---
{
  "id": "OP-SD-006-EN",
  "path": "/en/open-problems/space-dynamics/source-coupling",
  "title": "OP-SD-006 · Source Coupling",
  "title_en": "OP-SD-006 · Source Coupling",
  "category": "Space Dynamics",
  "summary": "With smooth all-space fields and zero far boundary, the local $sF$ candidate gives density supported with the core. Independent stretch admits a $1/r$ far field, but its source functional has not been derived from a stable matter core.",
  "template": "problem",
  "version": "1.0.0",
  "updated": "2026-09-16",
  "canonical": false,
  "source_tier": "research-notes",
  "theory_status": "OPEN",
  "evidence_status": "UNTESTED",
  "locale": "en",
  "module_key": "space-dynamics-research",
  "module_navigation": [
    {
      "path": "/en/theory/space-dynamics",
      "label": "Overview",
      "en": "Overview"
    },
    {
      "path": "/en/theory/space-dynamics/degrees-of-freedom",
      "label": "Degrees of freedom",
      "en": "Degrees of freedom"
    },
    {
      "path": "/en/theory/space-dynamics/longitudinal-field",
      "label": "Longitudinal field",
      "en": "Longitudinal field"
    },
    {
      "path": "/en/theory/space-dynamics/transverse-field",
      "label": "Transverse field",
      "en": "Transverse field"
    },
    {
      "path": "/en/theory/space-dynamics/wave-propagation",
      "label": "Wave propagation",
      "en": "Wave propagation"
    },
    {
      "path": "/en/theory/space-dynamics/longitudinal-waves",
      "label": "Longitudinal waves",
      "en": "Longitudinal waves"
    },
    {
      "path": "/en/theory/space-dynamics/longitudinal-transverse-coupling",
      "label": "L–T coupling",
      "en": "L–T coupling"
    },
    {
      "path": "/en/theory/space-dynamics/continuum-dynamics",
      "label": "Continuum dynamics",
      "en": "Continuum dynamics"
    },
    {
      "path": "/en/theory/space-dynamics/fcc-model",
      "label": "FCC-like model",
      "en": "FCC-like model"
    },
    {
      "path": "/en/theory/space-dynamics/master-equation",
      "label": "Master equation",
      "en": "Master equation"
    },
    {
      "path": "/en/tests/space-dynamics",
      "label": "Tests",
      "en": "Tests"
    }
  ],
  "canonical_scope": "Continuum foundation; status specified per claim",
  "source_chapter": "Chapter 4 / 第四章 · Chapter 5 / 第五章",
  "source_reference": "Ch. 4 §4.1; Ch. 5 §§4, 6",
  "source_version": "SD-51779505a476",
  "source_sha256": "51779505a4766d2211550c6598875bbbab0c3dac14d68dd3f2107778b05deb0b",
  "source_kind": "manifest",
  "source_records": [
    {
      "id": "CH4-9587f3c44d39",
      "title": "第四章-ASD空间本体论-出版整理稿.docx",
      "sha256": "9587f3c44d3974f44e387ed03d92691fa5473a90d7b1c9c989155adf0622849a",
      "format": "docx"
    },
    {
      "id": "CH5-ca737ec4e327",
      "title": "第五章-出版整理稿.docx",
      "sha256": "ca737ec4e327d72c5507bbc8e00295b6e56029c7583ebad8e505cdb9c68c6262",
      "format": "docx"
    }
  ],
  "source_manifest": "space-dynamics-source-manifest.json",
  "source_manifest_url": "/downloads/ASD_Space_Dynamics_Source_Manifest.json",
  "last_reviewed": "2026-09-15",
  "depends_on": [
    "/en/theory/space-dynamics/longitudinal-field",
    "/en/theory/space-dynamics/master-equation"
  ],
  "related": [
    "/en/theory/space-dynamics",
    "/en/open-problems/matter/mass-generation"
  ],
  "open_problems": [
    "/en/open-problems/space-dynamics/unified-dynamics",
    "/en/open-problems/space-dynamics/equal-speed",
    "/en/open-problems/space-dynamics/stable-topology",
    "/en/open-problems/space-dynamics/continuum-microscopic",
    "/en/open-problems/space-dynamics/longitudinal-wave-detection"
  ],
  "equations": [
    "sd-static-density",
    "sd-stretch-farfield",
    "sd-mass-match"
  ],
  "sources": [
    {
      "label": "CH4-9587f3c44d39 · 第四章-ASD空间本体论-出版整理稿.docx",
      "kind": "supplied-manuscript"
    },
    {
      "label": "CH5-ca737ec4e327 · 第五章-出版整理稿.docx",
      "kind": "supplied-manuscript"
    }
  ],
  "outline": [
    "Current baseline",
    "Work required",
    "Reviewable deliverable",
    "Limits and dependencies",
    "Matter research continuation"
  ],
  "seo_title": "OP-SD-006 · Source Coupling | Anisotropic Space Dynamics",
  "canonical_url": "https://asd-physics.org/en/open-problems/space-dynamics/source-coupling",
  "translation_path": "/open-problems/space-dynamics/source-coupling",
  "mathematical_review": "INCOMPLETE",
  "evidence_note": "Constraints and proposals are recorded separately; no new experimental fit.",
  "equation": "sd-static-density",
  "translation_of": "/open-problems/space-dynamics/source-coupling",
  "translation_version": "1.0.0",
  "problem": {
    "expertise": [
      "Field sources",
      "Nonlinear solutions",
      "Gravitational limits"
    ],
    "difficulty": "Open research",
    "missing_result": "A complete solution chain from stable matter core to gravitational far field, computing energy, active/passive gravitational mass and inertia from the same solution with independently specified coefficients.",
    "deliverable": "A complete solution chain from stable matter core to gravitational far field, computing energy, active/passive gravitational mass and inertia from the same solution with independently specified coefficients.",
    "current_state": "With smooth all-space fields and zero far boundary, the local $sF$ candidate gives density supported with the core. Independent stretch admits a $1/r$ far field, but its source functional has not been derived from a stable matter core."
  }
}
---
## Current baseline

With smooth all-space fields and zero far boundary, the local $sF$ candidate gives density supported with the core. Independent stretch admits a $1/r$ far field, but its source functional has not been derived from a stable matter core.

<Equation name="sd-static-density" />

<Equation name="sd-stretch-farfield" />

<Equation name="sd-mass-match" />

## Work required

Define the mapping and energies of observed gravitational stretch, displacement divergence and an independent scalar without double counting. Derive the source functional, feedback, active mass, inertia and external-field response from one finite-energy matter solution. Check far-field sign, normalization, boundaries, universality and conservation in motion.

## Reviewable deliverable

A complete solution chain from stable matter core to gravitational far field, computing energy, active/passive gravitational mass and inertia from the same solution with independently specified coefficients.

## Limits and dependencies

A displacement tail is not automatically a $1/r$ density tail. Imposing that density tail can make the corresponding energy diverge; calibrating normalization with known $G$ does not derive $G$.

[Longitudinal field](/en/theory/space-dynamics/longitudinal-field) · [Master equation](/en/theory/space-dynamics/master-equation)



## Matter research continuation

[OP-MAT-003: mass generation](/en/open-problems/matter/mass-generation) separately computes energy, inertial, active and passive gravitational masses on one solution.

<CanonicalSource />