🌐 [translation-sync] TEST: Sub-subsection added (####) (10 - lecture)

[mmcky]

Automated Translation Sync

This PR contains automated translations from QuantEcon/test-translation-sync.

Source PR

#957 - TEST: Sub-subsection added (####) (10 - lecture)

Files Added

• ✅ .translate/state/lecture.md.yml

Files Updated

• ✏️ lecture.md

Details

• Source Language: en
• Target Language: ml
• Model: claude-sonnet-5

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This PR was created automatically by the translation action.

[github-actions]

✅ Translation Quality Review

Verdict: PASS | Model: claude-sonnet-5 | Date: 2026-09-23
Routing: auto-merge — no gating findings; floors met

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📝 Translation Quality

Criterion	Score
Accuracy	9/10
Fluency	9/10
Terminology	9/10
Formatting	10/10
Overall	9.2/10

Summary: The translation of the changed sections (frontmatter, Applications in Economics, and the new Closure Property section) is accurate, terminologically consistent, and correctly formatted with intact math and code blocks. Minor fluency issues arise from mirroring English comma splices instead of splitting into separate Malayalam sentences, as the style guide prefers, but these are stylistic rather than accuracy problems. No syntax errors or terminology violations were found. The new 'Closure Property' section accurately preserves the mathematical formalism ($\alpha \mathbf{u} + \beta \mathbf{v} \in V$) and its explanation without distortion. Technical terms (closure property, convex combinations, feasible allocations, optimization problems) are consistently kept in English per the glossary and policy. Case-suffix attachment to English terms (e.g., 'space-ൽ', 'vectors-ഉം', 'V-ഉം') follows the required policy correctly. The 'Applications in Economics' section under Vector Spaces is clearly and accurately translated, preserving the economic reasoning about feasibility and debts/obligations.

Suggestions:

• [minor · fluency] lecture.md — #### Applications in Economics: The sentence 'economic modeling-ൽ vector space properties അടിസ്ഥാനപരമാണ്' places the domain-locative phrase before the topic without a comma, and combines two clauses joined by 'ഉം' pattern without clear clause-boundary punctuation as required by the policy for coordinated clauses. Specifically, 'closure property, feasible allocations-ന്റെ combinations feasible ആയി തുടരുന്നു എന്ന് ഉറപ്പാക്കുന്നു,… → Split into two sentences: '...feasible ആയി തുടരുന്നു എന്ന് ഉറപ്പാക്കുന്നു. inverses-ന്റെ നിലനിൽപ്പ് debts, obligations എന്നിവ model ചെയ്യാൻ നമ്മെ അനുവദിക്കുന്നു.'
• [minor · fluency] lecture.md — #### Closure Property: The sentence 'points-ന്റെ convex combinations space-ൽ തന്നെ തുടരും എന്ന് ഈ property ഉറപ്പുനൽകുന്നു, economics-ലെ optimization problems-ന് ഇത് അത്യന്താപേക്ഷിതമാണ്' joins two independent clauses with just a comma, mirroring the English comma splice rather than splitting into two Malayalam sentences as the style policy recommends. → Split into two sentences: '...തുടരും എന്ന് ഈ property ഉറപ്പുനൽകുന്നു. economics-ലെ optimization problems-ന് ഇത് അത്യന്താപേക്ഷിതമാണ്.'
• [nit · terminology] lecture.md — #### Closure Property: 'Formally,' at the sentence start is rendered as 'Formally,' in English which is acceptable per policy for discourse formulas, but consistency check: the term is kept correctly, no issue — noted only as a nit that surrounding clause 'ഏതെങ്കിലും vectors $\mathbf{u}, \mathbf{v} \in V$-ഉം scalars $\alpha, \beta \in \mathbb{R}$-ഉം ആയാൽ' is a bit dense but grammatically acceptable.

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🔍 Diff Quality

Check	Status
Scope Correct	✅
Position Correct	✅
Structure Preserved	✅
Heading-map Correct	✅
Overall	10/10

Summary: The new 'Closure Property' subsection was correctly translated and inserted in the same position, with proper structure and an accurate heading-map update.

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This review was generated automatically by action-translation review mode.

[Copilot]

Copilot review overview

🟢 Approval recommended

The added sub-subsection and the new translation state metadata are consistent with the document structure and existing translation-sync conventions.

Review effort: Lite
Findings: None

What changed in this PR

Automated translation-sync update for the Malayalam (ml) version of the lecture content, adding a new sub-subsection on the closure property and recording updated translation state metadata.

Changes:

• Added a new #### Closure Property sub-subsection under Vector Spaces → Basic Properties.
• Updated the translation front-matter headings map to include the new sub-subsection.
• Added .translate/state/lecture.md.yml to record sync metadata (source SHA, sync date, section-count, etc.).

File	Description
lecture.md	Adds the new “Closure Property” sub-subsection content and updates the translation heading map accordingly.
.translate/​state/​lecture.md.yml	Introduces translation-sync state metadata for lecture.md (source-sha, synced-at, model, mode, section-count, tool-version).

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[mmcky]

Closing for test reset