ANISOTROPIC SPACE DYNAMICS · OPEN RESEARCH

OP-MAT-004 · Spin and Statistics

Collective rotation and a conditional FR sign choice exist; the joint derivation of half-integer spin and exchange statistics is incomplete.

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-004 · P1

NEEDS THEORY · Needs theory

TopologyQuantum foundations

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01Existing basis

Collective rotation and a conditional FR sign choice exist; the joint derivation of half-integer spin and exchange statistics is incomplete.

ASD-WEB-MAT-013

Q_R(\mathbf x,t)=Q_0(R^{-1}(t)\mathbf x),\quad A\in SU(2),\quad A\mapsto R\in SO(3),\quad L_{\rm rot}=\tfrac12\Lambda_{ab}\Omega_a\Omega_b

Definition
A stable Q0 is needed before computing inertia; A lifts spatial rotations and must not be identified with the internal Q field.
Chapter reference: Ch. 4 (4.30)–(4.31) · ASD-BOOK-ddbade997b45

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

ASD-WEB-MAT-014

\psi(-A)=-\psi(A)\quad\Longrightarrow\quad j\in\{\tfrac12,\tfrac32,\ldots\}

Constitutive input
Requires a nontrivial rotation loop in the full configuration space and this quantization choice; it alone fixes neither j=1/2 nor exchange statistics.
Chapter reference: Ch. 4 (4.32); conditional Finkelstein–Rubinstein construction · ASD-BOOK-ddbade997b45

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

02Required work

Build collective coordinates, stabilizer and loops in full configuration space. State and motivate quantization, analyze exchange of identical structures, and compute rotational spectrum, angular momentum and EM response.

03Reviewable deliverable

Rotation/exchange homotopy proof, constrained quantum state space, ground-state/statistics selection and explicit missing ingredients for the g-factor calculation.

04Limits and dependencies

Do not equate 4π closure with spin 1/2 or use Dirac/Standard Model results as hidden premises.

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

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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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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

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Depends on

Spin: From Geometric Motivation to Quantum Representation Electron Candidate Topology

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