ASDANISOTROPIC
SPACE DYNAMICS
中文AI Researcher
THE ASD FRAMEWORK
ASDTheory中文
ANISOTROPIC SPACE DYNAMICS · OPEN RESEARCH

OP-MAT-002 · Topological Classification

The manuscript distinguishes compact phase, 3D SU(2) degree and internal winding; classification of the complete field space remains open.

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 2026-09-16MAT-d1034a344d58
OP-MAT-002 · P1

NEEDS THEORY · Needs theory

Topology
Discuss this task

01Existing basis

The manuscript distinguishes compact phase, 3D SU(2) degree and internal winding; classification of the complete field space remains open.

ASD-WEB-MAT-002
NC=12π∮Cdθ∈ZN_C=\frac1{2\pi}\oint_C d\theta\in\mathbb Z

Definition
Requires a compact phase defined along C; this is distinct from a three-dimensional degree.
Chapter reference: Ch. 4 (4.17) · ASD-BOOK-ddbade997b45

Assumptions and derivation Registry and dependencies Research this equation Discuss this equation
ASD-WEB-MAT-003
Q(∞)=Q∞,Q:Sspace3→SU(2)≃S3,π3(S3)=Z,π1(SU(2))=0Q(\infty)=Q_\infty,\quad Q:S^3_{\rm space}\to SU(2)\simeq S^3,\quad\pi_3(S^3)=\mathbb Z,\quad\pi_1(SU(2))=0

Mathematical result
The boundary orientation is direction independent; amplitude zeros or a different target require a new classification.
Chapter reference: Ch. 4 (4.18), §4.2.1 · ASD-BOOK-ddbade997b45

Assumptions and derivation Registry and dependencies Research this equation Discuss this equation
ASD-WEB-MAT-004
Bμ=ϵμνρσ24π2Tr⁡(LνLρLσ),Lμ=Q−1∂μQ,∂μBμ=0,NQ=∫B0 d3x∈ZB^\mu=\frac{\epsilon^{\mu\nu\rho\sigma}}{24\pi^2}\operatorname{Tr}(L_\nu L_\rho L_\sigma),\quad L_\mu=Q^{-1}\partial_\mu Q,\quad\partial_\mu B^\mu=0,\quad N_Q=\int B^0\,d^3x\in\mathbb Z

Mathematical result
x⁰=ct and ε⁰¹²³=+1; target orientation follows the manuscript. The identity requires smooth Q and fixed far boundary.
Chapter reference: Ch. 4 (4.25)–(4.26) · ASD-BOOK-ddbade997b45

Assumptions and derivation Registry and dependencies Research this equation Discuss this equation

02Required work

Define vacuum manifold, asymptotic boundary, equivalence relation and accessibility of amplitude zeros. Establish relations or independence among N_C, N_Q, N_int and N_em; distinguish electron, positron and proton and test equal-charge interspecies paths.

03Reviewable deliverable

A definition of full configuration space, relevant homotopy or relative classification, conservation conditions and counterexamples; enumerate physical identification inputs rather than using drawings as proofs.

04Limits and dependencies

Changing fields or boundaries requires reclassification; target-space homotopy is not automatically the rotation/exchange topology of configuration space.

Matter framework · Acceptance requirements

Canonical Source

Anisotropic Space Dynamics

Chapter 4 / 第四章 · Chapter 5 / 第五章

Ch. 4 §4.2; Ch. 5 §6

Module version
1.0.0
Source snapshot
MAT-d1034a344d58
Content review date
2026-09-16
Source files and checksums

The snapshot hash identifies the source manifest; each source file has its own checksum below.

  • 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

Download source manifest

Prepared from the final Chinese manuscripts identified above. A public reading link for the full manuscript has not yet been released.

RELATIONSHIP INDEX

Position within the framework

These links index inputs and research relationships. The completion status of each derivation is specified in its text. Untranslated supporting pages open in Chinese.

SOURCE & SCOPE

Chapter 4 / 第四章 · Chapter 5 / 第五章 · Ch. 4 §4.2; Ch. 5 §6

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-002 · Topological Classification. OP-MAT-002-EN. Version 1.0.0; 2026-09-16. https://asd-physics.org/en/open-problems/matter/topological-classification. Ch. 4 §4.2; Ch. 5 §6. Source MAT-d1034a344d58.

Discuss this page Download this page as MDX
CONTINUE RESEARCH

Continue with the assumptions, equations and sources.

Ask ASD ResearcherVerify DerivationChallenge This Argument

These links carry this page and its source version into the research workspace. Each request pins its knowledge snapshot. Model availability is shown in the workspace; retrieval and private export remain available.