ANISOTROPIC SPACE DYNAMICS · CANONICAL THEORY

Dynamics · Experimental Relations and Tests

Separate mathematical checks, observational constraints on universal coupling and dynamical tests that still need apparatus models.

Based on the final manuscript · Chapter 2

TheoryTheory · DERIVEDReviewMathematical review · CONDITIONALEvidenceEvidence · UNTESTEDCanonicalYesStatus, review and sources

ASD organizes stored energy, translational inertia, active gravitational sourcing and passive response within one core–accompanying-field system. Final equation (2.24c) adopts universal matching, and (2.24d) implements it in weak-field external potential energy; experiments test that matching together with the apparatus response.

01Reading experimental relations · Evidence Scope

Recomputable dynamical formulas do not establish that experiments have independently selected their microscopic interpretation. This page states the matching results and normalization conditions, then records observations actually cited by Chapter 2. A calculation without apparatus and data is not entered as an experimentally reproduced result.

DERIVED refers to derivation within the framework under explicit premises. The module’s overall evidence status remains UNTESTED. Individual cards use CONSISTENT or UNTESTED according to their own source material.

02Recomputable results · Mathematical Checks

Check	ASD conditions and result	Mathematical comparison	Experimental verification?
Low-speed limit	$p\to m_0v$ , $E_k\to m_0v^2/2$	Same form	NO; a limit check
Directional force	$F_\parallel=m_0\gamma^3a_\parallel$ , $F_\perp=m_0\gamma a_\perp$	Same form for fixed mass and common variables	NO; a derivative result
Energy consistency	With rest-energy normalization, $E^2-c^2p^2=m_0^2c^4$	Same form	NO; an algebraic check
Free action	Integrating momentum and fixing a constant gives Eq. (2.24b)	Same form	NO; constitutive and normalization inputs remain

Chapter 2 §III provides no independent beam-data reanalysis. This page does not invent observations or fits to fill a REPRODUCED category. A future data comparison should retain instruments, input quantities, residuals and uncertainties.

03Coupling different mass responses · Universal Coupling

Chapter 2 distinguishes energy mass, inertial mass, active gravitational mass and passive gravitational mass. If a common topological parameter $Q_0$ gives

m_i=C_iQ_0,\qquad m_g^{(a)}=C_aQ_0,\qquad m_g^{(p)}=C_pQ_0,

universal free fall requires $C_p/C_i$ to be composition independent. This observational requirement does not by itself establish equality of every coefficient or directly measure active gravitational mass.

Normalization

The common coupling adopted in the chapter

ASD-WEB-DYN-023

m_E=m_i=m_g^{(a)}=m_g^{(p)}=m_0

Normalization
Energy, inertial, active and passive gravitational mass are different responses of one structure; the chapter adopts universal coupling.
Chapter reference: Final collected manuscript · Chapter 2 §III.5 (2.24c) · ASD-BOOK-ddbade997b45

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

A complete structural theory must test the common origin of these responses. Binding energy, internal stresses and self-gravity enter composite totals; one cannot simply sum constituent rest masses.

ASD-WEB-DYN-024

U_{\mathrm{ext}}=m_0\Psi_{\mathrm{ext}}=\frac12m_0c^2(X_{\mathrm{ext}}-1),\qquad\mathbf F_g=-\nabla U_{\mathrm{ext}}=m_0\mathbf g_X

Constitutive input
An input interface for the later Gravity module; background-field and orbital equations are outside this module.
Chapter reference: Final collected manuscript · Chapter 2 §III.5 (2.24d) · ASD-BOOK-ddbade997b45

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

Here $X=1+2\Psi/c^2$ and $\mathbf g_X=-\nabla\Psi$ are Chapter 2’s weak-field external variables. This is the weak-field interface to the current orbital topic. This page checks inertial closure and limits without duplicating external-field solutions or orbital equations.

04An existing observation · Published Observation

REINTERPRETEDEvidence · CONSISTENT

MICROSCOPE: free fall of differently composed test bodies

Chapter 2, §III, Eqs. (2.24c)–(2.24d), reference [4]; Touboul et al., PRL 129, 121102 (2022). DOI: 10.1103/PhysRevLett.129.121102

READY · Ready for stated work

Ready to recalculate the stated limited model; not a completed distinct prediction.

Observed result: MICROSCOPE’s differential-acceleration measurement with titanium and platinum alloys found no significant weak-equivalence-principle violation, with constraints at the 10⁻¹⁵ scale.
ASD calculation / interpretation: Chapter 2 adopts universal mass coupling. At fixed internal state and weak field, the same m₀ cancels between force and inertia, giving composition-independent free fall.
Established-theory result: The equivalence principle expects universal free fall under the same test conditions.
Numerically different?: NO · The current ASD relation with universal coupling predicts no composition-dependent difference.
Interpretation different?: YES · ASD interprets the mass types as different responses of one spatial core.
Does this distinguish ASD?: NO
Current status: Consistent with the universal-coupling condition; no ASD mission-data refit or microscopic topology verification has been performed.
Required precision: The reported 10⁻¹⁵ scale characterizes this test. The chapter supplies no nonzero ASD–standard difference and hence no additional discriminatory precision target.

