OP-SD-001 · Unified Longitudinal–Transverse Dynamics
The local two-field parent action, both variations, reciprocal sources and energy-square completion are established. The manuscript also gives an independent frame-stretch extension for the gravitational far field, the coupled vacuum spectrum and an analytic radius for the scale model. The task is joint closure of these existing ingredients, not finding an entirely unwritten master equation.
Based on the final manuscript · 第五章
NEEDS THEORY · Needs theory
Discuss this task01Established results
The local two-field parent action, both variations, reciprocal sources and energy-square completion are established. The manuscript also gives an independent frame-stretch extension for the gravitational far field, the coupled vacuum spectrum and an analytic radius for the scale model. The task is joint closure of these existing ingredients, not finding an entirely unwritten master equation.
Constitutive input
For dimensionless σ and ΩT, gLT has units J/m³; the construction is not unique.
Chapter reference: Ch. 5 (5.4.19) · ASD-BOOK-ddbade997b45
Constitutive input
An explicit local dual-field action; Θ has real components and W subtracts vacuum energy. Specify stabilizers, constitutive parameters and target space; complete microscopic unification still needs joint solution.
Chapter reference: Ch. 5 (5.6.3)–(5.6.5) · ASD-BOOK-ddbade997b45
02Research still required
Select complete variables, symmetries, boundaries and microscopic parameters. Use one action to test feedback-renormalized longitudinal/transverse propagation, localized matter, long-range gravitational sources and motion families. Local density response and independent stretch are distinct variables; speeds must be matched after order-parameter feedback.
03The next reproducible deliverable
Deliver the full variation, conserved quantities, vacuum spectrum and parameter domain of one explicit truncation; map it to the static far field, stable localization and accompanying-field envelope, recording incompatible conditions.
04Scope and research links
Reciprocal variation, an energy lower bound and a radial stationary point are distinct established results; none alone completes the particle spectrum, nonradial stability or all measurement responses.
master equation · longitudinal transverse coupling · longitudinal transverse coupling · master equation · space dynamics
On this page
Adopted source, conditions and previous versions
第五章 §6 式（5.6.1）—（5.6.30）
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 retained in this adoption
- Reciprocal variation, an energy lower bound and a radial stationary point are distinct established results; none alone completes the particle spectrum, nonradial stability or all measurement responses.
Source locators: p2222 · p2232 · p2235 · p2244 · p2254 · p2262 · p2281 · p2300
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
SD-51779505a476 · Ch. 4 §4.1; Ch. 5 §§4, 6
CH4-9587f3c44d39 · 第四章-ASD空间本体论-出版整理稿.docx9587f3c44d3974f44e387ed03d92691fa5473a90d7b1c9c989155adf0622849a
CH5-ca737ec4e327 · 第五章-出版整理稿.docxca737ec4e327d72c5507bbc8e00295b6e56029c7583ebad8e505cdb9c68c6262
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.
Revision history
第五章 · 第五章 §6 式（5.6.1）—（5.6.30）
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 scopeASD: OP-SD-001 · Unified Longitudinal–Transverse Dynamics. OP-SD-001-EN. Version 1.0.0; 2026-10-24. https://asd-physics.org/en/open-problems/space-dynamics/unified-dynamics. 第五章 §6 式（5.6.1）—（5.6.30）. Source ASD-BOOK-ddbade997b45.
Continue with the assumptions, equations and sources.
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