Verification Units Rescaled Laws Cert

The rescaling certificate

In Recognition Science, a units pack is a choice of scale for the framework's basic quantities. The relation UnitsRescaled records when one units pack can be obtained from another by a rescaling of the anchors. The certificate named UnitsRescaledLawsCert is a machine-checked collection of formal theorems that verifies this relation satisfies the three defining properties of an equivalence relation: reflexivity (every units pack is rescaled to itself), symmetry (rescalings can be inverted), and transitivity (rescalings compose).

The certificate is a structure whose single field, verified, is a proposition asserting all three laws. The theorem verified_any proves that any certificate is verified, meaning the laws hold unconditionally. The proof is short: it uses the built-in reflexivity, symmetry, and transitivity of the underlying UnitsRescaled type. Because UnitsRescaled is a structure, the certificate records these laws at the proposition level via Nonempty, which is a way of saying that a witness exists.

In plain language, this certificate establishes that the framework's unit rescaling behaves like a proper equivalence relation: it is not a one-way operation but a well-behaved notion of sameness up to scale. This matters because it means that rescaling units is a consistent, reversible operation that can be composed, and that any two units packs that are rescaled to each other can be treated as equivalent in the framework's formal development. The certificate is a small but load-bearing piece of the framework's verification infrastructure, ensuring that the bookkeeping of units does not introduce inconsistencies.

structure UnitsRescaledLawsCert where
  deriving Repr

What this page does not claim

This certificate does not define what a units pack is, only the rescaling relation between them. This certificate does not establish any physical law; it only verifies a formal property of the rescaling relation. The proof does not depend on any specific choice of units, only on the structure of the relation itself.

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/Verification/UnitsRescaledLawsCert.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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