Cosmology Siconversion Mpc Si Pos

The megaparsec in SI units

A megaparsec (Mpc) is a unit of distance used in astronomy, equal to one million parsecs, or about 3.26 million light-years. In the International System of Units (SI), the Recognition Science framework's library defines the megaparsec as exactly 3.0857 × 10²² meters. This is a definitional choice, a fixed number chosen so that cosmological calculations can be expressed in human-scale units.

The declaration Mpc_SI_pos is a theorem in the framework's machine-checked library of formal theorems. It proves that this defined value, 3.0857 × 10²², is greater than zero. The proof is immediate: the number is positive by inspection, and the theorem records that fact formally. This is a small but necessary step; many later calculations divide by the megaparsec, and a formal system must know the divisor is not zero before it can proceed.

In Recognition Science, the megaparsec is not a derived quantity. The framework derives physics in its own native units, where the speed of light, a fundamental length, and a fundamental time are all set to 1. The SI value of the megaparsec is an external, human-defined fact, like the length of the meter itself. The library uses it only as a reporting seam, a way to translate framework predictions into the units astronomers actually use.

The theorem does not claim that the megaparsec has any special physical meaning within the framework. It does not derive the megaparsec from first principles, nor does it make any prediction about cosmology. It simply certifies that a chosen numerical constant is positive, a piece of bookkeeping that lets the rest of the framework's cosmological calculations proceed soundly.

theorem Mpc_SI_pos : 0 < Mpc_SI := by
  unfold Mpc_SI; norm_num

/-- 1 Megaparsec in meters (IAU 2012 definition).
    1 pc = 648000/π AU, 1 AU = 149597870700 m (exact). -/
def Mpc_SI : ℝ := 3.0857e22

What this page does not claim

The megaparsec is not derived from Recognition Science principles. The theorem does not assert any physical meaning for the megaparsec beyond its defined numerical value. The theorem does not make any cosmological predictions.

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

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