Cost Jcost Core

The compatibility surface

Jcost core is a small compatibility module in Recognition Science. It does not define the recognition cost function J(x) = (x + 1/x)/2 - 1; the canonical definitions live in the root module IndisputableMonolith.Cost. Instead, Jcost core re-exports that root surface and keeps the small set of additional instances and lemmas that older Intelligence modules used. Importing both modules no longer creates environment conflicts.

The module establishes that Jcost satisfies the structural properties the framework requires. It proves that Jcost agrees on the exponential axis, meaning the function's behavior on that axis is exactly the one the averaging structure expects. From that it builds instances for symmetric unit behavior, averaging derivation, and the Jensen sketch. Each instance is a formal certificate that Jcost meets the corresponding interface.

The module also records the derivative of Jcost: d/dx J(x) = (1 - x⁻¹²) / 2 away from zero. This is a plain calculus fact, established as a lemma. The derivative is what connects the cost function to later forcing arguments, though Jcost core itself only supplies the local fact.

In plain language: Jcost core is the glue that lets older modules treat Jcost as a well-behaved recognition cost without redefining it. It does not extend the theory; it makes the existing theory usable across module boundaries.

MODEL Jcost_agrees_on_exp · IndisputableMonolith/Cost/JcostCore.lean

THEOREM Jcost_agrees_on_exp · IndisputableMonolith/Cost/JcostCore.lean

THEOREM Jcost_agrees_on_exp · IndisputableMonolith/Cost/JcostCore.lean

THEOREM Jcost_deriv · IndisputableMonolith/Cost/JcostCore.lean

What this page does not claim

Jcost core does not define the Jcost function itself. Jcost core does not prove the uniqueness theorem for Jcost. Jcost core does not derive any physical constants or dimensions.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Cost/JcostCore.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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