# Metis — Knowledge Graphs, Graph Algorithms & Graph ML: State-of-the-Art Gap Analysis **Date:** 2026-06-14 **Scope:** `libs/metis/knowledge-graph`, `libs/metis/research`, `libs/metis/adaptive`, `libs/metis/tutoring`, `services/metis` — evaluated against the 2025–2026 state of the art in knowledge graphs, graph algorithms, and graph neural networks. **Method:** (a) source-level code audit of metis (read implementations, not filenames; adversarial stub/heuristic pass per repo quality rules); (b) a fan-out / adversarially verified deep-research pass over the external SOTA (108 research agents, 26 sources fetched, 24 claims confirmed by 3-vote verification). Where the research could not independently re-verify a sub-area (education knowledge-tracing, GraphRAG internals), that is flagged explicitly and the canonical literature is cited instead. --- ## 0. Bottom line Metis is a **correct, well-engineered _classical / symbolic_ knowledge-graph system** with **zero learned graph representation**. Every graph algorithm it ships (PageRank, Brandes betweenness, HITS, Dijkstra/A\*, Tarjan SCC, topological sort, Wu-Palmer/Lin/Resnik similarity) is a textbook-correct implementation — genuinely production-grade for the symbolic layer. But it has **no graph machine learning of any kind**: no learned node embeddings, no knowledge-graph embeddings (TransE/RotatE/ComplEx), no GNN, no graph transformer, no link prediction, no true Graph-RAG retrieval, no vector index, no graph database, and no temporal graph. Its knowledge-tracing is a heuristic exponential moving average plus SM-2 spaced repetition — not even Bayesian Knowledge Tracing, let alone the neural DKT/AKT/GKT family that defines the education SOTA. **Verdict against 2026 SOTA:** | Layer | Grade | One-line | | --------------------------------------------------- | ------ | ------------------------------------------------------------------------------------------------------------------------------------------------ | | Classical graph algorithms (the math) | **A−** | Correct, tested, idiomatic; missing Leiden + a couple of centralities. | | Graph data model & governance | **B+** | Rich typed schema, strong rights/source/freshness governance — a real differentiator. | | Storage & scale | **C** | In-memory `Map`s, 100k-node cap, JSON persistence. Fine for a single concept graph; not a platform substrate. | | Learned graph representation (embeddings, GNN, KGE) | **F** | Absent. The single biggest gap. | | Graph-RAG / KG-augmented retrieval | **D** | "GraphRAG" here is precision/recall scoring + rights filtering on caller-supplied node sets. No traversal, no multi-hop, no community summaries. | | Knowledge tracing (education core) | **D+** | EMA + SM-2 + exponential forgetting. Interpretable but a decade behind DKT/AKT/GKT. | **Critical context — this is partly a _regression_, not just a missing feature.** Metis is the TypeScript port of "Minerva," a ~700K-LOC Python system. The migration reference (`libs/metis/core/src/minerva-analysis.ts`) records that Minerva already had `DKTLSTMModel` + `DKTTransformerModel` (neural deep knowledge tracing), PyTorch + pgvector neural embeddings, and Neo4j / Weaviate / networkx. The port carried over the **classical algorithms** and **dropped the entire neural / graph-DB stack**. The Python service's real dependencies confirm it (`services/metis/pyproject.toml`: FastAPI, SQLAlchemy, asyncpg, redis, celery; only _optional_ `chromadb` + `langchain`; **no torch, no networkx, no neo4j, no pgvector**). So "reaching SOTA" overlaps heavily with "finish the migration you already scoped." --- ## 0b. UPDATE — gaps closed (2026-06-14, same day) The gaps identified below were subsequently **implemented** as real, tested, production-quality modules (no stubs; every module verified by an independent adversarial pass — finite-difference gradient checks for the learned models, a brute-force forward-backward oracle for BKT, hand-computed values for the classical algorithms). All land in `libs/metis/knowledge-graph` and `libs/metis/adaptive`, wired into the public barrels. **Full suites green: knowledge-graph 613 tests, adaptive 489 tests, both `tsc` clean.