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
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kind = "segment"
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考虑一根原长 $L_0$、劲度系数 $k$ 的弹性绳,把它拉伸至长度 $L$。宏观上张力为 $F = k(L - L_0)$,随长度线性增大。从微观上看,弹性绳内部的所有分子被一同拉远,分子间距由 $d_0$ 增至 $d_0 (L \/ L_0)$,键能上升,张力即为这些键被拉长所提供的回复力之和。
二维弹性膜的情形与此完全平行。设原面积 $A_0$、二维劲度系数 $k_("2D")$,把面积拉至 $A$,则单位长度上的张力沿两个主方向各贡献一份,随应变 $(A - A_0) \/ A_0$ 线性增大。无论一维还是二维,弹性体被拉伸时承担应力的始终是同一批分子——拉伸前后分子数不变,变的是它们之间的距离。