LinguaGraph — Cross-Lingual Knowledge Structure Analysis

Research Questions

Three complementary lenses on how the same knowledge is organized differently

RQ1: Language

How do different languages organize the same knowledge?

LDS-K reveals heterogeneous cross-linguistic relationships: ZH-DE (0.519) textbooks converge substantially; ZH-EN (0.934) and DE-EN (0.938) are near the within-language noise floor. A Null Model falsifies the language-divergence interpretation — the core signal is ΔLDS (cognitive minus textbook).

LDS-K: 0.519–0.938

RQ2: Discipline

How do different STEM subjects organize knowledge?

All three disciplines follow an early-peak-later-decline pattern. Knowledge density peaks at middle or elementary school, then drops sharply. Maximum prerequisite depth is bounded at 8.

CDS: 0.042–0.271 HDS: max 8

RQ3: Education System

How do different curricula organize the same subject?

Coverage scores range from 12.7% (NRW) to 95.4% (China). Granularity (safest reading) and governance (hypothesis, paper §8.6) both fit these differences.

CS: 12.7%–95.4%

Research Contributions

What this project delivers to the field

1

A multilingual STEM knowledge graph

1,140+ concepts and 1,100+ direct relations across mathematics, physics and chemistry in Chinese, English and German — extracted from 180 textbooks and validated against 92 gold-standard annotations (social F1 = 0.939; weighted overall 0.881).

2

Three structural metrics for knowledge organization

CDS (concept density), HDS (hierarchy depth) and LDS (language drift) quantify how knowledge is connected, sequenced and structured across languages and disciplines.

3

Curriculum coverage analysis framework

The Coverage Score measures textbook–curriculum alignment across four education systems (Germany, UK, US, China), revealing how different educational philosophies produce systematically different alignment patterns.

4

Empirical findings across 4 education systems

12 findings spanning density universals (F1–F3, F6–F8), cross-language divergence (F4–F5), curriculum design philosophy (F9–F10), and human-validation revision (F11–F12) — all independently verifiable from the released data and pipeline.

Methodology

From textbook text to structural insights in five steps

%%{init:{'theme':'default','themeVariables':{'primaryColor':'#f8fafc','primaryTextColor':'#0a1f3d','primaryBorderColor':'#c6cdd6','lineColor':'#1e3a8a','secondaryColor':'#f1f3f5','tertiaryColor':'#e7ebef'}}}%% graph LR T1[180 Textbooks
ZH · EN · DE] --> MIMO[LLM API
Concept Extraction] MIMO --> KG[Knowledge Graph
1,140+ Concepts · 1,100+ Relations] GL[92 Gold Labels
F1 = 0.939 social / 0.881 weighted] -.->|Validate| KG KG --> CDS[CDS: Concept Density] KG --> HDS[HDS: Hierarchy Depth] KG --> LDS[LDS: Language Divergence] KG --> CURR[4 Curricula
NRW · UK · US · CN] CURR --> CS[Coverage Score] CDS --> INSIGHTS[Educational Insights
F1–F12] HDS --> INSIGHTS LDS --> INSIGHTS CS --> INSIGHTS style GL fill:#f8fafc,stroke:#1e7e4d,stroke-dasharray:4 4

CDS

2|E| / (|V|·(|V|−1))

How densely connected knowledge is at each education level. Higher = more integrated.

HDS

max BFS depth(prerequisite)

Longest prerequisite chain for each concept. Measures hierarchical depth.

LDS

1 − mean(J_node, J_edge)

Cross-language structural divergence. 0 = identical, 1 = completely different.

CS

|V_tb ∩ V_cur| / |V_cur|

Textbook–curriculum alignment. How much of the official curriculum textbooks actually cover.

Fig 2 — How LDS is computed: two language graphs, alignment, two similarity components

Baseline-Glossar: 9 reference lines every finding is measured against

1. Structure Null: Grade-randomized graphs: the overlap expected by pure chance.
2. Size-matched bootstrap: k = 15/25/35: comparison at equal vocabulary size.
3. Within-language noise floor (0.97): Same-language divergence: the baseline no cross-language claim may sit below. (textbook legacy line; human line 0.92-0.96; LLM line 0.85-0.87)
4. Wikipedia aligned control: Domain-pure social concepts in ZH/EN/DE, independently extracted.
5. Human N=15 floor: Between-subject margin +0.015: no separable language signal at this N.
6. LLM within-subject signal: LDS-C 0.93–0.96 (LLM-as-subject), permutation p < 0.01: language code dominates.
7. Permutation test: Label shuffling, e.g. ZH-DE 55/55, p<0.004 (500 perm.).
8. Heterogeneity injection (q-scan): Consistency demonstration, not a causal proof of the human null.
9. Margin threshold (≥ 0.10): Operational heuristic for audit use, not a validated boundary.