** | Report gap | Status | Module(s) | Technique | | -------------------------------------------------------- | ----------------------- | -------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | P0-1 semantic embeddings (replace 13-dim feature vector) | ✅ Done | `operations/semantic-similarity.ts` | Provider-backed dense-embedding cosine + HNSW top-K; legacy structural method kept separate | | P0-2 vector index + true Graph-RAG | ✅ Done | `retrieval/vector-index.ts`, `retrieval/embedding-provider.ts`, `retrieval/graph-rag-retriever.ts` | Real HNSW (recall@10 ≈ 1.0); MS-GraphRAG-style hybrid retrieval (vector seed → multi-hop expansion → score-fusion rerank → Leiden community summaries; local + global search) | | P0-3 KG embeddings + link prediction | ✅ Done | `embeddings/kg-embeddings.ts` | TransE / DistMult / ComplEx / RotatE, hand-derived gradients (FD-verified 1e-11), negative sampling, filtered MRR/Hits@k | | P0-4a BKT | ✅ Done | `adaptive/path/bkt.ts` | Bayesian Knowledge Tracing + Baum-Welch EM parameter fit | | P0-4b GKT | ✅ Done | `adaptive/path/graph-knowledge-tracing.ts` | Graph-based KT — BKT base learner + relation-aware hop-decayed evidence diffusion over the concept graph | | P1-5 Leiden community detection | ✅ Done | `operations/community-detection.ts` | Louvain + Leiden with refinement (connectivity-guaranteed); Newman modularity | | P1-7 temporal graph | ✅ Done | `temporal/temporal-graph.ts` | Quadruplet (s,r,o,t) — half-open validity intervals, as-of snapshots, diff-over-time, timeline, history | | P1-8 entity resolution (embedding) | ✅ Done | `construction/embedding-entity-matcher.ts` (+ existing lexical `entity-resolver.ts`) | Embedding-based ER with ANN (HNSW) blocking + lexical/embedding score fusion; documented cross-domain caveat | | P1-9 FSRS spaced repetition | ✅ Done | `adaptive/path/fsrs.ts` | FSRS-5 (DSR model, canonical default weights) replacing/augmenting SM-2 | | P2-10 GNN | ✅ Done | `gnn/gnn.ts`, `gnn/node2vec.ts` | GCN (symmetric-normalized) + GraphSAGE (mean/pool) with real backprop; node2vec biased walks + skip-gram | | P2-12 closeness/eigenvector/Katz | ✅ Done | `operations/centrality-extended.ts` | Freeman closeness (Wasserman-Faust), eigenvector (power iteration), Katz | | P1-6 durable graph DB (Postgres + pgvector) | ✅ Done | `persistence/pgvector-graph-store.ts` | PostgreSQL + `pgvector` system-of-record — indexed node/edge tables, `vector(dim)` embeddings with an **HNSW** (`vector_cosine_ops`) index, transactional writes, ANN search (`embedding <=> q`), and hydrate ↔ in-memory `GraphStore` hot cache. **Integration-tested against the live dev pgvector DB** (6 tests). Neo4j intentionally not used locally — its dev profile requests 24G/8G-heap, unsafe on this machine; pgvector is the report's recommended option and sufficient. | | P2-11 GPU analytics (cuGraph) | ⊘ Intentionally skipped | — | Per §3/§4, over-engineering at concept-graph scale | With these, the verdict table in §0 moves from **F** (learned representation), **D** (Graph-RAG), **D+** (knowledge tracing), and **C** (storage) to production-grade implementations across the board. Every algorithmic gap (P0-1 through P2-12, excluding the intentionally-skipped GPU analytics) is now closed, **including the durable Postgres + pgvector store (P1-6), integration-tested against the live dev database**. Details of each algorithm and its tests are in the module headers and `*.spec.ts` files. --- ## 0c. Integration status — wired into the product The capabilities above are not just present in the libraries; they are **wired together and to platform infrastructure**, each seam tested: - **Real embeddings flow through the platform client.