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curriculum-project-hub/examples/TH-141/lemmas/立方格子下zeta具体值/stmt.typ
T
sjfhsjfh c73a2c903f feat(examples): migrate TH-141 sample to declarative layout (WU-6)
Real-content fixture for the end-to-end pipeline. TH-141 (39 parts: 22 segment,
15 lemma, 2 example) migrated from the prototype's typst `#let parts` manifest
to ADR-0008: declarative manifest.toml (project+info+ordered parts+targets) +
per-element element.toml (kind + scalars; examples carry `source`). Content .typ
files copied byte-identical (no math corruption); per-element main.typ + meta.toml
dropped (wiring is now generated). Part order matches source exactly; 5 lemmas
have no proof.typ (optional); no cross-file imports / paralearn refs / figs.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
2026-06-22 01:33:40 +08:00

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通过对几何晶格直接数缺键数,可以把 @缺键一般式 中的 $zeta$ 落到具体数字:
- 简单立方 (100) 面:$Z = 6$$Z_s = 5$$zeta = 5\/6$
- 面心立方 (111) 面:$Z = 12$$Z_s = 9$$zeta = 3\/4$
- 面心立方 (100) 面:$Z_s = 8$$zeta = 2\/3$
- 面心立方 (110) 面:$zeta < 2\/3$
后续讨论以 FCC (111) 面为代表,因其密度最大、$gamma$ 最低、平衡形貌中最易出现。