OP-SD-004 · Continuum-to-Microscopic Correspondence
The equal-connection FCC scalar model has a full-wave-number cosine dispersion, second moment and long-wave expansion. Continuous-time lattice propagation, the full multicomponent field and feedback-renormalized speeds are different checks. This review finds that Eq. (5.1.11), its following half-angle form and fourth-order expansion cannot all be identical with their printed coefficients; the FCC page records the specific difference.
Based on the final manuscript · 第五章
READY · Ready for stated work
Discuss this task01Established results
The equal-connection FCC scalar model has a full-wave-number cosine dispersion, second moment and long-wave expansion. Continuous-time lattice propagation, the full multicomponent field and feedback-renormalized speeds are different checks. This review finds that Eq. (5.1.11), its following half-angle form and fourth-order expansion cannot all be identical with their printed coefficients; the FCC page records the specific difference.
Mathematical result
Twelve neighbours, four sign combinations per group; a geometric result.
Chapter reference: Ch. 4 (4.3)–(4.4); Ch. 5 (5.1.3)–(5.1.4) · ASD-BOOK-ddbade997b45
Mathematical result
Equal-link scalar/selected-polarization channel, Γ₀>0 and c²=Γ₀a₀². Uses the full cosine spectrum (5.1.11)/(4.12); the printed half-angle coefficient preceding (5.1.12) is 2 rather than the equivalent 4, recorded locally.
Chapter reference: Ch. 4 (4.12)–(4.13); Ch. 5 (5.1.11); coefficient discrepancy preceding (5.1.12) · ASD-BOOK-ddbade997b45
02Research still required
First sum every neighbour and expand with one coefficient convention, retaining manuscript equation numbers and reporting the discrepancy instead of silently replacing it. Then derive all branches, coarse-graining weights and error orders from the full connection law, testing projection mixing in nonuniform backgrounds and microscopic refresh fronts.
03The next reproducible deliverable
Deliver a reproducible neighbour table, dynamical matrix, inter-equation coefficient check and reviewable correction options; only then provide coefficient-dependent dispersion plots, domains and directional experimental response.
04Scope and research links
High symmetry does not replace connection dynamics; second-order isotropy does not imply isotropy at every wave number, and finite adjacency in continuous time does not automatically give a strictly zero-response light cone.
fcc model · wave propagation · continuum dynamics · fcc model · space dynamics
On this page
Adopted source, conditions and previous versions
第五章 §1.1—§1.2 式（5.1.1）—（5.1.13）；§6.3 式（5.6.12）—（5.6.13）
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
- High symmetry does not replace connection dynamics; second-order isotropy does not imply isotropy at every wave number, and finite adjacency in continuous time does not automatically give a strictly zero-response light cone.
Specific unresolved source issues
- 式（5.1.11）与半角式及四阶展开的系数冲突待作者决定
Source locators: p1770 · p1772 · p1773 · p1774 · p2244 · p2303
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 §1.1—§1.2 式（5.1.1）—（5.1.13）；§6.3 式（5.6.12）—（5.6.13）
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-004 · Continuum-to-Microscopic Correspondence. OP-SD-004-EN. Version 1.0.0; 2026-10-24. https://asd-physics.org/en/open-problems/space-dynamics/continuum-microscopic. 第五章 §1.1—§1.2 式（5.1.1）—（5.1.13）；§6.3 式（5.6.12）—（5.6.13）. Source ASD-BOOK-ddbade997b45.
Continue with the assumptions, equations and sources.
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