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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>
14 lines
437 B
Typst
14 lines
437 B
Typst
把 @GG公式 给出的 $gamma_(S L) = (sqrt(gamma_(S G)) - sqrt(gamma_(L G)))^2$ 代入 @Young方程：
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$ cos theta = (gamma_(S G) - (sqrt(gamma_(S G)) - sqrt(gamma_(L G)))^2) / gamma_(L G) . $
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展开右端分子：
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$ gamma_(S G) - (gamma_(S G) - 2 sqrt(gamma_(S G) gamma_(L G)) + gamma_(L G)) = 2 sqrt(gamma_(S G) gamma_(L G)) - gamma_(L G) , $
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代回得
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$ cos theta = 2 sqrt(gamma_(S G) / gamma_(L G)) - 1 , $
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即 @GGZ判据。
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