Sources

Every textbook cited by at least one graph concept. Node cards show the top-3 sources per concept; this is the full inventory (204 titles).

Local texts (2026-09-12): 89 open files + CN 11 books OCR done, fact-level (51 chapter txts). Text-grounded: physics ZH 66.5% / EN 62.1%, chemistry ZH 65.9% / EN 53.2% (semantic layer; substring 33.8/25.5) (college nodes out of high-school scope; DE link-only).

Mathematics · 32 titles

Title	Lang	Refs
A First Course in Probability (Sheldon Ross)	en	24
AP Calculus AB/BC	en	34
Abitur Mathematik Leistungskurs (Baden-Württemberg)	de	28
Cambridge IGCSE Mathematics (0580)	en	21
Differential Equations and Linear Algebra (Edwards & Penney)	en	14
Erwin Fischer: Lineare Algebra	de	10
Gewöhnliche und partielle Differentialgleichungen	de	14
Gilbert Strang: Introduction to Linear Algebra (18.06)	en	28
IB Mathematics: Analysis and Approaches SL/HL	en	18
Khan Academy Mathematics 3-4	en	10
Khan Academy Mathematics 3rd-5th Grade	en	21
Khan Academy Mathematics 5-6	en	15
Khan Academy Mathematics 6th-8th Grade	en	37
Khan Academy Mathematics K-2	en	13
Lambacher Schweizer 5-8 Klasse	de	17
Lambacher Schweizer Mathematik (erweitert)	de	30
Otto Forster: Analysis 1	de	21
Otto Forster: Analysis 2	de	7
Stewart Calculus (8th ed.)	en	31
Wahrscheinlichkeitsrechnung und Statistik	de	24
Westermann Mathematik Klasse 9-10	de	26
人教版《偏微分方程基础》	zh	8
人教版初中数学七年级	zh	15
人教版初中数学九年级	zh	18
人教版初中数学八年级	zh	17
人教版小学数学一年级上册	zh	10
人教版小学数学一年级下册	zh	11
人教版小学数学二年级上册	zh	9
人教版小学数学二年级下册	zh	9
人教版高中数学选修2-2	zh	85
同济大学《线性代数》	zh	64
浙江大学《概率论与数理统计》	zh	64

Physics · 83 titles

Title	Lang	Refs
A-Level Physics (AQA)	en	136
A-Level Physics (OCR)	en	136
AP Physics 1	en	136
AP Physics 2	en	136
AP Physics C: E&M	en	136
AP Physics C: Mechanics	en	136
Arfken: Mathematical Methods	de	127
Auer: Physik	de	93
BBC Bitesize: KS3 Physics	en	93
Cambridge IGCSE Physics	en	136
CK-12: Elementary Physical Science	en	10
CK-12: Middle School Physics	en	93
Cornelsen: Physik aktiv	de	93
Cornelsen: Physik entdecken	de	10
Cornelsen: Physik Oberstufe	de	136
Demtröder: Experimentalphysik	de	381
Dorn-Bader: Physik	de	136
DUDEN: Physik Abitur	de	136
Duden: Physik Kompakt	de	103
Feynman Lectures on Physics	en	254
GCSE AQA Physics	en	136
GCSE Edexcel Physics	en	136
Glencoe: Physics: Principles and Problems	en	93
Greiner: Klassische Mechanik	de	127
Greiner: Quantenmechanik	de	127
Greiner: Thermodynamik und Statistische Mechanik	de	127
Griffiths: Introduction to Electrodynamics	en	127
Halliday Resnick Walker: Fundamentals of Physics	en	254
Holt: Middle School Science	en	93
IB Physics SL/HL	en	136
IGCSE Physics (0625)	en	136
Jackson: Klassische Elektrodynamik	de	127
Kern: Physik	de	136
Khan Academy Physics	en	93
Khan Academy: Elementary Science	en	20
Kittel: Introduction to Solid State Physics	en	127
Kleintolkroemer: Classical Electrodynamics	en	127
Klett: Physik	de	93
Lambacher Schwere: Physik	de	186
Landau Lifshitz: Mechanics	en	127
LEIFIphysik Induktion	de	1
National Geographic: Force, Motion, and Simple Machines	en	10
NPTEL Sensor Technologies	en	1
Pearson: Prentice Hall Science Explorer	en	93
Schiff: Quantenmechanik	de	127
Schrödinger: Quantum Mechanics	en	127
Serway Jewett: Physics for Scientists and Engineers	en	254
Thieme: Physik	de	136
Tipler: Physik	de	254
Westermann: Physik	de	103
Westermann: Physik Oberstufe	de	136
Young Freedman: University Physics	en	254
人教版初中物理九年级全一册	zh	93
人教版初中物理八年级上	zh	93
人教版初中物理八年级下	zh	93
人教版小学科学三年级上	zh	10
人教版小学科学五年级上	zh	10
人教版小学科学四年级上	zh	10
人教版高中物理必修第一册	zh	136
人教版高中物理必修第三册	zh	136
人教版高中物理必修第二册	zh	136
人教版高中物理选择性必修第一册	zh	136
人教版高中物理选择性必修第三册	zh	136
人教版高中物理选择性必修第二册	zh	136
光学（赵凯华）	zh	127
力学（漆安慎）	zh	127
北师大版初中物理八年级	zh	93
北师大版小学科学四年级	zh	10
原子物理学（杨福家）	zh	127
大学物理（马文蔚）	zh	254
普通物理学（程守洙）	zh	254
沪教版小学科学三年级	zh	10
沪科版初中物理八年级	zh	93
沪科版高中物理	zh	136
热学（汪志诚）	zh	127
理论力学（梁昆淼）	zh	127
电动力学（郭硕鸿）	zh	127
电磁学（赵凯华）	zh	127
粤教版初中物理八年级	zh	93
粤教版高中物理	zh	136
苏科版初中物理八年级	zh	93
量子力学（曾谨言）	zh	127
鲁科版高中物理	zh	136

