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ANISOTROPIC SPACE DYNAMICS · OPEN RESEARCH

OP-MAT-001 · Stable Finite-Energy Electron Solution

ASD describes the electron as a closed orientation structure in the minimal negative-charge sector. Chapter 4 supplies the orientation field, finite-energy boundary, topological current and charge matching. Chapter 5 supplies the unique positive stationary radius and radial second-derivative check of a one-parameter energy model. The scale-stabilization mechanism is analytic; the next task is the full three-dimensional electron configuration.

Based on the final manuscript · 第四、五章

TheoryTheory · OPENReviewMathematical review · INCOMPLETEEvidenceEvidence · UNTESTEDCanonicalNoStatus, review and sources
OP-MAT-001 · P0

NEEDS THEORY · Needs theory

PDETopologyNumerical physics
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01Established results

ASD describes the electron as a closed orientation structure in the minimal negative-charge sector. Chapter 4 supplies the orientation field, finite-energy boundary, topological current and charge matching. Chapter 5 supplies the unique positive stationary radius and radial second-derivative check of a one-parameter energy model. The scale-stabilization mechanism is analytic; the next task is the full three-dimensional electron configuration.

ASD-WEB-MAT-001
Φ(x)→Φ0 (∣x∣→∞),E[Φ]=∫R3(H[Φ]−H0) d3x<∞\Phi(\mathbf x)\to\Phi_0\ (|\mathbf x|\to\infty),\qquad E[\Phi]=\int_{\mathbb R^3}(\mathcal H[\Phi]-\mathcal H_0)\,d^3x<\infty

Definition
Φ denotes all participating fields; approaching the vacuum alone does not ensure convergence.
Chapter reference: Ch. 4 §4.2, (4.18), (4.34); conditions collected for review · ASD-BOOK-ddbade997b45

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ASD-WEB-SD-032
Qλ(x)=Q(x/λ),E(λ)=λE2+λ−1E4+λ3EV,E2−E4+3EV=0(λ=1),E(R)=A2R+A4/R+A0R3,E′(R)=A2−A4/R2+3A0R2,R∗2=A22+12A0A4−A26A0(A0>0),=2A4A2+A22+12A0A4(A0≥0),R∗2=A4/A2(A0=0),E′′(R∗)=2A4R∗3+6A0R∗>0.\begin{aligned}Q_\lambda(\mathbf x)&=Q(\mathbf x/\lambda),\\E(\lambda)&=\lambda E_2+\lambda^{-1}E_4+\lambda^3E_V,\\E_2-E_4+3E_V&=0\quad(\lambda=1),\\E(R)&=A_2R+A_4/R+A_0R^3,\\E'(R)&=A_2-A_4/R^2+3A_0R^2,\\R_*^2&=\frac{\sqrt{A_2^2+12A_0A_4}-A_2}{6A_0}\quad(A_0>0),\\&=\frac{2A_4}{A_2+\sqrt{A_2^2+12A_0A_4}}\quad(A_0\ge0),\\R_*^2&=A_4/A_2\quad(A_0=0),\\E''(R_*)&=\frac{2A_4}{R_*^3}+6A_0R_*>0.\end{aligned}

Mathematical result
Retains Chapter 4’s convention that increasing λ enlarges the profile; R is a physical length. A₂,A₄>0, A₀≥0. The 6A₀ denominator requires A₀>0; the rationalized expression includes A₀=0. Units: A₂ J/m, A₄ J·m, A₀ J/m³. The analytic radial minimum is not a complete three-dimensional solution or full perturbation stability.
Chapter reference: Ch. 4 (4.20)–(4.22); Ch. 5 (5.6.23)–(5.6.25) · ASD-BOOK-ddbade997b45

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02Research still required

Fix the common action, target space, coefficient sources and boundary, then solve the finite-energy configuration in the minimal-charge sector. Calculate nonradial perturbations and translation/rotation zero modes, and test fission and radiation. Retained amplitude variables require an unwinding-through-zero check; periodic cores require Floquet analysis.

03The next reproducible deliverable

First deliver a reproducible electron-sector solution with equation residuals, boundary/grid convergence, vacuum-subtracted energy, topological integrals and perturbation spectra. Calculate charge, mass and rotational response from that same core–surrounding-field system, identifying calibrated parameters.

04Scope and research links

A radial scale minimum does not replace a full three-dimensional solution or stability against all perturbations; a 2π internal-phase label alone does not determine the three-dimensional mapping degree.

stability · electron · localization · stability · master equation · matter

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STATUS & REVIEW
Theory StatusTheory · OPEN
Mathematical ReviewMathematical review · INCOMPLETE
Overall Evidence StatusEvidence · UNTESTEDNOT YET UNIQUELY TESTED · observed particle properties are requirements, not validation of candidate topology.
Canonical ASDNo · Research notesCanonical research framework · not a closed particle theory
Module version 1.0.0Reviewed 2026-09-16ASD-BOOK-ddbade997b45
Adopted source, conditions and previous versions

第四章 §2 式（4.17）—（4.29）；第五章 §6 式（5.6.21）—（5.6.30）

已得结果、继续研究任务与下一份交付；保留原问题 ID、优先级及状态。

Conditions retained in this adoption

  • A radial scale minimum does not replace a full three-dimensional solution or stability against all perturbations; a 2π internal-phase label alone does not determine the three-dimensional mapping degree.

Source locators: p1363 · p1375 · p1377 · p2281 · p2307

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

Download source identity manifest

The manifest identifies the source; it is not the complete manuscript. Adopting this source does not upgrade evidence or grant a new licence.

Previous source, retained as history

MAT-d1034a344d58 · Ch. 4 §4.2; Ch. 5 §6

CH4-9587f3c44d39 · 第四章-ASD空间本体论-出版整理稿.docx
9587f3c44d3974f44e387ed03d92691fa5473a90d7b1c9c989155adf0622849a

CH5-ca737ec4e327 · 第五章-出版整理稿.docx
ca737ec4e327d72c5507bbc8e00295b6e56029c7583ebad8e505cdb9c68c6262

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SOURCE & SCOPE

第四、五章 · 第四章 §2 式（4.17）—（4.29）；第五章 §6 式（5.6.21）—（5.6.30）

This research task is based on the cited final Chinese manuscript. It is not a new canonical result. Both languages use the same source snapshot; original equation numbers and website IDs remain distinct.

Knowledge scope
CITATION & SOURCE FILE

ASD: OP-MAT-001 · Stable Finite-Energy Electron Solution. OP-MAT-001-EN. Version 1.0.0; 2026-10-24. https://asd-physics.org/en/open-problems/matter/electron-solution. 第四章 §2 式（4.17）—（4.29）；第五章 §6 式（5.6.21）—（5.6.30）. Source ASD-BOOK-ddbade997b45.

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