The mission team’s original paper and results. This observation constrains the weak equivalence principle. It does not directly measure ASD’s near-core density profile, inertial angular distribution or stable topology.

05A direction for comparison · Proposed Tests

POTENTIALLY DISCRIMINATINGEvidence · UNTESTED

Controlled momentum–energy and directional-response comparison

Chapter 2, §III, Eqs. (2.11)–(2.24b); website task OP-DYN-01

NEEDS THEORY · Needs theory

Source, coupling, readout or statistical mapping remains open; instrument precision cannot replace it.

Observed result: Chapter 2 §III supplies no beam dataset, apparatus inputs or speed–energy table ready for fitting.
ASD calculation / interpretation: Use this module’s momentum, work and directional response as a baseline, then model the actual force, detection and nonuniform structural response.
Established-theory result: Compare results using identical calibrations, trajectories, internal states and apparatus responses, beyond matching formula names.
Numerically different?: The free-motion baseline has the same form; a measurable difference from further constitutive effects has not been derived.
Interpretation different?: YES · Structural interpretations of inertia and energy differ.
Does this distinguish ASD?: POTENTIALLY / PROPOSED TEST
Current status: An apparatus-modelling task only; no experimental prediction curve or reproduction record has been generated.
Required precision: First calculate a difference from a completed apparatus model, then evaluate speed, force, energy, direction and detection noise.

Matching free-motion $p,E$ alone supplies no distinguishing signal. If a force is electromagnetic, the field and probe relations must also be declared. A standard Lorentz force must not silently replace an ASD response not yet established for that configuration. OP-DYN-01 (Chinese) · Chinese original first addresses constitutive and normalization origins.

06Review and source · Review and Sources

The tasks are to compute inertial weight, static energy and mass couplings from one microscopic structure, then map them to the same measured output in an actual apparatus. If baseline predictions still agree, report no discrimination. If a response function is absent, retain an undetermined result.

This module does not expand Chapter 2’s deflection, Shapiro-delay or orbital results or use their observations as independent verification of this inertial closure.

On this page

STATUS & REVIEW

Theory StatusTheory · DERIVED

Mathematical ReviewMathematical review · CONDITIONAL

Overall Evidence StatusEvidence · UNTESTED

Canonical ASDYes · canonical theory baselinePreface · Chapters 1–2

Mathematical Review Note

Momentum follows after the inertial constitutive closure; total energy additionally uses E₀ = m₀c². These inputs remain explicit and require microscopic matching.

Read the formal review items

Module version 1.0.0Reviewed 2026-09-14ASD-BOOK-ddbade997b45

Adopted source, conditions and previous versions

§III.5 (2.24c)—(2.24d) and chapter summary

Core–accompanying-field inertial constitution, momentum integration, inverse force response and energy; retain correct existing derivations.

Conditions retained in this adoption

Uniform background, fixed internal state, 0≤v<c and no net radiation.
The LVE directional law and inertial angular weight are separate inputs.
m₀=C_m m_def; adopt C_m=1 and universal mass normalization.

Specific unresolved source issues

The microscopic core profile, inertial weight and four mass responses still require one common structural solution.

Source locators: p0669 · p0671 · p0672 · p0674 · p0675 · p0936

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

FND-3dde8d8e081d · Chapter 2, §III, Eqs. (2.24c)–(2.24d), PDF p. 10; reference [4]; test interface for Eqs. (2.11)–(2.24b)

PREF-125df9543371 · 序章.pdf
125df9543371f89656a2c29d552e1166e5edcc9ff5f6ec1ef1e438c7688d6ec5

CH1-46d43c8c39bf · 第一章(2).pdf
46d43c8c39bfd47f06ad699a6780e1142adc14bdd3520e2d5603d37a696cd9e9

CH2-f9598318d123 · 第二章-ASD理论-修订书稿 (2).pdf
f9598318d123c1f85a7d720af9cecbed8392e0b399910e3f9bfb675d49494709

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.

Depends on

Dynamics · Inertia and Momentum Dynamics · Energy and Action

Revision history

2026-09-14

CONTENT REVISION

Foundations and Dynamics v1.0 · Chinese and English canonical modules

Editorial record (Chinese)

· Chinese original

SOURCE & SCOPE

Chapter 2 · §III.5 (2.24c)—(2.24d) and chapter summary

This is the English translation of the Chinese canonical module, based on the same final-manuscript source snapshot. The Chinese final manuscript remains authoritative. Website equation IDs are stable citation identifiers; original manuscript numbers are listed separately.

Knowledge scope

CITATION & SOURCE FILE

ASD: Dynamics · Experimental Relations and Tests. ASD-DOC-EN-THEORY-DYNAMICS-TESTS. Version 1.0.0; 2026-10-24. https://asd-physics.org/en/theory/dynamics/tests. §III.5 (2.24c)—(2.24d) and chapter summary. Source ASD-BOOK-ddbade997b45.

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