Constants External Anchors Empirical Anchors

The calibration seam

In the Recognition Science framework, the declaration EmpiricalAnchors is a list of measured numbers from the outside world. It stores the central values and uncertainties for the inverse fine-structure constant and for two particle mass ratios, all taken from the CODATA 2022 adjustment. This declaration is the one place where external calibration data enters the framework; its purpose is to enable comparison with experimental reality, not to derive anything.

The framework's core is a pure cost derivation that must not import this declaration. This creates a clean mechanical separation: the cost core and the RS-native constants never see empirical data, while any declaration that does import ExternalAnchors explicitly acknowledges that it uses external calibration. Every definition in this declaration is tagged with an attribute for audit purposes, so tools can grep for the calibration seams.

The declaration stores the CODATA 2022 values: alpha_inv = 137.035999177 with uncertainty 0.000000021, electron-muon ratio = 4.83633169e-3, and proton-electron ratio = 1836.15267343. It also stores SI-unit constants like the speed of light c = 299792458 m/s, the Planck constant h = 6.62607015e-34 J s, and the gravitational constant G = 6.67430e-11 with its uncertainty. These are definitions, not derived results; the declaration simply records what experiment gives.

The declaration also defines a predicate withinSigma that checks whether a predicted value falls within n standard deviations of an empirical value, and a special case within3Sigma. This is the honesty mechanism: when the framework derives a prediction, it can be tested against these anchored values using the standard sigma language. The bounds structures store the 3-sigma windows for the inverse fine-structure constant and the mass ratios.

What EmpiricalAnchors does not claim is as important as what it stores. It does not prove that the framework's predictions match these values; it only provides the reference points against which such comparisons can be made. The declaration does not derive the fine-structure constant or any particle mass. It is a calibration seam, a place where the framework admits it needs the measured world, not a place where the framework claims to have produced that world from pure logic.

/-- **EXTERNAL ANCHOR**: Inverse fine structure constant (CODATA 2022).
    α⁻¹ = 137.035999177(21) -/
@[simp]
noncomputable def alpha_inv_CODATA : ℝ := 137.035999177

/-- **EXTERNAL ANCHOR**: α⁻¹ uncertainty (1σ). -/
noncomputable def alpha_inv_CODATA_uncertainty : ℝ := 0.000000021

/-- **EXTERNAL ANCHOR**: The default empirical anchors (CODATA 2022). -/
noncomputable def empiricalAnchors : EmpiricalAnchors := {}

/-- **EXTERNAL ANCHOR**: Check if a predicted value is within nσ of the empirical anchor. -/
def withinSigma (predicted empirical sigma : ℝ) (n : ℝ) : Prop :=
  |predicted - empirical| ≤ n * sigma

/-- **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

EmpiricalAnchors does not prove any framework prediction matches these measured values. The declaration does not derive the fine-structure constant or any particle mass. The CODATA values are recorded as definitions, not as theorems.

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: