Constants Codata G Ne Zero

G_ne_zero and its scope

Newton's gravitational constant G is the number that sets the strength of gravity in Newton's law of universal gravitation. In the International System of units, its measured value is about 6.67430 × 10⁻¹¹ cubic meters per kilogram per second squared. That value is not derived from any theory; it is an empirical input, measured in laboratory experiments, and the CODATA 2018 adjustment reports it with a relative uncertainty of about 2.2 × 10⁻⁵.

The machine-checked library (a collection of formal theorems verified by a computer) contains a module that stores this empirical value as a definition. The declaration G_ne_zero is a lemma in that module. It states that G is not equal to zero, a fact that follows immediately from the recorded value being positive. In plain terms, the declaration establishes that the gravitational constant, as stored in this library, is a nonzero number.

In Recognition Science, this lemma plays a purely bookkeeping role. The module is explicitly quarantined from the framework's certified surface: the top-level certificate chain does not depend on these empirical numeric values. The framework derives its own value for G, namely φ⁵/π, from its forcing chain, but that derivation is separate from this empirical record. The lemma G_ne_zero does not prove that the derived value equals the measured one, nor does it validate the framework's derivation. It only asserts that the empirical constant used for comparisons is nonzero.

What G_ne_zero does not claim is just as important. It does not claim that G is positive in any physical sense, only that it is not zero. It does not claim that the recorded value is accurate, current, or theoretically necessary. The value 6.67430 × 10⁻¹¹ is a 2018 adjustment, not a 2022 one; the later CODATA adjustment reports a slightly different value. The lemma is a formal convenience, ensuring that division by G is permitted in the library's arithmetic, not a statement about the physical universe.

The consequence for a reader is simple: G_ne_zero is a trivial but necessary guardrail in a formal system. It lets other theorems divide by G without running into a zero-denominator error. It says nothing about whether gravity's strength is fundamental, derived, or variable. That larger question belongs to the framework's derivation of G from first principles, which is a separate claim entirely.

lemma G_ne_zero : G ≠ 0 := ne_of_gt G_pos

lemma G_ne_zero : G ≠ 0 := ne_of_gt G_pos

What this page does not claim

G_ne_zero does not prove that the framework's derived value φ⁵/π equals the measured value. G_ne_zero does not claim that the recorded 2018 value is the current or most accurate measurement. G_ne_zero does not establish that G is positive, only that it is nonzero.

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/Constants/Codata.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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