Constants External Anchors Electron Mass Me V Pos

The electron mass anchor

The electron rest mass is one of the standard constants of physics, the mass of a single electron at rest. In the SI unit system it is measured as 9.1093837139 × 10⁻³¹ kilograms. Physicists more often quote it in million electronvolts (MeV), a unit of energy where one MeV equals about 1.602 × 10⁻¹³ joules; in that unit the electron mass is 0.51099895069 MeV. That value comes from CODATA 2022, the internationally agreed set of physical constants, and it is a measurement, not a theoretical prediction.

In the Recognition Science framework, this number enters through a component that is deliberately quarantined from the framework's core derivations. The component exists for one purpose: to let the framework compare its own derived quantities against experimental reality. The declaration electron_mass_MeV_pos is a small lemma stating that the electron mass in MeV is a positive number. Its proof is a direct numeric check: 0.51099895069 is greater than zero. The lemma carries no physics content beyond that positivity; it is a bookkeeping step that lets later formal work assume the mass is a valid positive real number.

What the declaration does not claim is more important than what it does. It does not claim that the framework derives the electron mass from first principles. The mass is an external anchor, a measured input, not an output of the framework's forcing chain. The framework's core cost derivation never imports this component; the separation is mechanical and enforced. Any later result that uses the electron mass is explicitly acknowledging that it leans on external calibration data. The framework's own constants, such as the reduced Planck constant and the gravitational constant, are derived from its internal logic, but the electron mass is not among them.

This quarantine is the framework's honesty mechanism. It marks the seam where theory meets experiment, and it makes that seam auditable: a reader can see exactly which results depend on measured inputs and which do not. The electron mass anchor is a small but load-bearing piece of that architecture, a reminder that a framework which derives much still must import the world's measurements at some point.

/-- **EXTERNAL ANCHOR** -/
@[simp]
noncomputable def electron_mass_MeV : ℝ := 0.51099895069

lemma electron_mass_MeV_pos : 0 < electron_mass_MeV := by norm_num [electron_mass_MeV]

/-- **EXTERNAL ANCHOR**: A complete set of external anchors for comparison. -/
structure EmpiricalAnchors where
  /-- α⁻¹ central value -/
  alpha_inv : ℝ := alpha_inv_CODATA
  alpha_inv_sigma : ℝ := alpha_inv_CODATA_uncertainty
  /-- Electron-muon ratio -/
  electron_muon : ℝ := electron_muon_ratio_CODATA
  electron_muon_sigma : ℝ := electron_muon_ratio_uncertainty
  /-- Proton-electron ratio -/
  proton_electron : ℝ := proton_electron_ratio_CODATA
  proton_electron_sigma : ℝ := proton_electron_ratio_uncertainty
  /-- Source year -/
  codata_year : Nat := 2022

What this page does not claim

The framework derives the electron mass from first principles. The electron mass is a prediction of the cost-first core. The positivity lemma carries any physics content beyond the number being greater than zero.

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: