choke_cost_axioms
plain-language theorem explainer
Recognition Science records the cost axiom bundle as a closed choke point whose consequence is that J is uniquely determined. Researchers tracing the inevitability of the framework cite this entry when they enumerate the six necessity gates that any alternative must break. The definition is a direct record construction that marks status closed by reference to T5.
Claim. The cost axiom bundle is the choke point given by the record with name ``Cost Axiom Bundle'', status ``closed'' (T5 proven), and consequence ``J is uniquely determined''.
background
The module formalizes the inevitability structure of Recognition Science by relocating degrees of freedom to cost minimization under CPM. Alternatives organize into three buckets, and the cost axioms form one of the six necessity gates that any competing framework must violate. A ChokePoint is the structure with fields name (String), status (String, e.g. ``closed''), and consequence (String describing what closure proves). Upstream, PhiForcingDerived.of supplies the structure of J-cost while the module doc states that under analyticity plus symmetry plus convexity plus normalization, J is unique with T5: J(x) = ½(x + x⁻¹) - 1.
proof idea
The definition is a direct record construction that populates the three fields of the ChokePoint structure. It sets status to closed by citing that T5 is proven and states the consequence as uniqueness of J.
why it matters
This supplies the second entry in all_choke_points, which aggregates the full list of necessity gates. The module doc positions it as Choke Point 2 in the inevitability theorem, specifically the Cost Uniqueness gate that forces J via T5. It supports the claim that any zero-parameter framework must reduce to RS or break one of the listed gates.
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