ANISOTROPIC SPACE DYNAMICS · OPEN RESEARCH

Strong-field closure

Derive strong-field X, radial scale and standard-process coupling from a longitudinal–transverse action, source boundary conditions and stable solutions; identify microscopically fixed coefficients.

Based on the final manuscript · Chapter 2

TheoryTheory · OPENReviewMathematical review · OPEN REVIEWEvidenceEvidence · UNTESTEDCanonicalNoStatus, review and sources

OP-GRV-001 · P2

NEEDS THEORY · Needs theory

AstrophysicsPDE

Discuss this task

01Task

An open research task extracted from the final Chapter 2 manuscript, not a new canonical derivation.

02Current state

Both radial-length integrals are analytic in the adopted exterior model, and photon-sphere and capture scales have been obtained. Boundary-cell counting gives area entropy, while the fixed-parameter sequence gives temperature and a first law. Unclosed tasks are termination-boundary formation, microstate capacity, correlation corrections and joint boundary–exterior evolution; these gaps do not erase the existing analytic results.

ASD-WEB-GRV-002

\Omega=\left(1-\frac{2G_0M}{c^2r}\right)^{-1/2},\quad\Phi=\Omega^{-1}

Constitutive input
r is areal radius with r > 2G₀M/c². The full strong-field function is a constitutive input, not uniquely fixed by weak redshift.
Chapter reference: Final collected manuscript · Chapter 2 §I.2 (2.3)—(2.4) · ASD-BOOK-ddbade997b45

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

ASD-WEB-GRV-003

X=\Phi^2=1-\frac{2G_0M}{c^2r},\quad\Psi=\frac{c^2}{2}(X-1)=-\frac{G_0M}{r}

Definition
Conditional on the stated inputs and domain. Manuscript numbering is separate from the website ID.
Chapter reference: Final collected manuscript · Chapter 2 §II.2 (2.6) · ASD-BOOK-ddbade997b45

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

ASD-WEB-GRV-005

\nabla^2\Psi=4\pi G_0\rho_g,\quad\nabla^2X=\frac{8\pi G_0}{c^2}\rho_g,\quad M=\frac{c^2}{8\pi G_0}\oint\nabla X\cdot d\mathbf S

Constitutive input
Weak static source equations in reference coordinates, not a closed dynamical strong-field master equation.
Chapter reference: Final collected manuscript · Chapter 2 §II.2 (2.7a)—(2.7b) · ASD-BOOK-ddbade997b45

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

ASD-WEB-GRV-038

\begin{aligned}\ell_s(r_h,r)&=\sqrt{r(r-r_h)}+r_h\ln\frac{\sqrt r+\sqrt{r-r_h}}{\sqrt{r_h}},\\\ell_{\mathrm{opt}}(r_1,r_2)&=(r_2-r_1)+r_h\ln\frac{r_2-r_h}{r_1-r_h}.\end{aligned}

Mathematical result
Exact analytic integrals for the adopted X=1−r_h/r, with r>r_h and r₂≥r₁>r_h. Actual length remains finite while the reference optical path diverges logarithmically as its inner endpoint approaches the boundary.
Chapter reference: Final collected manuscript · Chapter 2 §V.1 (2.60)—(2.62) · ASD-BOOK-ddbade997b45

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

ASD-WEB-GRV-050

\begin{aligned}c^2\frac{dM}{dt}&=P_{\rm in}-P_{\rm out},\qquad A_h=\frac{16\pi G_0^2M^2}{c^4},\\N_h&=\frac{A_h}{a_*},\quad W=g_*^{N_h},\\S_{\rm bdy}&=k_B\ln W=k_B\sigma_hA_h,\qquad\sigma_h=\frac{\ln g_*}{a_*}.\end{aligned}

Mathematical result
Nonrotating uncharged quasistatic sequence at fixed G₀; counting model of approximately independent area cells and accessible states. The microscopic a_*, g_* and correlation corrections remain to be determined.
Chapter reference: Final collected manuscript · Chapter 2 §V.7 (2.84)—(2.87) · ASD-BOOK-ddbade997b45

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

ASD-WEB-GRV-051

\begin{aligned}T_{\rm bdy}&=\frac{c^6}{32\pi k_B\sigma_hG_0^2M},\qquad dE_{\rm bdy}=T_{\rm bdy}\,dS_{\rm bdy},\\\sigma_h=\frac{c^3}{4G_0\hbar}&\ \Longrightarrow\ T_{\rm bdy}=\frac{\hbar c^3}{8\pi G_0k_BM},\qquad C_{\rm bdy}=-\frac{Mc^2}{T_{\rm bdy}},\\dE_{\rm bdy}&=T_{\rm bdy}\,dS+\omega_{\rm bdy}\,dJ+\mathcal V_{\rm bdy}\,dQ.\end{aligned}

Mathematical result
Fixed G₀, c and σ_h with E=Mc²; the temperature coefficient adopts the Bekenstein–Hawking reference normalization. The last line assumes differentiable E(S,J,Q), not an already solved rotating strong-field microstate.
Chapter reference: Final collected manuscript · Chapter 2 §V.8 (2.88)—(2.94) · ASD-BOOK-ddbade997b45

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

03Required work

04Deliverable and boundary

A reviewable action, field equations, exterior solution, weak-field matching and stability analysis, with adopted inputs distinguished from outputs.

Weak-field redshift does not uniquely select a full strong-field function; X=0 of an adopted function does not prove boundary formation.

05Sources and collaboration

Final collected manuscript · Chapter 2 §五.1—8 (2.59)—(2.94)及小结第四项

Gravity · Tests

On this page

STATUS & REVIEW

Theory StatusTheory · OPEN

Mathematical ReviewMathematical review · OPEN REVIEW

Overall Evidence StatusEvidence · UNTESTEDOpen research task; no new confirmed observational result.

Canonical ASDNo · Website guideResearch task from Chapter 2

Mathematical Review Note

Results are conditional on the stated scale, path and coupling inputs; mathematical reproduction and microscopic closure are distinct.

Read the formal review items

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

Adopted source, conditions and previous versions

§V.1—8 (2.59)—(2.94) and summary item 4

Update open-problem progress with established results; retain problem IDs and unresolved tasks.

Conditions retained in this adoption

Fixed G₀; isolated, static, spherically symmetric, uncharged exterior.
Areal radius, actual spatial length and reference optical path are defined separately.
Weak-field perturbation, slow-rotation far field and boundary statistics each have separate conditions.

Specific unresolved source issues

Strong-field, microscopic and full apparatus closure remain task-specific research.

Source locators: p0784 · p0786 · p0794 · p0796 · p0820 · p0822 · p0876 · p0878 · p0886 · p0891 · p0899 · p0937

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 / 第二章 · §I–II, §IV conclusion, §V.1; pp. 3–6, 17–18

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

Gravity · Spatial Structure and Observables

RESEARCH LEDGER

Revision history

2026-09-14

CONTENT REVISION

Gravity v1.0 · Canonical content release

Editorial record

SOURCE & SCOPE

Chapter 2 · §V.1—8 (2.59)—(2.94) and summary item 4

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: Strong-field closure. OP-GRV-001-EN. Version 1.0.0; 2026-10-24. https://asd-physics.org/en/open-problems/gravity/strong-field-closure. §V.1—8 (2.59)—(2.94) and summary item 4. Source ASD-BOOK-ddbade997b45.

Discuss this page Download this page as MDX

CONTINUE RESEARCH

Continue with the assumptions, equations and sources.

Ask ASD Researcher Verify Derivation Challenge 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.