validation
Modelled[M] modelled package — not free public theorem; see doctrine v1.0.3 residual chips on /status.Derived Physical Constants
Physical constants are not free parameters in the CPT framework. This table shows which constants are banked under packages or calibrated (see tags), which are calibration inputs, and which remain open.
Introduction
The CPT framework aims to derive all physical constants from geometry and the single fundamental force (Weber). This page serves as the master reference for the status of constant derivations.
- [E] Exact / [M] Modelled: Predicted from axioms with no measured input.
- [C] Calibration inputs: Measured values used to fix the scale (only 2 used for the V4 engine: electron mass and deuteron binding energy).
- [O] Open: The framework should predict these, but the derivation is currently incomplete.
Master Table of Constants
| Constant | Symbol | Value | CPT Status | Source in framework |
|---|---|---|---|---|
| Fine-structure constant | 1/137.036 | [E] / [M] | wave-mech scaling [E], full derivation [M] | |
| Newton's G | 6.6743 × 10⁻¹¹ N·m²/kg² | [M/P] | M13 invert; external H₀ ~percent-class; 0.04% is circular | |
| Speed of light | 2.998 × 10⁸ m/s | [C] | calibration (defines length scale) | |
| Electron mass | 9.109 × 10⁻³¹ kg | [C] | calibration input to V4 engine | |
| Proton mass | 1.673 × 10⁻²⁷ kg | [M] | from T(2,3) Weber hold; precise [M] | |
| Planck constant | 1.055 × 10⁻³⁴ J·s | [M] | from confined photon energy E=ℏω | |
| Elementary charge | 1.602 × 10⁻¹⁹ C | [E] | from Hopf winding number | |
| Classical electron radius | 2.818 × 10⁻¹⁵ m | [E] | r_e = ke²/m_ec² from Weber | |
| Proton/electron mass ratio | 1836.15 | [O] | should follow from T(2,3)/T(1,1) ratio | |
| Compton wavelength | 2.426 × 10⁻¹² m | [E] | from torus confinement | |
| Hubble constant | ~70 km/s/Mpc | [M] | from Mach closure; exact value [O] | |
| Cosmological constant | 1.1 × 10⁻⁵² m⁻² | [O] | S³ curvature gives order-of-magnitude | |
| Proton charge radius | 0.841 fm | [O] | distinct from Weber tube radius R_m | |
| Weinberg angle | 28.17° | [O] | not yet derived from octonion geometry | |
| Strong coupling | 0.118 | [O] | colour confinement from knot topology [M] |
Calibration Philosophy
Only 2 measured values enter the V4 nuclear engine ( and the deuteron binding energy). All 116-element predictions are parameter-free beyond these two inputs, demonstrating the high predictive power of the geometric framework.
M13 Master Equation
Status: Established Derivations
The derivations of the fine structure constant, elementary charge, and classical electron radius represent core successes of the framework, showing how macroscopic fundamental constants emerge directly from the topology and geometry of S³.
Source Documents
The primary research documents underlying this page. All files are freely viewable and downloadable. They represent the working research as written — including integrity tags, equations, and finding IDs.
Documents open in the CPT Research Library — a formatted viewer for all source research files.