Chemistry · 89 titles

Title	Lang	Refs
A-Level Chemistry (AQA)	en	51
A-Level Chemistry (OCR)	en	51
AP Chemistry	en	51
Atkins: Physical Chemistry	en	123
Atkins: Physikalische Chemie	de	123
Auer Chemie	de	46
BBC Bitesize KS3 Chemistry	en	46
Brown: Chemistry	en	123
Bruice: Organic Chemistry	en	123
Bruice: Organische Chemie	de	123
Cambridge IGCSE Chemistry	en	51
Chang: Chemistry	en	123
CK-12 Chemistry	en	46
Clayden: Organic Chemistry	en	123
Clayden: Organische Chemie	de	123
Cornelsen Chemie entdecken	de	46
Cornelsen Chemie Oberstufe	de	51
Dorn-Bader Chemie	de	46
Dorn-Bader Chemie Abitur	de	51
DUDEN Chemie Abitur	de	51
Duden Chemie Kompakt	de	46
Edexcel GCSE Chemistry	en	51
Engel: Physical Chemistry	en	123
Engel: Physikalische Chemie	de	123
GCSE AQA Chemistry	en	51
GCSE AQA Combined Science	en	51
GCSE Edexcel Chemistry	en	51
Glencoe Chemistry	en	46
Harris: Quantitative Chemical Analysis	en	123
Harris: Quantitative Chemische Analyse	de	123
Holt Chemistry	en	46
Housecroft: Anorganische Chemie	de	123
Housecroft: Inorganic Chemistry	en	123
IB Chemistry SL/HL	en	51
IGCSE Chemistry (0620)	en	51
Kern Chemie Abitur LK	de	51
Khan Academy Chemistry	en	46
Klett Chemie	de	46
Laidler: Physikalische Chemie	de	123
Levine: Physical Chemistry	en	123
Levine: Physikalische Chemie	de	123
Mortimer: Physikalische Chemie	de	123
Pearson: Prentice Hall Chemistry	en	46
Petrucci: General Chemistry	en	123
Shriver & Atkins: Anorganische Chemie	de	123
Shriver & Atkins: Inorganic Chemistry	en	123
Silberberg: Chemie	de	123
Silberberg: Chemistry	en	123
Skoog: Analytical Chemistry	en	123
Skoog: Analytische Chemie	de	123
Solomons: Organic Chemistry	en	123
Thieme Chemie	de	51
Wade: Organic Chemistry	en	123
Westermann Chemie	de	46
Westermann Chemie Oberstufe	de	51
Zumdahl: Chemistry	en	123
人教版初中化学九年级上	zh	46
人教版初中化学九年级下	zh	46
人教版高中化学必修第一册	zh	51
人教版高中化学必修第二册	zh	51
人教版高中化学选择性必修第一册（化学反应原理）	zh	51
人教版高中化学选择性必修第三册（有机化学基础）	zh	51
人教版高中化学选择性必修第二册（物质结构与性质）	zh	51
分析化学（华东理工）	zh	123
分析化学（武汉大学）	zh	123
化工原理（柴诚敬）	zh	123
北师大版初中化学	zh	46
无机化学（大连理工）	zh	123
无机化学（武汉大学）	zh	123
有机化学（汪小兰）	zh	123
有机化学（邢其毅）	zh	123
材料化学（曾兆华）	zh	123
沪教版初中化学	zh	46
沪科版高中化学	zh	51
湘教版初中化学	zh	46
湘教版高中化学	zh	51
物理化学（傅献彩）	zh	123
物理化学（南京大学）	zh	123
环境化学（戴树桂）	zh	123
生物化学（王镜岩）	zh	123
科粤版初中化学	zh	46
粤教版初中化学	zh	46
粤教版高中化学	zh	51
结构化学（周公度）	zh	123
苏教版初中化学	zh	46
苏教版高中化学	zh	51
高分子化学（潘祖仁）	zh	123
鲁教版初中化学	zh	46
鲁科版高中化学	zh	51

Refs = citations across concepts. New textbooks are appended here on ingestion (see docs/physics_sourcing.md for the gap list). Raw excerpts live in data/textbook/.