** `IrisEmbeddingProvider` wraps `@iris/embeddings`' `IrisEmbeddingClient` (the same tiered client the tutoring understanding-classifier uses). `ConceptSimilarity`'s `embedding` method now uses real cached text embeddings once `indexEmbeddings()` runs (feature-vector fallback otherwise — backward compatible). - **Retrieval is governance-aware and pgvector-backed.** `GraphRagRetriever` accepts a `rightsNodeFilter` (the real `KnowledgeGraphRightsFilter`), an optional pgvector seed provider (`createPgVectorSeedProvider`), and an injectable LLM community summarizer. - **The learning loop drives the tracing engine.** `AdaptiveKnowledgeEngine` composes BKT + GKT + FSRS; the tutoring `adaptive-loop`'s previously-empty `mastery-update` step is implemented by `createAdaptiveMasteryUpdater` / `createBktMasteryUpdater` (tutoring now depends on `@metis/adaptive`). The decoupled libs hand off via the tested `toConceptEdges`/`toConceptGraph` contract. - **Recommenders use semantics.** `ContentRecommender` and `AdaptiveLearningConnector` gained optional semantic re-ranking. - **Storage is a managed migration.** `createKnowledgeGraphMigration` is a versioned `@oshun/database`-compatible migration; an end-to-end test composes the whole stack (persist → ANN → hydrate → Leiden → GraphRAG → link prediction) **against the live dev pgvector database**. - **Everything is exported** through the `@metis/knowledge-graph` and `@metis/adaptive` barrels. Suites: knowledge-graph 667, adaptive 506, tutoring 1278 — all green, all three libs `tsc`-clean, 0 lint errors. Remaining beyond this work (deployment, not code): point `ApiEmbeddingProvider` at a live embedding endpoint with credentials, run the migration in the real `metis` database via the deploy pipeline, and adopt the wired modules from the Python `services/metis` (or a TS BFF) at request time. ## 1. The 2026 State of the Art (the yardstick) ### 1.1 Knowledge-graph representation & construction - **Representational progression.** The field is framed as a four-stage evolution: **static KG** (subject–relation–object triples) → **dynamic KG** (continuously updated) → **temporal KG** (time-attached **quadruplets** `(s, r, o, t)`, with `t` a timestamp or validity interval) → **event KG** (event-centric). This is the lens for asking "does my concept graph capture _when_ a fact/prerequisite was true, or only _that_ it is?" [arXiv:2310.04835v3; arXiv:2308.02457; arXiv:2403.04782] - **Construction is now LLM-driven.** NER / relation-extraction moved from CRF / Pointer-Network → contextual embeddings (ELMo, Flair, BERT) → **generative LMs** (GPT, BART, **REBEL** as a BART-based seq2seq relation extractor). [arXiv:2310.04835v3] - **Entity resolution.** Fine-tuning LLMs for entity matching helps **small** models a lot (Llama-3.1-8B ≈ +17 F1) but is **mixed for large** models, and **improves in-domain while degrading cross-domain** transfer (often below zero-shot). Takeaway: don't assume a single fine-tuned matcher generalizes across subjects. [arXiv:2409.08185] ### 1.2 Knowledge-graph embeddings (KGE) Two canonical families, both still the working vocabulary in 2026: - **Translational:** TransE (`h + r ≈ t`) → TransH (relation hyperplanes) → TransR (relation-specific spaces) → **RotatE** (complex-valued, relation = rotation). - **Tensor-factorization / bilinear:** RESCAL → DistMult → **ComplEx** → SimplE (TuckER generalizes these). - **Temporal extensions** are built directly on top: TTransE (on TransE), ChronoR (on RotatE), TComplEx/TeLM (on ComplEx). [arXiv:2310.04835v3; arXiv:2308.02457] These give you **link prediction / KG completion** (suggest missing prerequisite or "related" edges), **typed similarity**, and **embeddings for downstream ML** — none of which a hand-crafted feature vector provides. ### 1.3 Classical graph algorithms & the production stack - **Community detection:** **Leiden is the production default.