EQUATION REGISTRY

Alternative potential-gradient candidate

Uses the ordinary reference spherical gradient; demonstrates nonuniqueness of a field reconstruction from the length factor. Web motion angle φ corresponds to the manuscript’s ϕ in this section, without changing its meaning.

Theory · CANDIDATE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 3

ASD-WEB-EM-013
Φcand=q4πε0RK(ϕ),−∇Φcand=q4πε0R2(R^K+K′K2ϕ^)\Phi_{\rm cand}=\frac{q}{4\pi\varepsilon_0RK(\phi)},\quad-\nabla\Phi_{\rm cand}=\frac{q}{4\pi\varepsilon_0R^2}\left(\frac{\hat{\mathbf R}}K+\frac{K^{\prime}}{K^2}\hat{\boldsymbol\phi}\right)

Uses the ordinary reference spherical gradient; demonstrates nonuniqueness of a field reconstruction from the length factor. Web motion angle φ corresponds to the manuscript’s ϕ in this section, without changing its meaning.
Chapter reference: Final collected manuscript · Chapter 3, equations (3.18) · ASD-BOOK-ddbade997b45

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Final collected manuscript · Chapter 3, equations (3.18)

Uses the ordinary reference spherical gradient; demonstrates nonuniqueness of a field reconstruction from the length factor. Web motion angle φ corresponds to the manuscript’s ϕ in this section, without changing its meaning.

Conditions retained in this adoption

  • Special two-body result: uniform exterior background, equal parallel velocities, transverse separation and virtual displacement at fixed velocity.
  • Free Maxwell representation: long waves, weak perturbations, transverse constraint, constant coefficients and normalization.
  • Minimal-coupling sources: macroscopic coarse graining, low-speed point sources or a low-frequency near zone; high-speed closed sources require separate construction.

Specific unresolved source issues

  • Local results do not automatically close high-speed topological sources, full instrument mapping or global directed propagation.

Source locators: p1021 · p1023 · p1024 · p1026 · p1027 · p1173 · p1224 · p1230 · p1283 · 最终合订稿 · 第三章式 (3.18)

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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EM-f06476f55cae · 第三章 / Chapter 3 · (3.18), PDF p. 6

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