Findings

Five finding sections covering twelve numbered results (F1–F12): how knowledge is organized across disciplines, languages, education systems, and individuals

Finding A: Knowledge density peaks early

All three STEM disciplines concentrate their densest knowledge connections at introductory stages, not advanced ones.

Mathematics peaks at middle school (CDS = 0.271). Physics peaks at elementary school (CDS = 0.222). Chemistry shares the same middle school peak (CDS = 0.042). After the peak, density drops sharply — a 3.7× decline from middle to high school in mathematics.

This contradicts the natural assumption that "more advanced knowledge is more densely connected." Instead, curricula are designed to maximize connection density during foundational stages (early integration) before branching into specialization (later differentiation).

0.271

Math CDS (Middle)

0.222

Physics CDS (Elementary)

3.7×

Middle → High drop

✓

ZH/EN/DE independent verification

Fig 3 — Mathematics CDS peaks at middle school, then declines 3.7×

Fig 7 — The same early-peak pattern holds across all three STEM disciplines

Details · how Fig 3 / Fig 7 are made

Source. CDS per level from the math graph (Fig 3) and the three-discipline matrix (outputs/physics_comparison.json + chemistry_comparison.json, Fig 7) — the same numbers as the CDS Terrain view.

Method. CDS = 2|E|/(|V|·(|V|−1)) per level cell; the math graph renders 238 of 525 relations. Nothing is rescaled.

Reading. Height = density; an early peak then decline in all three subjects (math middle 0.271, physics elementary 0.222, chemistry middle 0.042).

Metric: CDS F1, F2, F6, F8 Disciplines: Math, Physics, Chemistry

Finding B: Knowledge structures stay shallow

Educational knowledge has a universal upper bound on prerequisite depth, regardless of discipline.

Maximum prerequisite chain depth is HDS ≤ 8 for mathematics and HDS ≤ 6 for physics. Mean depth is even lower: 0.40 for math, 0.85 for physics. Over 83% of math concepts have no prerequisite chains at all (root concepts).

Physics has 2.1× more sequential depth than mathematics (60% roots in physics vs 83% in math), reflecting its more cumulative knowledge structure. But both disciplines respect the same shallow upper bound — suggesting a pedagogical or cognitive constraint on how knowledge can be sequenced.

8

Math HDS (max)

0.40

Math HDS (mean)

83%

Root concepts (Math)

2.1×

Physics depth vs Math

Fig 5 — HDS distribution: most concepts have zero depth; the longest chain reaches only 8

Metric: HDS F3, F7 Disciplines: Math, Physics

Finding C: Languages organize knowledge differently

Textbook LDS-K shows convergence (ZH-DE 0.519, ZH-EN 0.934, DE-EN 0.938) — an observation consistent with curriculum tradition; the core signal is ΔLDS.

Textbook structures look more convergent than random expectation — but decontamination falsifies this reading. ZH-DE (LDS-K = 0.519) collapses to 0.990 once de-labels containing Chinese text (167/219) are removed: the apparent convergence is a label artifact, not content convergence. ZH-EN (0.934) and DE-EN (0.938) sit near the within-language noise floor (0.97, textbook line) either way.

The pattern is also topic-dependent: within each language pair, LDS varies by up to 0.2 across the 5 social topics analyzed, suggesting that some knowledge domains are more culturally inflected than others.

0.519

ZH–DE (0.519)

0.938

DE–EN (0.938)

0.934

ZH–EN (0.934)

~0.2

Topic variance

Fig 4 — Null Model Suite: Full vs Structure Null. Textbook structures converge more than random expectation

Fig 8: LDS-K decontamination — convergence collapses after label cleaning

Fig 8 — Decontamination (T1): removing CJK-contaminated de-labels collapses ZH-DE 0.52 → 0.99. Verdict: artifact

Metric: LDS F4, F5 Languages: ZH, EN, DE

Honesty note (T1 decontamination, 2026-09): ZH-DE J_node 0.556 → 0.020 after removing CJK-contaminated de-labels; size-matched bootstrap reverses the wiki comparison at every k. Verdict: label artifact (paper §3.8, Fig 8).

Finding D: Education systems emphasize different curriculum designs

Textbook–curriculum coverage varies dramatically — not necessarily quality differences: granularity (safest reading) and governance (hypothesis, paper §8.6) both fit the data.

Coverage scores range from 12.7% (NRW) to 95.4% (China). China shows near-perfect alignment under a centralized national curriculum. The UK (37.3%) shows moderate alignment through its national curriculum. The US (17.2%) and NRW (12.7%) reflect broad or detailed standards that afford local adaptation. These differences are consistent with educational governance (hypothesis, paper §8.6) — but granularity (A) remains the safest interpretation; the data fit all three explanations below.