** It fixes Louvain's defect of internally-disconnected communities via a refinement phase (Louvain leaves "up to 25% badly connected, up to 16% disconnected"). Caveats: still has a resolution limit and only yields hard (non-overlapping) partitions. [Traag et al. 2019, arXiv:1810.08473; GVE-Leiden, ICPP 2024, 10.1145/3673038.3673146] - **Library / DB landscape:** **igraph, NetworKit, cuGraph / nx-cugraph (GPU), Neo4j GDS.** `nx-cugraph` gives zero-code-change GPU acceleration of PageRank, HITS, betweenness / degree / eigenvector / Katz centrality, Louvain **and Leiden**, and Dijkstra / Bellman-Ford. [github.com/rapidsai/nx-cugraph] - **Link prediction in production** is offered as ML pipelines, not just heuristics — **Neo4j GDS** ships logistic-regression, random-forest, and MLP link-prediction models selected by cross-validation. [Neo4j GDS docs] ### 1.4 Graph neural networks & graph transformers - **Unifying view:** **Transformers are message-passing GNNs over a fully-connected graph of tokens.** They dominate not because they're more expressive but because dense matmul "wins the hardware lottery" over sparse message passing on GPUs/TPUs. [arXiv:2506.22084, Joshi 2025] - **Message-passing GNNs** (GCN, **GraphSAGE**, **GAT**) remain the workhorses and, when properly tuned, are **strong baselines that still beat many graph transformers** — GTs are _not_ a blanket replacement. [arXiv:2406.08993, NeurIPS 2024] - **Graph transformers** (Graphormer = shortest-path attention bias + degree encoding; SAN = learned Laplacian PE; TokenGT = nodes+edges as tokens; **GraphGPS** = the modular recipe of positional/structural encoding + local message passing + global attention) target **over-smoothing** and **over-squashing** via global attention. [arXiv:2502.16533v2; arXiv:2205.12454] - **Scalability SOTA:** **Polynormer** reaches **linear complexity** via local-to-global attention and scales to **millions of nodes** where quadratic GTs OOM. [arXiv:2403.01232] (Relevant only at large scale — see §5 honesty note: a concept graph is small.) ### 1.5 Graph-RAG & KG-augmented LLMs - **Microsoft GraphRAG** is the reference pattern: LLM extracts entities/relations from a corpus → builds a KG → **Leiden community detection** → LLM-generated **community summaries** → **global search** (map-reduce over community summaries for corpus-wide "sensemaking" questions) and **local search** (entity-centered multi-hop neighborhood traversal). The verified research specifically confirms Leiden as GraphRAG's community-detection step. [Microsoft Research GraphRAG] - The general principle: KG structure gives LLMs **multi-hop reasoning, provenance, and global context** that flat vector-RAG cannot. Hybrid retrieval (vector similarity **+** graph traversal **+** rerank) is the 2026 baseline for serious KG-backed assistants. ### 1.6 Education-specific: knowledge tracing & prerequisite graphs > The deep-research pass fetched education sources but **none of its KT-specific > claims survived 3-vote verification within the budget** — so this sub-area is > presented from the canonical literature and flagged as a research-confidence > gap, not a freshly re-verified result. - **Knowledge tracing ladder (interpretable → neural):** - **BKT** (Bayesian Knowledge Tracing, Corbett & Anderson 1994) — 2-state HMM per skill (learn / slip / guess). The standard _interpretable baseline_. - **IRT / Elo** — psychometric ability estimation; cheap, explainable, strong baselines. - **DKT** (Piech et al., NeurIPS 2015) — LSTM over interaction sequences; the deep-learning inflection point. - **DKVMN** (Zhang et al., WWW 2017) — memory-augmented, per-concept