Admissible Action Space as a Precondition for Energy and Risk Scalability

Technical Appendix / Formal Note Status: Formal clarification note.Relation: Clarifies form of knowledge presented in Zenodo record 18047627.Does not extend scope. Title Admissible Action Space as a Precondition for Energy and Risk Scalability Purpose To express the core claim of the engineering letter as a single formal result suitable forinternal review, expert testimony, and independent verification. Definitions Let A be the set of all operations available to a system.Let S be the set of system states.Let O(s, a) be an outcome function mapping a state–operation pair to an outcome.Let Success be a well-defined, system-internal criterion of successful completion. Assumption An operation a ∈ A is non-viable if and only if: For all s ∈ S, there does not exist any s′ ∈ S such thatO(s, a) = Success. Construction Define the admissible action space: A′ = { a ∈ A | there exists s′ ∈ S such that O(s, a) = Success } All operations in A \ A′ are excluded from existence within the system’soperational reality. Central Result In any scalable system, allowing non-viable operations to exist in the action spacenecessarily increases both energy consumption and systemic risk as scale increases. This follows from: - combinatorial growth of evaluation paths involving non-viable operations,- irreversible resource expenditure on operations with no reachable success,- expansion of control and failure surfaces proportional to |A \ A′|. Consequence Excluding non-viable operations prior to evaluation or execution yields: - reduction of total computational and physical energy expenditure,- reduction of systemic risk without additional control mechanisms,- bounded growth of complexity under scale. Scope Limitation This result does not depend on: - industry domain,- specific algorithms,- organizational structure,- regulatory or policy assumptions. Status Statement This note formalizes an architectural invariant already stated in the referencedpublication. No new claims are introduced.Attached source and canonical renderings: PDF (canonical), TEX (LaTeX source), TXT (plain-text mirror).