EQUATION REGISTRY

Source normalization and mass matching

Define all four masses from the same complete core–field system. Equality and the Zφ condition require source–energy matching, not ontology alone. Setting coefficients by observed G is effective normalization.

Theory · CANDIDATE MODELEquation version 1.0.0

Based on the final manuscript · Chapters 4 and 5

ASD-WEB-SD-033
ME=E0/c2,Lcoll(2)=−E0+12MijX˙iX˙j,Mg=c2Glim⁡r→∞rφ(r)=∫Jg d3r4πGZφ,qg=−∂Etest∂φ∣φ=0,Mp=qg/c2,∫Jg d3r=E0, Mg=ME ⟹ Zφ=c24πG,ME=Mi=Mg=Mp(matching requirement).\begin{aligned}M_E&=E_0/c^2,\quad L_{\rm coll}^{(2)}=-E_0+\tfrac12M_{ij}\dot X_i\dot X_j,\\M_g&=\frac{c^2}{G}\lim_{r\to\infty}r\varphi(r)=\frac{\int\mathcal J_g\,d^3r}{4\pi GZ_\varphi},\\q_g&=-\left.\frac{\partial E_{\rm test}}{\partial\varphi}\right|_{\varphi=0},\quad M_p=q_g/c^2,\\\int\mathcal J_g\,d^3r=E_0,\ M_g=M_E&\ \Longrightarrow\ Z_\varphi=\frac{c^2}{4\pi G},\\M_E=M_i=M_g=M_p&\quad\text{(matching requirement).}\end{aligned}

Define all four masses from the same complete core–field system. Equality and the Zφ condition require source–energy matching, not ontology alone. Setting coefficients by observed G is effective normalization.
Chapter reference: Ch. 5 (5.6.26)–(5.6.29) · ASD-BOOK-ddbade997b45

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Adopted source, conditions and previous versions

Ch. 5 (5.6.26)–(5.6.29)

Registered formula checked individually against the final manuscript; semantic potential phi→varphi; four independent mass definitions and explicit matching identity; source-grounded scope note synchronized

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  • Define all four masses from the same complete core–field system. Equality and the Zφ condition require source–energy matching, not ontology alone. Setting coefficients by observed G is effective normalization.

Source locators: p2283–2294

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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SD-51779505a476 · Ch. 5 (5.6.26)–(5.6.29)

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