render-obsidian

Render Obsidian Wiki

Generate a rich Obsidian vault (gaia-wiki/) from a Gaia knowledge package.

Vault Architecture

gaia-wiki/
├── claims/
│   ├── holes/              Leaf premises — reasoning chain endpoints
│   ├── intermediate/       Derived but not exported
│   ├── conclusions/        Exported claims ★ + questions
│   └── context/            Settings, background, structural
├── sections/               Narrative chapters (DSL module order)
│   ├── 01 - Introduction.md
│   ├── ...
│   ├── 07 - Weak Points.md
│   └── 08 - Open Questions.md
├── meta/                   beliefs table, holes list
├── _index.md               Claim Index + Sections + Reading Path
├── overview.md             Simplified Mermaid
└── .obsidian/

• Claims = atomic content units, numbered by topological order. Each carries full derivation + prior justification.
• Sections = narrative chapters following the paper's arc. Agent rewrites titles. Last two sections are Weak Points and Open Questions.
• Wikilinks use labels, filenames use titles, aliases bridges them.

Pipeline

Step 1: gaia compile + gaia infer
Step 2: gaia render --target obsidian → skeleton
Step 3: Read inputs (IR, beliefs, DSL, artifacts/)
Step 4: Rewrite every page
Step 5: Cross-reference audit

Step 3: Read Inputs

cat .gaia/ir.json
cat .gaia/beliefs.json
cat src/<package>/*.py
ls artifacts/

Read artifacts/ cover-to-cover before writing any page.

Step 4: Rewrite Every Page

Core principle: Faithful reproduction. Each page replaces reading the paper for its topic.

Language: Follow user's preference. Frontmatter/wikilinks/Mermaid stay English.

---

Claim pages (claims/{holes,intermediate,conclusions,context}/*.md)

Each claim is a self-contained article. #XX number = position in reasoning chain.

Section ordering:

1. Title — Descriptive in user's language. Keep #XX prefix.
2. Content — Full explanation, all numbers/equations/conditions.
3. Background — Scientific context from artifacts/. What problem? Prior work? Gap? Embed figures with ![[file]] + italic caption.
4. Derivation — Reproduce the paper's FULL argument:
   • All equations with step-by-step explanation
   • Physical reasoning behind each step
   • Why each approximation is justified
   • Numerical validations from the paper
   • Appendix material
   • Use [[label|#XX label]] for cross-references
5. Review — From beliefs.json and priors.py:
   • **Prior**: 0.95
   • **Justification**: omega_D/E_F ~ 0.005; Migdal theorem validated.
   • **Belief**: 0.71
6. Supports — Downstream claims.
7. Significance — Why it matters. What breaks if wrong?
8. Caveats — Limitations, alternative explanations, uncertainties.

Depth by claim type:

Type	Depth
Conclusions (★)	Most detailed — full derivation chain, multiple paragraphs per section
Holes	Focus on source provenance — where does this evidence come from? Method, precision, limitations
Intermediate	Full derivation of this step in the chain
Context	Brief — what it establishes and why it's assumed

---

Section pages (sections/*.md)

Sections are narrative chapters that tell the paper's story. Claims within each section are sorted by topological order (evidence → derivation → conclusion).

Goal: A reader who reads sections 01 through 06 in order should understand the paper's complete argument without ever opening the original paper. Each section is a self-contained chapter of a "textbook rewrite" of the paper.

Page structure (from top to bottom):

1. Title — Descriptive narrative title in user's language. Keep number prefix.

2. Overview (10%) — 2-3 paragraphs setting up the section's question, approach, and key result.

3. Per-section Mermaid — Keep as-is.

4. Claims narrative (70% of the page — THIS IS THE MAIN BODY) — For EVERY claim in topo order, write a ### heading + 1-3 paragraphs. This is NOT optional. Every claim listed in the skeleton MUST appear with its narrative.

   CRITICAL: This section is the bulk of the page. Do NOT skip it. The skeleton has ### [[label|#XX title]] entries — the agent must expand EACH ONE into a full narrative paragraph.

   For each claim:

   • ### [[label|#XX title]] heading (keep the wikilink)
   • What this claim says in plain language, with key numbers and equations
   • Why this result matters for the section's argument
   • How it connects to the previous and next claims (logical flow)
   • If exported (★): highlight as a key conclusion with a callout block
   • Belief analysis: what does the prior→belief change reveal?

   Exported conclusions should be highlighted:

   ### [[downfolded_bse|#43 下折叠 BSE]] ★
   
   > [!IMPORTANT] 核心结论
   > 完整的动量-频率 BSE 可以严格化简为仅依赖频率的一维积分方程，
   > 误差仅 0.2%。
   
   这是本章最重要的结果...
   

5. Chapter summary (10%) — 本章建立了什么，为下一章准备了什么。

Full section page example (showing the required structure):

# 03 - 从微观推导下折叠 Bethe-Salpeter 方程

## 概述

(2-3 paragraphs: question, approach, key result)

(Mermaid graph)

## 推理链

### [[pair_propagator_decomposition|#18 配对传播子分解]]

配对传播子 $GG$ 可以精确分解为低能相干部分 $\Pi_{\mathrm{BCS}}$
和高能非相干余项 $\phi$。这不是一个近似——而是一个数学恒等式。
相干部分携带 Cooper 对数 $\ln(\omega_c/T)$，定义了低能配对通道。

论文选择在双电子通道（而非传统的粒子-空穴通道）引入能量尺度
分离，这是一个关键创新——传统方案会导致低能区域库仑相互作用
失去屏蔽。这一选择为下面的交叉项压制论证奠定了基础。