state. - **SAKT / AKT** (2019–2020) — self-attention; **AKT** adds monotonic attention + Rasch (IRT-style) embeddings and is a long-standing strong SOTA reference. - **GKT — Graph-based Knowledge Tracing** (Nakagawa et al., 2019) and successors (GIKT, HGKT, Bi-CLKT) — cast knowledge tracing **on the concept graph itself**, propagating mastery along prerequisite/related edges with a GNN. This is the single most relevant SOTA family for a platform that _already has a concept graph_. - **Forgetting-aware** variants (DKT-Forget) model decay explicitly. - **Prerequisite-relation learning (PRL):** learn prerequisite edges from content + learner data rather than authoring them all by hand — directly complementary to a concept KG. [Education sources fetched: dl.acm.org/10.1145/3569576; arXiv:2407.20824; AAAI 32156; MDPI 11/12/2780; MDPI 15/1/238 — claims not individually re-verified.] --- ## 2. What metis actually implements today (verified inventory) All claims below were read at source level and spot-checked independently. ### 2.1 Graph algorithms — **real and correct** | Module (file) | Technique | Verdict | | ---------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------- | | `knowledge-graph/.../graph-analytics.ts` | Degree / **Brandes betweenness** / **PageRank** (damping 0.85) / **HITS** / **label-propagation** communities / density / connected components | Real, textbook-correct | | same | Bottleneck identification | Heuristic (betweenness proxy + reachability simulation, not true articulation points) — honestly documented | | `.../pathfinding.ts` | BFS, **Dijkstra** (min-heap), **A\*** (weak char-overlap heuristic), all-paths DFS, **critical path** (topo+DP), topological sort (Kahn), single-source SP | Real | | `.../prerequisite-chains.ts` | Chain extraction, **Tarjan SCC** cycle detection, transitive reduction, topological levels, min-prereq closure, parallel-learning grouping | Real | | `.../concept-similarity.ts` | Path-based, **Wu-Palmer / Lin / Resnik** (IC-based), feature Jaccard, weighted combination | Real | ### 2.2 The "embedding" and "Graph-RAG" misnomers — **the core gaps in disguise** - **`concept-similarity.ts:239` `buildFeatureVector()`** — the "embedding-based" similarity is a **hand-crafted 13-dimension feature vector** (one-hot type over 5 categories + difficulty, importance, learning-time, label length, word count, keyword count, in/out degree) compared by cosine. This is **not a learned embedding** — it carries no semantic meaning of the concept text. (Verified by reading the function.) - **`knowledge-graph/.../graph-rag-benchmark.ts`** — computes precision/recall/F1 of a **caller-supplied** retrieved-node set against an expected set, then layers source-credibility, freshness, and rights filtering. There is **no graph traversal, no multi-hop expansion, no community summarization, no reranking** — i.e., it is a governance - evaluation harness, **not** a GraphRAG _retriever_. - **`research/src/embeddings/embeddings.ts`** — correct cosine/Euclidean/dot/Manhattan + L2-normalize, and a table of model dimensions (MiniLM, MPNet, E5, OpenAI ada/3-small/large). But it is **types + vector math only**; no embedding _generation_ is wired in. ### 2.3 Knowledge tracing — heuristic, not probabilistic/neural - **`adaptive/.../knowledge-tracer.ts:127`** — per-concept mastery updated by an **exponential moving average** with a difficulty adjustment, plus a transfer-learning spread to related concepts and a forgetting curve `P·exp(−decay·Δdays)`. Reasonable and explainable — but **not BKT** (no slip/guess/transit parameters, no Bayesian posterior). - **`adaptive/.../spaced-repetition.ts`** — a real **SM-2** (SuperMemo-2) scheduler. Legitimate, but a 1987 algorithm; SOTA spaced repetition (FSRS, half-life regression) is newer and data-driven. - **`adaptive/.../mastery-progression.ts`** — exponential mastery decay + gates/milestones. ### 2.4 Storage - **`knowledge-graph/.../graph-store.ts:29`** — in-memory `Map`s + adjacency/reverse-adjacency, default caps **100k nodes / 500k edges**, optional JSON-file persistence, no transactions, single-process. **Not a graph database; no vector index (HNSW/IVF); no pgvector.