95.4%

🇨🇳 China (highest)

37.3%

🇬🇧 UK

17.2%

🇺🇸 US

12.7%

🇩🇪 NRW Germany

Fig 8 — Overall Coverage Score (paper §8.5: NRW 12.7% · UK 37.3% · US 17.2% · China 95.4%)

Details · how Fig 8 is made

Source. Overall column of config/expert_graphs/coverage_all_curricula.json (paper §8.5) — the same table behind the coverage cards and Coverage Towers.

Method. Keyword bridge + 2-overlap threshold; overall = matched/total across all stages per system.

Reading. Bar = system overall; the gap runs China 95.4% down to NRW 12.7%.

F9 Coverage scores vary dramatically across education systems (12.7%–95.4%). Granularity (safest reading) and governance (hypothesis, paper §8.6) both fit these differences.
F10 China's near-perfect alignment (95.4%) versus NRW's low alignment (12.7%) reflects the spectrum from centralized curriculum to local adaptation.

Metric: CS F9 F10 Systems: DE, UK, US, CN

Finding E: N=15 falsifies ΔLDS > 0 between-subject — language signal needs within-subject design

Extended human study (N=15) lands on the split-half floor: between-subject designs cannot separate language from participant variance. LLM within-subject (§5) shows the signal clearly.

Extended study (6 DE · 6 ZH · 3 EN): concept-level LDS-C (human) is 0.93–0.96 — indistinguishable from the within-language split-half floor (0.92–0.96) and label permutation (0.94). Concept-level ΔLDS ≈ 0 (−0.05…+0.05); relation-level Δ is not comparable across sparsity regimes. Pilot N=8 values (0.70–0.75) were not replicated and are reported for transparency only. The earlier human-vs-simulation comparison (p=0.05) is withdrawn (measurement-scale drift).

0.93–0.96

Human LDS-C (N=15)

0.92–0.96

Split-half floor

≈0

Concept ΔLDS

+0.08–0.09

LLM within-subject margin

Level	DE–ZH	DE–EN	ZH–EN	Rank Order
Human N=15 (Between)	0.93–0.96	0.93–0.96	0.93–0.96	≈ floor
LLM Within-Subject	≫ floor (+0.08–0.09)	≫ floor	≫ floor	signal
Textbook LDS-K	0.519	0.938	0.934	✓
Simulation Baseline	0.646	0.655	0.640	withdrawn*

F11 N=15 falsifies ΔLDS > 0 between-subject: human LDS-C ≈ split-half floor — between-subject designs cannot separate language from participant variance.
F12 Concept-level ΔLDS ≈ 0; LLM within-subject margin (+0.08–0.09) shows the signal exists — earlier simulation comparison withdrawn.

Metric: LDS F11, F12 N=15 participants, 300 simulation (exploratory)

Interactive CognitiveSpace

Explore the mathematics subgraph in an interactive 3D knowledge graph — 556 nodes · 525 relations · 219 groups

Switch between zoom, rotate and fly modes. Explore the graph in three languages or switch discipline. Compare how different education systems structure the same mathematical knowledge.

Open Full Screen Gallery 556 nodes · 525 relations · 219 groups

Gallery Math 3D Physics 3D CDS Terrain Margin Proof Coverage Towers

Limitations

Transparent assessment of methodological boundaries and potential biases

Textbook Selection Bias

The corpus is not a comprehensive sample of all textbooks in each language. Chinese textbooks are predominantly one series (Renjiao), which may not represent the full diversity of Chinese mathematics education. German textbooks are weighted toward senior-level university texts (Forster, Fischer) with fewer primary-level resources.

Mitigation: Multi-source triangulation across 68 math textbooks (180 total, all subjects)

Limited Discipline Coverage

Only three STEM disciplines (mathematics, physics, chemistry) were analyzed. The framework has not been validated on humanities, social sciences, or professional fields. The universal claims (e.g., "knowledge density peaks early") are therefore limited to STEM education.

Mitigation: Framework is design-agnostic and extendable

Curriculum Granularity Mismatch

Curriculum documents vary enormously in granularity: the US math curriculum contains 2,124 concepts while the UK science curriculum has 397 (paper §8: NRW 299 · UK 397 · US 2,124 · CN 87). Higher granularity mechanically lowers coverage scores when matched against the same textbook graph. This is partially mitigated by normalizing per-curriculum, but cross-system comparisons remain approximate.

Mitigation: Analysis focuses on within-system trajectories, not absolute values

LLM Extraction Reliability

Concept extraction depends on a single production model. The 19-model benchmark (F1 range 0.55–0.67) confirms extraction consistency across architectures. While F1 = 0.939 on social concepts, the math domain achieves only 0.674 overall (German as low as 0.506). Extraction errors propagate through all downstream metrics. Relation extraction (prerequisite links) is less reliable than concept identification.