### [[cross_term_suppressed|#19 交叉项压制]]

有了配对传播子分解，关键问题是：库仑和声子通道的交叉项是否
会破坏可分离性？论文利用等离子体极子模型给出了严格的上界估计：
交叉项被压制在 $O(\omega_c^2/\omega_p^2) \leq 1\%$。

这是整条推理链中最脆弱的一环——belief 仅 0.50，反映了 1% 这个
边界条件的不确定性。如果交叉项实际上更大，整个下折叠理论的
精度保证就会失效。

### [[downfolded_bse|#43 下折叠 BSE]] ★

> [!IMPORTANT] 核心结论
> 频率-only 下折叠 BSE：$\Lambda_\omega = \eta_\omega + \pi T
> \sum (\lambda - \mu_{\omega_c}) z^{ph}_{\omega'}/|\omega'| \Lambda_{\omega'}$

结合配对传播子分解和交叉项压制，完整 BSE 化简为仅含频率的
一维积分方程。$\mu^*$ 和 $\lambda$ 获得了精确的微观定义...

(... more claims ...)

## 本章小结

本章从微观出发严格推导了下折叠 BSE，为 $\mu^*$ 和 $\lambda$
提供了精确定义。这为第四章通过 vDiagMC 计算 $\mu^*$ 和第五章
验证 DFPT $\lambda$ 的可靠性奠定了理论基础。

DO NOT write a section page with only the overview and Mermaid — the claims narrative is the main content that readers come here to read.

Weak Points section

Goal: A reader should understand WHERE the argument is weakest, WHY it's weak, and WHAT could fix it. This is a critical assessment, not a data dump.

The skeleton provides a table of the 10 lowest-belief claims. Agent should rewrite into a structured analysis:

1. Executive summary (1 paragraph) — The single most important takeaway. What is the weakest link in the entire reasoning chain? If you had to bet on which claim will fail, which one and why?

2. Structural analysis — Group weak points by their position in the reasoning graph:

   • Foundation weaknesses — Are any leaf premises (holes) controversial? If a widely-accepted fact turns out to be wrong, what collapses?
   • Bottleneck weaknesses — Are there single claims that many conclusions depend on? A low-belief bottleneck is more dangerous than a low-belief leaf.
   • Propagation effects — Does the reasoning graph amplify uncertainty? (e.g., "the downfolded BSE has belief 0.33 not because it's intrinsically unreliable, but because it depends on cross-term suppression which has belief 0.50, and the uncertainty propagates through 3 derivation steps")

3. For each major weak point (top 3-5), write a full paragraph:

   • What the claim says and where it sits in the reasoning chain
   • WHY the belief is low — trace the reasoning graph backwards to find the root cause
   • What the reviewer's justification says about the uncertainty
   • What competing explanation or alternative approach exists
   • What specific evidence or experiment would resolve the uncertainty
   • What downstream conclusions would be affected if this claim fails

4. Comparison with the paper's own assessment — Does the paper acknowledge these weaknesses? Does the reasoning graph reveal weaknesses the paper doesn't discuss?

Open Questions section

Goal: A reader should know exactly what work remains to be done, prioritized by impact. This is a research roadmap derived from the reasoning graph.

The skeleton lists holes and questions. Agent should rewrite into:

1. Overview (1-2 paragraphs) — The big picture: what would make this knowledge package "complete"? What's the most impactful single improvement?

2. Open questions from the paper — If the IR has type: question nodes, explain each:

   • What the question asks
   • Why it matters for the overall argument
   • What the paper suggests (if anything) as an approach
   • What the reasoning graph says about its impact (which conclusions depend on it?)

3. Evidence gaps (grouped by theme):

   Experimental gaps:

   • What measurements are missing or imprecise?
   • Which claims rely on the weakest experimental evidence?
   • What experiments would most reduce uncertainty?

   Computational gaps:

   • What calculations are approximate that could be made exact?
   • What parameters have the largest error bars?
   • What computational advances would help?

   Theoretical gaps:

   • What derivations rely on uncontrolled approximations?
   • Where does the theory break down (validity limits)?
   • What extensions would broaden applicability?

4. Impact analysis — For each gap, trace forward through the reasoning graph:

   • If this hole were filled with higher confidence, which conclusions would improve?
   • Rank the holes by "information value": how much would filling this hole reduce overall uncertainty?

5. Suggested next steps — Prioritized list of 3-5 actionable research directions, each with:

   • What to do
   • Why it's high-impact (which conclusions it would strengthen)
   • Estimated difficulty/feasibility

---

Overview, _index, meta

• Overview — Citation + abstract + simplified Mermaid graph.
• _index — Package description + statistics + Claim Index table (with numbers) + Sections table + Reading Path.
• Meta — beliefs.md: intro + full belief table. holes.md: intro + leaf premises table.

---

Quality standard

Faithful reproduction, not summarization. If the paper devotes 3 pages to a derivation, reproduce them in readable form. Include appendix material.

Every page must include:

• All relevant numerical values (units, error bars)
• Key equations with step-by-step explanation
• Derivation steps from the paper (including appendix)
• Figure embeds with italic captions
• Cross-references with claim numbers [[label|#XX label]]
• Review justification where available

Figure embeds — every ![[file]] must have italic caption:

![[8_0.jpg]]
*图 4：vDiagMC 计算的 μ_EF(r_s)。改编自 Cai et al.*

DO NOT

• Leave skeleton English content
• Write thin summaries
• Use Gaia jargon (noisy_and, abduction, factor graph, BP)
• Modify frontmatter or wikilink targets
• Embed images without captions
• Duplicate full derivations in section pages
• List weak points without explaining WHY they're weak