** ### 2.5 Python service - `services/metis/src/metis/...` is **orchestration/CRUD** (concept-graph build/validate delegating to helpers; a course-sequencing recommendation wrapper). **No graph ML.** --- ## 3. Gap analysis — SOTA vs metis (prioritized) Severity reflects impact on "industry-leading for an adaptive-learning concept graph," not generic graph-ML completeness. A concept graph is **small** (thousands–hundreds of thousands of nodes), so several scale-oriented SOTA items are explicitly _not_ priorities. ### P0 — closes the largest, most defensible gaps 1. **Semantic node/edge embeddings (replace the 13-dim feature vector).** Generate dense embeddings for concept text via an embedding model (the repo already references E5 / OpenAI 3-large and an `llm-client`). Store them and use cosine for "related-concept" similarity, dedup, and clustering. This is the difference between "similar because both are `procedure` nodes with similar degree" and "similar because they're about the same idea." _Smallest-effort, highest-impact change._ 2. **A vector index + true Graph-RAG retriever.** Add ANN search (pgvector/HNSW, or the already-optional `chromadb`) and a retriever that does **hybrid retrieval**: vector seed → **multi-hop graph expansion** along prerequisite/related edges → rerank → (optionally) Leiden community summaries for global/"sensemaking" questions. Rename/refactor `graph-rag-benchmark` to sit _on top_ of a real retriever rather than scoring caller-supplied sets. [MS GraphRAG pattern] 3. **Knowledge-graph embeddings + link prediction (KG completion).** Add a KGE model (start ComplEx/RotatE; these are small and CPU-trainable at this scale) to **suggest missing prerequisite / related edges** for human review, score edge confidence, and detect contradictions. Directly improves authoring throughput and graph quality. [TransE/RotatE/ComplEx families] 4. **Upgrade knowledge tracing: BKT now, GKT next.** Ship **BKT** as the probabilistic baseline (small, interpretable, standard) behind the existing EMA tracer; then add **GKT / graph-based knowledge tracing** that propagates mastery over the concept graph you already maintain — the highest-leverage neural method _because the graph already exists_. Restores (and modernizes) the `DKTLSTMModel` / `DKTTransformerModel` capability Minerva had. [DKT/AKT/GKT literature] ### P1 — strong improvements, moderate effort 5. **Leiden community detection** alongside label-propagation. Leiden gives connectivity- guaranteed, modularity-optimized concept clusters (topic discovery, curriculum modules, GraphRAG community summaries). Label propagation is fast but unstable and not SOTA. [Traag 2019] 6. **Durable graph store with proper indexing.** Move off in-memory `Map`s for the system-of-record: either a graph DB (Neo4j/Memgraph — Minerva already used Neo4j) or Postgres + adjacency tables + **pgvector**. Keep the in-memory store as a hot cache. Removes the 100k-node ceiling and enables concurrent writers/transactions. 7. **Temporal / versioned edges.** Add `validFrom/validTo` (quadruplet `(s,r,o,t)`) so the graph can express "this prerequisite was revised," support content versioning, and power freshness/invalidation rather than only timestamp metadata. [TKG quadruplet] 8. **LLM-assisted construction with entity resolution.** Formalize NER/RE extraction (REBEL or an LLM seq2seq extractor) feeding the concept graph, with an explicit **entity-resolution / dedup** step (embedding blocking + match). Mind cross-domain generalization limits if fine-tuning. [arXiv:2310.04835v3; arXiv:2409.08185] 9. **Modern spaced repetition (FSRS).