---
{
  "id": "OP-MAT-003-EN",
  "path": "/en/open-problems/matter/mass-generation",
  "title": "OP-MAT-003 · Mass Generation",
  "title_en": "OP-MAT-003 · Mass Generation",
  "category": "Matter & Topology",
  "summary": "The final manuscript separately defines rest-energy mass, translational inertia, active gravitational source and passive response, and states the source-coupling and normalization matching needed for equality. Local divergence coupling has zero exterior density response; an independent frame-stretch extension supplies an integrable 1/r far field.",
  "template": "problem",
  "version": "1.0.0",
  "updated": "2026-10-24",
  "canonical": false,
  "source_tier": "research-notes",
  "theory_status": "OPEN",
  "evidence_status": "UNTESTED",
  "locale": "en",
  "module_key": "matter-research",
  "module_navigation": [
    {
      "path": "/en/theory/matter",
      "label": "Overview",
      "en": "Overview"
    },
    {
      "path": "/en/theory/matter/localization",
      "label": "Localization",
      "en": "Localization"
    },
    {
      "path": "/en/theory/matter/topological-matter",
      "label": "Topology",
      "en": "Topology"
    },
    {
      "path": "/en/theory/matter/stability",
      "label": "Stability",
      "en": "Stability"
    },
    {
      "path": "/en/theory/matter/mass",
      "label": "Mass",
      "en": "Mass"
    },
    {
      "path": "/en/theory/matter/charge",
      "label": "Charge",
      "en": "Charge"
    },
    {
      "path": "/en/theory/matter/spin",
      "label": "Spin",
      "en": "Spin"
    },
    {
      "path": "/en/theory/matter/electron",
      "label": "Electron",
      "en": "Electron"
    },
    {
      "path": "/en/theory/matter/proton",
      "label": "Proton",
      "en": "Proton"
    },
    {
      "path": "/en/theory/matter/antimatter",
      "label": "Antimatter",
      "en": "Antimatter"
    },
    {
      "path": "/en/theory/matter/creation",
      "label": "Creation",
      "en": "Creation"
    },
    {
      "path": "/en/theory/matter/annihilation",
      "label": "Annihilation",
      "en": "Annihilation"
    },
    {
      "path": "/en/tests/matter",
      "label": "Requirements",
      "en": "Requirements"
    }
  ],
  "canonical_scope": "Canonical research framework · not a closed particle theory",
  "source_chapter": "第五章",
  "source_reference": "第五章 §6.7 式（5.6.26）—（5.6.29）；§6.4 式（5.6.14）—（5.6.17）",
  "source_version": "ASD-BOOK-ddbade997b45",
  "source_sha256": "dace8ff491b4e4ae8a59b2b98e2a6c9c10e689079021ce0bc117985baba68e86",
  "source_kind": "manifest",
  "source_records": [
    {
      "id": "ASD-BOOK-ddbade997b45",
      "title": "各向异性空间动力学（最终合订稿）",
      "filename": "各向异性空间动力学.docx",
      "format": "docx",
      "size_bytes": 503564,
      "sha256": "ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e"
    }
  ],
  "source_manifest": "final-manuscript-source-manifest.json",
  "source_manifest_url": "/downloads/ASD_Final_Manuscript_Source_Manifest.json",
  "last_reviewed": "2026-09-16",
  "depends_on": [
    "/en/theory/matter/mass",
    "/en/theory/space-dynamics/longitudinal-transverse-coupling"
  ],
  "related": [
    "/en/theory/matter"
  ],
  "open_problems": [
    "/en/open-problems/matter/electron-solution",
    "/en/open-problems/matter/topological-classification",
    "/en/open-problems/matter/spin-statistics",
    "/en/open-problems/matter/proton-structure",
    "/en/open-problems/matter/mass-spectrum",
    "/en/open-problems/matter/creation-annihilation"
  ],
  "equations": [
    "mat-mass-equality",
    "sd-mass-match"
  ],
  "sources": [
    {
      "label": "Final combined manuscript — adopted scope documented on this page",
      "kind": "final-combined-manuscript",
      "url": "/downloads/ASD_Final_Manuscript_Source_Manifest.json"
    },
    {
      "label": "Previous source: CH4-9587f3c44d39 · 第四章-ASD空间本体论-出版整理稿.docx",
      "kind": "historical-source"
    },
    {
      "label": "Previous source: CH5-ca737ec4e327 · 第五章-出版整理稿.docx",
      "kind": "historical-source"
    }
  ],
  "outline": [
    "Established results",
    "Research still required",
    "The next reproducible deliverable",
    "Scope and research links"
  ],
  "seo_title": "OP-MAT-003 · Mass Generation | Anisotropic Space Dynamics",
  "canonical_url": "https://asd-physics.org/en/open-problems/matter/mass-generation",
  "translation_path": "/open-problems/matter/mass-generation",
