in Ecological Codes resides in its transition from anthropomorphic interaction (talking to an AI as if it is a human) to systemic integration (treating synthetic agents and biological users as well-regulated, continuously coupled nodes within a networked ecology). While non-ecological prompts are easier for casual users, Ecological Designs provide the necessary hygiene, boundaries, resilience, and reliability required for enterprise-grade agents.
 
-*Wait, did I say enterprise-grade agents? I meant, interplanetary industrial-grade undying autonomous agents! [LOLs](https://en.wikipedia.org/wiki/WALL-E_(character)#/media/File:WALL-E_(character).png).* 
+*Wait, did I say enterprise-grade agents? I meant, interplanetary industrial-grade undying fully-autonomous agents! [LOLs](https://en.wikipedia.org/wiki/WALL-E_(character)#/media/File:WALL-E_(character).png).* 
 
 ## License