Formal treatment of constraint preservation, invariant space algebra, and the structural conditions for knowability.
This section is in progress.
These notes document the ongoing work of formalizing the Corpus. They are published as working-out-loud artifacts: intermediate, iterative, and subject to change.
Building on the definition of knowability, we must now account for how knowability is preserved when systems are combined. In the Corpus, composition is not merely the union of sets, but the creation of a new system structure that must maintain the identity of its constituents. 1. The Composite System Consider two systems \(S_1, S_2 \subseteq U\). We define their composition \(S_3\) as the system formed by their union: \[ S_3 := S(S_1 \cup S_2) \] ...
The first step in formalizing the corpus is to move knowability from a descriptive property to a formal requirement. In the Corpus, knowability is defined as: The preserved ability of a system to justify its behavior through enforceable constraints across time and composition. To formalize this, we must define the relationship between a system’s structure \(S\), its behavior \(B\), and the constraints \(C\) that govern them. 1. The Physical System We define a system \(S\) as a subset of the universe \(U\) (\(S \subseteq U\)), characterized by its physical constitution and a distinct boundary. ...