FCC continuum consistency
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
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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.
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.
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.
01Established 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.
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.
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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
·
第五章 §1.1—§1.2 式（5.1.1）—（5.1.13）；§6.3 式（5.6.12）—（5.6.13）
- Final combined manuscript — adopted scope documented on this page
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