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>
This commit is contained in:
2026-06-22 01:33:40 +08:00
parent 752a5c661d
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kind = "lemma"
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设下半空间体相分子的数密度为 $n_v = 1 \/ d^3$。固定一个表面分子作为参考分子,对其与下半空间所有体相分子的相互作用求和。由对称性,相对参考分子距离 $r$ 在下半空间内的体积元为 $dif V = 2 pi r^2 dif r$。下限取 $r = d$,上限取 $infinity$
$ Delta U = 2 pi n_v integral_d^infinity u(r) thin r^2 dif r . $
代入 $u(r)$,用 $integral r^2 dot r^(-n) dif r = r^(3 - n) \/ (3 - n)$ 化简,得
$ Delta U tilde.op epsilon . $
$Delta U$ 乘以单位面积分子数 $n_s tilde.op 1 \/ d^2$,由 @骨架公式 即得
$ sigma tilde.op epsilon / d^2 , $
@LJ标度。
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设分子间对势为 LennardJones 6-12 形式
$ u(r) = 4 epsilon [(d \/ r)^(12) - (d \/ r)^6] . $
把一个表面分子与下半空间所有分子的相互作用积分求和,得到
$ sigma tilde.op epsilon / d^2 . $ <LJ标度>
此式与量纲估计 @量纲估计 同标度。