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ANISOTROPIC SPACE DYNAMICS · OPEN RESEARCH

OP-SD-006 · Source Coupling

With smooth all-space fields and zero far boundary, the local $sF$ candidate gives density supported with the core. Independent stretch admits a $1/r$ far field, but its source functional has not been derived from a stable matter core.

Theory StatusTheory · OPEN
Mathematical ReviewMathematical review · INCOMPLETE
Overall Evidence StatusEvidence · UNTESTEDConstraints and proposals are recorded separately; no new experimental fit.
Canonical ASDNo · Research notesContinuum foundation; status specified per claim
Module version 1.0.0Reviewed 2026-09-15SD-51779505a476
OP-SD-006 · P1

NEEDS THEORY · Needs theory

PDE
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01Current baseline

With smooth all-space fields and zero far boundary, the local sFsF candidate gives density supported with the core. Independent stretch admits a 1/r1/r far field, but its source functional has not been derived from a stable matter core.

ASD-WEB-SD-028
∇2(Kus+gLF)=0⟹s=−gLKuF,σ=gLKuF\nabla^2(K_us+g_LF)=0\quad\Longrightarrow\quad s=-\frac{g_L}{K_u}F,\quad\sigma=\frac{g_L}{K_u}F

Mathematical result
Smooth fields on all space, localized source, no singular harmonic term and zero boundary at infinity.
Chapter reference: Ch. 5 (5.6.14)–(5.6.15) · ASD-BOOK-ddbade997b45

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ASD-WEB-SD-030
Zφ(∂t2−c2∇2)φ=Jg,φ(r)=14πZφc2∫Jg(r′)∣r−r′∣ d3r′Z_\varphi(\partial_t^2-c^2\nabla^2)\varphi=\mathcal J_g,\quad\varphi(\mathbf r)=\frac{1}{4\pi Z_\varphi c^2}\int\frac{\mathcal J_g(\mathbf r')}{|\mathbf r-\mathbf r'|}\,d^3r'

Mathematical result
Dimensionless varphi; the right side is the static Green integral for a localized source and zero far boundary. Spherical compact support gives exact exterior 1/r; an integrable tail gives an asymptote. Matter fixes the source and feedback.
Chapter reference: Ch. 5 (5.6.17) · ASD-BOOK-ddbade997b45

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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}

Normalization
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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02Work required

Define the mapping and energies of observed gravitational stretch, displacement divergence and an independent scalar without double counting. Derive the source functional, feedback, active mass, inertia and external-field response from one finite-energy matter solution. Check far-field sign, normalization, boundaries, universality and conservation in motion.

03Reviewable deliverable

A complete solution chain from stable matter core to gravitational far field, computing energy, active/passive gravitational mass and inertia from the same solution with independently specified coefficients.

04Limits and dependencies

A displacement tail is not automatically a 1/r1/r density tail. Imposing that density tail can make the corresponding energy diverge; calibrating normalization with known GG does not derive GG.

Longitudinal field · Master equation

05Matter research continuation

OP-MAT-003: mass generation separately computes energy, inertial, active and passive gravitational masses on one solution.

Canonical Source

Anisotropic Space Dynamics

Chapter 4 / 第四章 · Chapter 5 / 第五章

Ch. 4 §4.1; Ch. 5 §§4, 6

Module version
1.0.0
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SD-51779505a476
Content review date
2026-09-15
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  • CH4-9587f3c44d39 · 第四章-ASD空间本体论-出版整理稿.docx
    DOCX
    9587f3c44d3974f44e387ed03d92691fa5473a90d7b1c9c989155adf0622849a
  • CH5-ca737ec4e327 · 第五章-出版整理稿.docx
    DOCX
    ca737ec4e327d72c5507bbc8e00295b6e56029c7583ebad8e505cdb9c68c6262

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SOURCE & SCOPE

Chapter 4 / 第四章 · Chapter 5 / 第五章 · Ch. 4 §4.1; Ch. 5 §§4, 6

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CITATION & SOURCE FILE

ASD: OP-SD-006 · Source Coupling. OP-SD-006-EN. Version 1.0.0; 2026-09-16. https://asd-physics.org/en/open-problems/space-dynamics/source-coupling. Ch. 4 §4.1; Ch. 5 §§4, 6. Source SD-51779505a476.

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