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fix definition-system link
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README.md

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@@ -19,7 +19,7 @@ An agent that passes the test of abiding by these ecological codes, is said to b
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|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.|
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|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.|
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|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-v1.3.0.md`.|
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|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_0.md](./definition-system-v1_3_0.md).|
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|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.|
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|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: the word "dimension" here refers exclusively to a particular direction along a Principal Axis — it is a direction, not a measurement. "Size" is the magnitude along that direction. This differs from the common usage in architecture or civil engineering, where "dimensions" often denotes physical extents such as length, width, or height. In that usage, what is called a "dimension" is in fact a size in the sense defined here. The two must not be conflated: dimension is direction; size is magnitude along a direction.*|
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