  "mathematical_review": "INCOMPLETE",
  "evidence_note": "NOT YET UNIQUELY TESTED · observed particle properties are requirements, not validation of candidate topology.",
  "equation": "mat-mass-equality",
  "translation_of": "/open-problems/matter/mass-generation",
  "translation_version": "1.0.0",
  "problem": {
    "expertise": [
      "Variational methods",
      "Continuum dynamics",
      "Gravitational response"
    ],
    "difficulty": "Open research",
    "missing_result": "Compute all four masses independently on one localized solution and motion family, with one accounting of core, accompanying field, interaction and boundary contributions. Retain the full Legendre transform when a source depends on velocity, and test whether one microscopic parameter set yields the required normalization.",
    "deliverable": "Deliver integrals or response calculations for all four definitions, units, convergence checks and differences; identify which of G and the source coefficients are inputs and which are independently calculated.",
    "current_state": "The final manuscript separately defines rest-energy mass, translational inertia, active gravitational source and passive response, and states the source-coupling and normalization matching needed for equality. Local divergence coupling has zero exterior density response; an independent frame-stretch extension supplies an integrable 1/r far field."
  },
  "section_anchors": [
    "current-results",
    "remaining-work",
    "next-deliverable",
    "scope-and-links"
  ],
  "legacy_anchors": {
    "s0": "current-results",
    "s1": "remaining-work",
    "s2": "next-deliverable",
    "s3": "scope-and-links"
  },
  "final_source": {
    "source_id": "ASD-BOOK-ddbade997b45",
    "chapter": "第五章",
    "reference": "第五章 §6.7 式（5.6.26）—（5.6.29）；§6.4 式（5.6.14）—（5.6.17）",
    "locators": [
      "p2248",
      "p2251",
      "p2254",
      "p2284",
      "p2294"
    ],
    "adopted_scope": "已得结果、继续研究任务与下一份交付；保留原问题 ID、优先级及状态。",
    "conditions": [
      "m=E/c² defines energy mass; fixing a normalization with measured G does not derive G. Distinct definitions do not imply necessarily unequal masses."
    ],
    "unresolved": [],
    "migration_status": "reviewed",
    "manuscript_sha256": "ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e",
    "source_manifest": "final-manuscript-source-manifest.json",
    "body_review": "updated"
  },
  "previous_source": {
    "source_chapter": "Chapter 4 / 第四章 · Chapter 5 / 第五章",
    "source_reference": "Ch. 4 §4.2; Ch. 5 §6",
    "source_version": "MAT-d1034a344d58",
    "source_sha256": "d1034a344d5830113b6599e6941ee0d1a6d22872f18c593eccf87cf21ccf2a7e",
    "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": "matter-source-manifest.json",
    "source_manifest_url": "/downloads/ASD_Matter_Source_Manifest.json",
    "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"
      }
    ]
  }
}
---
## Established results

The final manuscript separately defines rest-energy mass, translational inertia, active gravitational source and passive response, and states the source-coupling and normalization matching needed for equality. Local divergence coupling has zero exterior density response; an independent frame-stretch extension supplies an integrable 1/r far field.

<Equation name="mat-mass-equality" />

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

## Research still required

Compute all four masses independently on one localized solution and motion family, with one accounting of core, accompanying field, interaction and boundary contributions. Retain the full Legendre transform when a source depends on velocity, and test whether one microscopic parameter set yields the required normalization.

## The next reproducible deliverable

Deliver integrals or response calculations for all four definitions, units, convergence checks and differences; identify which of G and the source coefficients are inputs and which are independently calculated.

## Scope and research links

m=E/c² defines energy mass; fixing a normalization with measured G does not derive G. Distinct definitions do not imply necessarily unequal masses.

[mass](/en/theory/matter/mass) · [source coupling](/en/open-problems/space-dynamics/source-coupling) · [mass](/en/theory/matter/mass) · [longitudinal transverse coupling](/en/theory/space-dynamics/longitudinal-transverse-coupling) · [matter](/en/theory/matter)

<CanonicalSource />