Mitigation: 92 gold labels ensure measurable quality bounds

Language Coverage Gap

Only three languages (ZH, EN, DE) were analyzed. These represent only two language families (Sino-Tibetan, Germanic) and one educational tradition cluster (Western Europe + East Asia). The framework's applicability to Romance, Slavic, Arabic, or other language families remains untested.

Mitigation: Existing three-language comparison already reveals systematic patterns

Gold Label Sample Size

92 gold labels, while sufficient for overall F1 estimation (especially for social concepts, n=72), are limited for fine-grained per-language, per-domain analysis. The mathematical domain has only 20 labels across 3 languages, and the German math F1 estimate (0.506) has high variance.

Mitigation: Social concept results (n=72) are statistically robust

Curriculum Analysis

How four education systems align their curricula with textbook content

🇩🇪 NRW (Germany)

12.7%

Coverage decreases toward upper-secondary specialization. Teachers exercise curricular freedom — they select from the curriculum rather than covering all of it. Reflects a specialization-driven philosophy.

Stages: Sek I → Sek II · Overall 12.7% (paper §8.5)

🇬🇧 UK National Curriculum

37.3%

The exam-driven system drives comprehensive textbook coverage — every curriculum point must be taught because it might be tested. Moderate overall alignment (37.3%, paper §8.5).

Stages: Key Stage 1–4 · Overall 37.3% (paper §8.5)

🇺🇸 US (CCSS + NGSS)

17.2%

Low overall coverage with stable trajectory across stages. The US standards define broad learning goals rather than detailed syllabi, giving textbook authors interpretive freedom while maintaining curriculum alignment.

Stable across stages · Standards: Common Core + NGSS · Overall 17.2% (paper §8.5)

🇨🇳 China National Curriculum

95.4%

Near-perfect alignment with a centralized national curriculum. Chinese textbooks closely follow the national syllabus, resulting in the highest coverage across all four systems. The highly selective, curriculum-driven textbook market aligns textbooks tightly with government standards.

Stable · centralized curriculum alignment · Overall 95.4% (paper §8.5)

Details · how the coverage cards are made

Source. Per-stage rows of config/expert_graphs/coverage_all_curricula.json — the same table behind Coverage Towers.

Method. Keyword bridge + 2-overlap threshold (≥2 shared keywords = covered); card headline = system overall.

Reading. Each card narrates one system; the numbers match the bright overall bars in Coverage Towers.

Three Competing Explanations

× A: Curriculum Granularity

Claims: Dense curricula produce higher coverage. Evidence: Counter-indicated — the US has the densest curriculum (2,124 concepts) but one of the lowest coverages (17.2%).

✓ B: Educational Philosophy Hypothesis (paper §8.6)

Coverage patterns reflect educational governance: CN centralized (95.4%), UK national curriculum (37.3%), US broad standards (17.2%), NRW per-track specifications (12.7%).

! C: Division of Labor

Some concepts may be taught in other subjects (e.g., physics in chemistry). Plausible but unverified — cross-subject concept mapping could reveal systematic transfers.

Validation

Gold standard annotations and model benchmarks

Gold Dataset: 92 Labels

Human-annotated gold standard covering social concepts and mathematical concepts across all three languages. Validated against production-model extraction.

Domain	ZH F1	DE F1	EN F1	Overall	n
Social Concepts	0.974	0.949	0.882	0.939	72
Mathematics	0.857	0.506	0.711	0.674	20
All (weighted)	0.951	0.842	0.844	0.881	92

Note: The low German math F1 (0.506) is a domain mismatch — the math gold labels use Chinese/English mathematical terminology not present in the German textbook corpus. Social concept extraction is uniformly strong across all three languages.

Model Benchmark: 19 Models

All free-quota Bailian API models tested on 92 gold labels. The production extraction model was selected by overall F1.

Production model: extraction model (F1=0.666) · Best overall: hy3-preview (0.674) · Best DeepSeek: v4-flash (0.608) · 19 models tested, F1 range 0.55–0.67

Details · how the benchmark chart is made

Source. 19 models scored on 92 gold labels (model-selection benchmark, Validation section).

Method. F1 on gold labels; the production extraction model was selected by overall F1. Range 0.55–0.67.

Reading. Bar = F1 per model. Used only for extractor selection — never for language claims (that is the 55-run replication below).

Replication roster: 55 full runs + 31 collecting (file truth 56/51/168 incl. qwen-max n=29/30)

CN run western run (7)

Fused view — all 55 full-run ZH-DE margins (LDS-C minus split-half floor) under one P1 protocol (ZH/DE/EN × 10); all 55 ZH-DE p<0.01; 8 EN n.s. among 165 (500 permutations). Western runs in red. The 31 collecting runs (incl. qwen-max n=29/30, per paper §8.15) withhold margins until n=30. Source: data/lds_c/llm_subject/multi_model_replication_20260910.json + paper §5.10.

