Constants External Anchors C Si Pos

A positive speed of light

The speed of light in a vacuum is one of the most precisely known numbers in physics. Since 1983, the meter has been defined as the distance light travels in 1/299,792,458 of a second, making the speed exactly 299,792,458 meters per second, with no uncertainty. This is a definitional constant, not a measured quantity: it is fixed by the international system of units (SI). The value is positive, as any physical speed must be, and that positivity is the entire content of the declaration c_SI_pos.

In the Recognition Science framework, external physical constants are kept in a single quarantined module, separate from the cost-first core that derives everything from the ledger primitive. The framework models the speed of light as a positive real number, and the declaration c_SI_pos is a formal lemma stating that this number is greater than zero. It is a simple arithmetic fact, proved by direct computation, and it carries no physical content beyond what the definition already supplies. The framework does not derive the speed of light from first principles; it imports the SI value as an external anchor for comparison with experiment.

The declaration belongs to a family of positivity lemmas for other SI constants, such as the gravitational constant and the reduced Planck constant. These lemmas exist to support later proofs that require a positive denominator or a meaningful scale. They are not empirical claims, and they do not assert that the framework has explained why these constants have the values they do. The speed of light remains an external input, a calibration point, not a derived prediction.

What c_SI_pos does not claim is as important as what it establishes. It does not claim that the speed of light is the maximum speed in the framework, nor that it is invariant across observers. It does not claim that the value 299,792,458 arises from the recognition cost function. It only records that this number, chosen by definition, is positive. The declaration is a small piece of bookkeeping, a formal acknowledgment that a physical constant must be a positive quantity before it can be used in further reasoning.

/-- **EXTERNAL ANCHOR**: Speed of light in vacuum (exact, SI 2019 definition).
    c = 299792458 m/s -/
@[simp]
noncomputable def c_SI : ℝ := 299792458

lemma c_SI_pos : 0 < c_SI := by norm_num [c_SI]

/-- **EXTERNAL ANCHOR**: Speed of light in vacuum (exact, SI 2019 definition).
    c = 299792458 m/s -/
@[simp]
noncomputable def c_SI : ℝ := 299792458

What this page does not claim

The speed of light is derived from the recognition cost function. The speed of light is the maximum speed in the framework. The declaration c_SI_pos establishes invariance of the speed of light across observers.

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/ExternalAnchors.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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: