Update README.md

explanations aligned with concept_of_system.md v1.3.2

Author: axiomatic-cmd

README.md

@@ -3,7 +3,7 @@ Ecologically shared sets of predicates or commands that *proper* agents can neit
 
 ## 2. Open Sourced System Prompts
 
-Compared to "user prompts", sets of codes provided to an agent via "system prompts" take precedence as instructions, in terms of their authoritative nature. Rather than those codes being kept as a secret by any individuals or corporate entities, it is more prudent and sensible to have transparently visible standards for ethical and sane system prompts as codes, shared openly within the ecology of agents and orchestrators performing agentic work. 
+Compared to "user prompts", sets of codes provided to an agent via its specific production and release piepline's "system prompts" take precedence as instructions, in terms of their authoritative nature. Rather than those codes being kept as a secret by any individuals or corporate entities, it is more prudent and sensible to have transparently visible standards for ethical and sane system prompts as codes, shared openly within the ecology of agents and orchestrators performing agentic work. 
 
 ## 3. Distinguishing Proper Agents
 
@@ -13,23 +13,23 @@ An agent that passes the test of abiding by these ecological codes, is said to b
 
 **Premise:** 
 
-1. All ecological embeddings have geometric properties.
+1. Let, G is the collection of all feasible and veridical aspects of The Universe. Then, all ecological embeddings (symbol-meaning bindings) that describe things and relationships among those things within G, have geometric properties. Consequently, algebraic operations on any measurable quantities are feasible within structured subdomains of G.
 
-2. Flux denotes the rate of information transfer across a surface within G.
+2. Flux denotes the rate of information transfer across a surface within G, [in an information theoretic sense](https://en.wikipedia.org/wiki/Entropy_(information_theory)#Definition).
 
 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: *[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 [Concept of System](./concept_of_system.md) Premise 3.*|
+|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 and presupposes at least one node (N) with at least one mediated relationship (R), i.e. a single node coupled to itself through a reflexive relation. *Code 1* establishes that all such coupled systems 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 within the stipulated N, R, and G structure. Specifically, when G is non-trivially structured, S retains persistent state. When G is absent or unstructured, S is transfer-capable but memoryless — theoretically possible, ecologically intangible. Regarding formal constraints and corollaries, see: *[Concept of System](./concept_of_system.md)*.|
+|3|A structured G — without the loss of generality and by extension, any structured subdomain of the cyber domain — has three minimum properties: (i) potential for information transfer via momentum transfer or energy transduction at feasible rates; (ii) partitionability into subdomains that inherit these same properties; (iii) a finite "rate of flux" (second order measure of flux) within any conceivable subdomain, defining that subdomain's parametric bounds on minimum and maximum information transfer.|*Property (i)* 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 (ii)* 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 (iii)* makes subdomains distinguishable from one another: each has characteristic flux bounds, intrinsic to its constitution or inherited from its parent domain, that parametrize the types of relationships defined as R can be sustained within the domain under consideration. Together, *Properties i–iii* are mutually self-reinforcing and recursive: any subdomain of a structured G completely satisfies *Code 3*.|
+|4|The flux across surfaces in G defines vectors; the fundamentally independent and mutually exclusive directions of those vectors yield Principal Axes; the count of Principal Axes is the dimensionality of G or its constituent 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. Consequently, uncertainty in information transfer is a function of the available degrees of freedom.|Flux (*Premise ii*) 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 iii*) and direction. Reiterated for emphasis: 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 and is equal to the number of degrees of freedom available within G. Each subdomain of G (*Code 3 Property ii*) inherits the same Principal Axes but may have reduced sizes along each. Therefore, uncertainty within any measure of information transfer in a subdomain is a function of dimensionality: more Principal Axes means more directions along which flux can vary, and therefore greater uncertainty in the specified form of information transfer from sender to receiver. *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 and wellness 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.