** Replace/augment SM-2 with FSRS or half-life regression — data-driven, materially better retention scheduling than 1987-era SM-2. ### P2 — only if scale or research ambition demands it 10. **Lightweight GNN (GraphSAGE/GAT) for learned node representations** — useful if you want inductive embeddings that fuse text + structure for recommendation/cold-start. A well-tuned GraphSAGE/GAT is the right tier; **graph transformers / Polynormer are unnecessary** at concept-graph scale. [arXiv:2406.08993 — classic GNNs are strong baselines] 11. **GPU graph analytics (nx-cugraph)** — only if graphs grow to millions of edges. Currently over-engineering. 12. **Closeness / eigenvector centrality, motif mining** — nice-to-have analytics; low priority vs. the learned-representation gaps. --- ## 4. What is genuinely _fine_ as-is (don't over-correct) - The **classical algorithm implementations are correct and well-tested** — keep them; they remain SOTA for what they do. The gap is _additive_ (learned methods), not a rewrite. - **Governance** (rights posture, source-backing, credibility, freshness windows) is a real strength and ahead of typical KG systems — preserve it as a first-class filter layer over any new retriever. - **Graph transformers, linear-attention GTs, distributed GNN training, GPU analytics** are **not** gaps for a concept graph of this size. Pursuing them would be cargo-culting "SOTA" against a problem that doesn't have the scale to need it. The honest SOTA target here is **learned embeddings + KGE/link-prediction + true GraphRAG + graph-based knowledge tracing**, not the biggest models in the literature. --- ## 5. Suggested sequence 1. P0-1 (semantic embeddings) → unlocks P0-2 (vector index + GraphRAG retriever). 2. P0-4a (BKT) in parallel — small, independent, immediate product value. 3. P0-3 (KGE/link prediction) once embeddings infra exists. 4. P1-5/6/7 (Leiden, durable store, temporal edges) as the platform substrate. 5. P0-4b (GKT) once durable store + embeddings are in place. 6. P1-8/9 and P2 items as ambition/scale warrant. This ordering also **re-lands the neural capabilities Minerva already had** (DKT, neural embeddings, Neo4j) in modern form, which is likely the fastest path to "industry-leading" because the design space was already explored once. --- ## Appendix — sources **External SOTA (3-vote verified unless noted):** KG evolution & construction & KGE — arXiv:2310.04835v3; temporal KGs — arXiv:2308.02457, arXiv:2403.04782; entity matching — arXiv:2409.08185; Leiden — Traag et al. 2019 (arXiv:1810.08473), GVE-Leiden ICPP 2024 (10.1145/3673038.3673146); GPU analytics — github.com/rapidsai/nx-cugraph; Neo4j GDS link prediction — Neo4j GDS docs; Transformers-as-GNNs — arXiv:2506.22084; graph-transformer survey — arXiv:2502.16533v2; GraphGPS — arXiv:2205.12454; Polynormer — arXiv:2403.01232; classic-GNN baselines — arXiv:2406.08993 (NeurIPS 2024); GraphRAG — Microsoft Research. **Education (canonical, not re-verified this pass):** BKT (Corbett & Anderson 1994); DKT (Piech et al. 2015); DKVMN (Zhang et al. 2017); SAKT (2019); AKT (Ghosh et al. 2020); GKT (Nakagawa et al. 2019); plus fetched surveys dl.acm.org/10.1145/3569576, arXiv:2407.20824, AAAI 32156, MDPI 11/12/2780, MDPI 15/1/238. **Metis code evidence:** `libs/metis/knowledge-graph/src/operations/{graph-analytics, pathfinding,prerequisite-chains,concept-similarity}.ts`; `.../applications/ graph-rag-benchmark.ts`, `.../governance.ts`; `libs/metis/knowledge-graph/src/construction/ graph-store.ts`; `libs/metis/research/src/{embeddings,knowledge-graph}/`; `libs/metis/adaptive/src/path/{knowledge-tracer,mastery-progression,spaced-repetition}.ts`; `libs/metis/core/src/minerva-analysis.ts`; `services/metis/pyproject.toml`.