forked from bai/curriculum-project-hub
feat(cph): implement nested outline manifest and batch/combined export
ADR-0029 — nested outline manifest, supersedes ADR-0008's flat [[parts]]:
- cph-model: recursive loader over manifest.toml containers / element.toml
leaves; Lesson.parts (pure elements, DFS order) + Lesson.outline (elements
interleaved with section headings at their DFS-open position); rejects
ambiguous/incomplete folders and root-vs-container table misplacement
- cph-diag: new DiagCode::ManifestMalformed for carrier-document structure
errors (discharges an existing TODO)
- cph-typst: augmented manifest now serializes the outline (element/section
entries) instead of a flat parts array
- render/lib.typ: render-lesson renders section headings at their depth
- examples/TH-141 migrated to 5 nested section containers + 3 root segments,
byte-identical element order; smoke-verified via cph check/build + pdftotext
ADR-0030 — batch & combined export, extends ADR-0009/0011:
- cph build with no --target batches every declared target (repeatable
--target for an explicit subset); any target failure => non-zero exit,
per-target ledger, independent per-target execution
- cph-model: bundle.toml loader (directory + [info]/[targets.*]/ordered
lessons with per-lesson target overrides)
- cph-typst: augmented bundle manifest (path-prefixed member outlines),
Engine::{compile_check_bundle,build_bundle_pdf}
- render/lib.typ: render-bundle assembles member lessons under per-lesson
headings, depth-shifts their own section headings, resets example/lemma
counters at each lesson boundary by default
- cph-cli: `cph bundle <path> --target <name>` subcommand, same batching
contract as `cph build`
- new bundle fixtures/tests (cph-model unit + cph-typst through-template PDF
compile), smoke-verified via a real 2-lesson merged PDF
Verification: cargo fmt/clippy/test clean across the workspace (68 tests);
real cph check/build/bundle runs against TH-141 and a bundle fixture, PDF
content inspected via pdftotext.
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kind = "lemma"
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不同晶面的表面原子缺键数不同，故 $gamma_(S G)$ 随晶面指数 $(h k l)$ 而变。以简单立方为例：(100) 缺 1 键、(110) 缺 2 键、(111) 缺 3 键，从而
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$ gamma_(S G)^((100)) < gamma_(S G)^((110)) < gamma_(S G)^((111)) . $ <晶面各向异性>
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kind = "lemma"
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设固体体积 $V$、表面积 $A$，应变 $epsilon$ 为均匀小量。体相单位体积的自由能 $f_b = Y epsilon^2 \/ 2$，表面单位面积的自由能 $gamma(epsilon)$，总自由能
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$ F = V f_b + A gamma(epsilon) . $
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对均匀拉伸 $V epsilon$ 求导得单位横截面承担的应力
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$ sigma_("tot") = (partial F) / (partial (V epsilon)) = Y epsilon + A / V dot (dif gamma) / (dif epsilon) , $
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即 @总应力。
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对横截面被均匀拉伸的固体，单位横截面承担的总应力为
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$ sigma_("tot") = Y epsilon + A / V dot (dif gamma) / (dif epsilon) , $ <总应力>
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其中 $Y$ 为杨氏模量、$epsilon$ 为应变、$A \/ V$ 为表面积与体积之比。第一项为体相弹性贡献，第二项为表面贡献。
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kind = "lemma"
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固气界面 $gamma_(S G)$ 的缺键模型公式由 @缺键一般式 直接迁移，只把摩尔汽化热 $L_m$ 替换为摩尔升华热 $L_s$：
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$ gamma_(S G) = (1 - zeta) thin L_s thin rho^(2\/3) / (mu^(2\/3) thin N_A^(1\/3)) . $ <固气缺键式>
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物理来源也只是把"把分子从液体里拉出来"换成"把原子从晶格里拉出来"，骨架公式 @骨架公式 与单键计数过程不变。
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[group]
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title = "固气界面"
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[[children]]
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kind = "segment"
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path = "segments/固气界面导言"
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[[children]]
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kind = "segment"
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path = "segments/表面能γ与表面应力f"
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[[children]]
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kind = "lemma"
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path = "lemmas/拉伸固体的总应力"
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[[children]]
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kind = "lemma"
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path = "lemmas/缺键模型迁移到固气"
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[[children]]
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kind = "lemma"
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path = "lemmas/固体表面能的晶面各向异性"
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[[children]]
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kind = "segment"
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path = "segments/不同物质γ量级对比"
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kind = "segment"
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不同物质的表面张力系数差异可达两个量级。
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#figure(
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table(
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columns: (auto, auto),
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align: (left, left),
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table.header[*物质*][*$gamma$ ($"J/m"^2$)*],
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[水（液气界面）], [$approx 0.072$],
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[分子晶体], [$0.05 thin "—" thin 0.1$],
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[离子晶体], [$0.2 thin "—" thin 1$],
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[金属（Au、Fe、W）], [$1 thin "—" thin 3$],
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),
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caption: [常见物质表面张力系数的典型量级]
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) <γ量级表>
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该量级谱可由缺键模型 @固气缺键式 解释。分子晶体的键合主要是范德瓦尔斯力，$L_s$ 小、$gamma$ 小；离子晶体的键合包含库仑作用，$L_s$ 上升一个量级，$gamma$ 也随之上升；金属内部的金属键键合最强，$L_s$ 最大、$gamma$ 最大。同一公式横跨四个数量级的物理体系都给出对的量级。
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kind = "segment"
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= 固气界面 $sigma_(S G)$ 的微观建模
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固体表面没有"流动补缺"这条退路。从物理上讲，"创造新表面"与"拉伸已存在表面"在固体中是两件独立的事，对应两个不同的物理量——表面能 $gamma$ 与表面应力 $f$。本节先把这二者分清，再把缺键模型 @缺键一般式 中的摩尔汽化热替换为摩尔升华热，得到固气界面的 $gamma_(S G)$。最后讨论 $gamma_(S G)$ 的晶面各向异性以及不同物质的 $gamma$ 量级谱。
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kind = "segment"
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液体的 $sigma$ 同时描述两件事：创造单位新表面要付出的能量代价，以及拉伸单位已有表面的弹性反应。它们在液体里合二为一——液体可自由流动，"拉伸"等价于"补充新分子"。
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固体不能流动，这两件事必须分开。设单位面积的表面能为 $gamma$，其定义为创造单位新表面所需的可逆功。再设单位长度的表面应力为 $f$，其定义为把已有的单位面积表面拉伸应变 $epsilon$ 所需的功面密度。两者之间的关系由 Shuttleworth 给出
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$ f = gamma + (dif gamma) / (dif epsilon) , $
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其中右端第二项反映 $gamma$ 本身随应变变化的部分。一般有 $f eq.not gamma$。
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本节及之后所有讨论以 $gamma$ 为对象。$f$ 仅在真正"拉固体"的场景下登场，例如薄膜应力、纳米颗粒形变，本节不展开。
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