Details · how the margin chart is made

Source. 55 full runs from data/lds_c/llm_subject/multi_model_replication_20260910.json — the same rows as the Margin Proof view and the roster table below. 31 collecting runs (n<30) withhold margins.

Method. Margin = LDS-C minus split-half floor, one P1 protocol for all runs; 500 permutations, all 55 ZH-DE p<0.01; 8 EN n.s. among 165. Sorted descending; nothing rescaled.

Reading. Bar = margin, all 55 positive. Red = western (scattered = no origin clustering). The roster table below lists every row.

Full 55-row margin table (collecting runs listed below)

Model	Origin	ZH-DE margin	Signif.
command-a-03-2025	West · Cohere · CA	+0.42	p<0.01
gpt-5.6-luna	West · origin undisclosed	+0.22	p<0.01
nemotron-3-super-120b-a12b	West · NVIDIA · US	+0.17	p<0.01
nemotron-3-ultra	West · NVIDIA · US	+0.16	p<0.01
gpt-oss-20b	West · OpenAI-weights · US	+0.13	p<0.01
laguna-s-2.1 · direct	West · Poolside · US	+0.10	p<0.01
laguna-s-2.1 · kilo	West · Poolside · US	+0.07	p<0.01
deepseek-v3.1	CN	+0.29	p<0.01
qwen-turbo	CN	+0.25	p<0.01
qwen3-max	CN	+0.24	p<0.01
deepseek-v3	CN	+0.24	p<0.01
qwen3.8-max	CN	+0.21	p<0.01
glm-5	CN	+0.19	p<0.01
qwen3.5-397b-a17b	CN	+0.18	p<0.01
qwen3.7-max	CN	+0.18	p<0.01
glm-5.2-fast-preview	CN	+0.18	p<0.01
qwen3.5-plus	CN	+0.18	p<0.01
deepseek-v3.2	CN	+0.17	p<0.01
deepseek-v4-flash · dashscope	CN	+0.16	p<0.01
MiniMax-M2.5	CN	+0.16	p<0.01
qwen3.6-plus	CN	+0.16	p<0.01
glm-5.2 · direct	CN	+0.16	p<0.01
qwen3.7-plus	CN	+0.15	p<0.01
glm-4.6	CN	+0.15	p<0.01
glm-5.1	CN	+0.14	p<0.01
longcat-2.0	CN	+0.14	p<0.01
kimi-k2.6 · direct	CN	+0.14	p<0.01
glm-4.7	CN	+0.13	p<0.01
kimi-k2.6 · dashscope	CN	+0.13	p<0.01
MiniMax-M2.1	CN	+0.13	p<0.01
kimi-k2.5	CN	+0.12	p<0.01
kimi-k2.7-code	CN	+0.12	p<0.01
qwen3.5-27b	CN	+0.12	p<0.01
glm-5.2 · dashscope	CN	+0.12	p<0.01
qwen3.6-27b	CN	+0.11	p<0.01
deepseek-v4-pro · dashscope	CN	+0.11	p<0.01
qwen-flash	CN	+0.11	p<0.01
Kimi-K2-Instruct	CN	+0.10	p<0.01
deepseek-r1-distill-qwen-14b	CN	+0.10	p<0.01
qwen-plus	CN	+0.10	p<0.01
qwen3.5-35b-a3b	CN	+0.10	p<0.01
qwen3.5-flash	CN	+0.09	p<0.01
qwen3.5-122b-a10b	CN	+0.09	p<0.01
kimi-k2-thinking	CN	+0.09	p<0.01
qwen3.6-35b-a3b	CN	+0.08	p<0.01
deepseek-v4-flash · direct	CN	+0.08	p<0.01
qwen3-235b-a22b	CN	+0.08	p<0.01
mimo-v2.5	CN	+0.08	p<0.01
deepseek-v4-pro · direct	CN	+0.07	p<0.01
qwen3.7-flash	CN	+0.07	p<0.01
deepseek-r1-distill-qwen-32b	CN	+0.07	p<0.01
qwen3.6-flash	CN	+0.05	p<0.01
deepseek-r1	CN	+0.05	p<0.01
deepseek-r1-distill-qwen-7b	CN	+0.04	p<0.01
deepseek-r1-0528	CN	+0.03	p<0.01

