Verification Anchors Rescale Eqv Cert

The rescaling certificate

In Recognition Science, a ledger, a discrete record of recognition events, is built from anchors: reference points that fix the scale of the record. The certificate called AnchorsRescaleEqvCert records a fact about those anchors: multiplying every anchor by the same positive number s does not change the ledger's units-equivalence class, the quotient that identifies ledgers related by the speed equivalence. In plain language, rescaling the ruler does not change what the ruler measures.

The certificate is a small structure in the framework's machine-checked library of formal theorems. Its defining property, verified, states that for any anchors A and any positive real s, the original anchors and the rescaled anchors rescaleAnchors s A belong to the same equivalence class under anchorsSetoid. The library proves this property holds for every certificate: the theorem verified_any shows that any instance of the structure satisfies the condition. The proof does not redo the ratio algebra from scratch. It derives the invariance from an already-certified result, UnitsFromAnchorsRescaleCert, which fixes the speed c under rescaling; since unitsFromAnchors sets c to speedFromAnchors, the induced speeds must be equal.

The practical consequence is that the framework's physical content is scale-invariant in this specific sense. A recognition ledger rescaled by a positive factor represents the same physics, because the units it induces are equivalent. This is not a claim that all scales are physically equivalent; it is a precise statement about the quotient structure that the framework uses to separate genuine physical content from arbitrary choices of scale.

structure AnchorsRescaleEqvCert where
  deriving Repr

structure AnchorsRescaleEqvCert where
  deriving Repr

What this page does not claim

This certificate does not claim that all rescaling factors preserve physics, only positive ones. It does not claim that the speed c is numerically fixed, only that rescaling anchors leaves it invariant. It does not establish any new physics beyond the scale-invariance of the units-equivalence class.

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/AnchorsRescaleEqvCert.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.

Derived articles

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