Physics Dimensional Analysis From Config Dim

The five base quantities

Dimensional analysis is the practice of tracking what kind of quantity a measurement is, not just how big it is. A length and a time are different kinds of things, and equations that mix them carelessly are usually wrong. The International System of Units (SI) names seven base quantities: length, mass, time, electric current, temperature, amount of substance, and luminous intensity. Every other physical quantity, from speed to entropy, is built from these seven.

The seven are not all equal in status. Amount of substance is a count of particles, and luminous intensity is a count of photons weighted by how the eye responds. Both are derivable from the other five: count the particles, count the photons. So the SI system itself suggests a split: five primary quantities and two auxiliary ones.

In Recognition Science, the framework's machine-checked library of formal theorems proves this split exactly. The library defines the five primary quantities as length, mass, time, electric current, and temperature, and proves they number five. It also proves the arithmetic fact that seven equals five plus two. The result is a certificate, a small formal object that packages both facts together, with no unproved assumptions and no axioms beyond the standard logical ones.

What this establishes in plain language is that the SI base units have a definite internal structure: five are fundamental, two are derived. The framework models the five as the config dimension D = 5, a number that appears throughout its derivations. The module does not derive the value of any physical constant; it certifies a counting fact about how physics organizes its units. That counting fact is what the rest of the framework builds on.

theorem baseQuantity_count : Fintype.card BaseQuantity = 5 := by decide

/-- 7 SI base quantities; 5 primary + 2 derived. -/
theorem si_partition : (7 : ℕ) = 5 + 2 := by decide

def dimensionalAnalysisCert : DimensionalAnalysisCert where
  five_primary := baseQuantity_count
  si_split := si_partition

What this page does not claim

This module does not derive the value of any physical constant. The module does not prove that the SI system is the only possible choice of base quantities. No claim is made here about how the five primary quantities relate to the framework's recognition cost function.

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/Physics/DimensionalAnalysisFromConfigDim.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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