Model	Origin	Progress	Status
Collecting — incomplete runs (n<30, margin withheld):
qwen-max	repo	n=29/30	collecting
gpt-oss-20b	repo	n=20/30	collecting
grok-4.6	repo	n=18/30	collecting
llama-3.3-70b-instruct-fp8-fast	repo	n=15/30	collecting
ling-3.0-tiny	repo	n=12/30	collecting
nemotron-3-ultra-550b-a55b	repo	n=11/30	collecting
mistral-medium-latest	repo	n=10/30	collecting
nemotron-3-nano-30b-a3b	repo	n=6/30	collecting
laguna-s-2.1	repo	n=5/30	collecting
north-mini-code	repo	n=3/30	collecting
glm-4.5	repo	n=3/30	collecting
glm-4.5-air	repo	n=3/30	collecting
qwen3-14b	repo	n=3/30	collecting
qwen3-30b-a3b	repo	n=3/30	collecting
qwen3-32b	repo	n=3/30	collecting
qwen3-8b	repo	n=3/30	collecting
qwq-plus	repo	n=3/30	collecting
gemma-4-26b-a4b-it	repo	n=3/30	collecting
gemma-4-31b-it	repo	n=3/30	collecting
ling-3.0-tiny	repo	n=3/30	collecting
nemotron-3-super-120b-a12b	repo	n=3/30	collecting
nemotron-3-ultra-550b-a55b	repo	n=3/30	collecting
laguna-xs-2.1	repo	n=3/30	collecting
gemini-3.8-flash	repo	n=2/30	collecting
mistral-large	repo	n=2/30	collecting
gemma-4-31b-it	repo	n=2/30	collecting
mistral-small-3.1-24b-instruct	repo	n=1/30	collecting
mistral-small-latest	repo	n=1/30	collecting
nemotron-3-ultra-550b-a55b	repo	n=1/30	collecting
gpt-oss-120b	repo	n=1/30	collecting
muse-spark-1.3-contributor	repo	n=1/30	collecting

Scope note: F1-benchmark (19 models, gold-label model selection) ≠ replication (55 runs, language signal) ≠ collecting (31 incomplete incl. qwen-max n=29/30, margin withheld). Families per paper §5.10: Qwen 20 · DeepSeek 12 · GLM 7 · Kimi 6 · MiniMax 2 · mimo · laguna · longcat · nemotron · gpt-oss · command-a · luna.

Extended replication (2026-09, paper §5.10): 55 measurements / 50 models — all 55 ZH-DE pairs significant (margin +0.03…+0.42); 8 EN-pair tests n.s.

Paper

Preprint manuscript available in the repository

Abstract

LinguaGraph asks whether language shapes the structural organization of knowledge. Two pipelines — textbook graphs (556 concepts, 525 relations, 219 groups) and LLM-as-subject (55 runs, 50 models) — isolate the language signal ΔLDS: N=15 falsifies it between-subject; within-subject shows it clearly (paper §5).

Read Abstract · PDF (217 KB)

Sections

Three Conclusions · Introduction · Related Work · Methodology · Results · Discussion · Conclusion · Physics Results · LPA Analysis

9 files · ~161 KB md · 217 KB PDF · Read Methodology

Cite this work

@misc{linguaGraph2026,
  author = {Rong, Jiajun and Lan, Zhenxi},
  title = {LinguaGraph: Cross-Lingual Knowledge Structure Analysis Framework},
  year = {2026},
  publisher = {GitHub},
  journal = {BWKI 2026 — Bundeswettbewerb Künstliche Intelligenz},
  url = {https://github.com/jjjjjjjjnnjnn/BWKI-2026-LinguaGraph}
}

Open Science

All data, code and results are publicly available

How do different languagesand educational systemsorganize the same knowledge?

Research Questions

RQ1: Language

RQ2: Discipline

RQ3: Education System

Research Contributions

A multilingual STEM knowledge graph

Three structural metrics for knowledge organization

Curriculum coverage analysis framework

Empirical findings across 4 education systems

Methodology

Sources

Findings

Finding A: Knowledge density peaks early

Finding B: Knowledge structures stay shallow

Finding C: Languages organize knowledge differently

Finding D: Education systems emphasize different curriculum designs

Finding E: N=15 falsifies ΔLDS > 0 between-subject — language signal needs within-subject design

Interactive CognitiveSpace

Limitations

Textbook Selection Bias

Limited Discipline Coverage

Curriculum Granularity Mismatch

LLM Extraction Reliability

Language Coverage Gap

Gold Label Sample Size

Curriculum Analysis

🇩🇪 NRW (Germany)

🇬🇧 UK National Curriculum

🇺🇸 US (CCSS + NGSS)

🇨🇳 China National Curriculum

Three Competing Explanations

× A: Curriculum Granularity

✓ B: Educational Philosophy Hypothesis (paper §8.6)

! C: Division of Labor

Validation

Gold Dataset: 92 Labels

Model Benchmark: 19 Models

Replication roster: 55 full runs + 31 collecting (file truth 56/51/168 incl. qwen-max n=29/30)

Paper

Abstract

Sections

Cite this work

Open Science

Source Code

Datasets

Paper

Figures

Benchmarks

Contact

How do different languages
and educational systems
organize the same knowledge?