ix

Test model robustness with adversarial attacks and defenses

Multi-armed bandit simulation — epsilon-greedy, UCB1, Thompson sampling

Benchmark and compare ix algorithm performance

Embedded Redis-like cache with TTL, LRU, pub/sub, and RESP protocol

Category theory primitives — monad laws verification, free-forgetful adjunction

Chaos theory analysis — Lyapunov exponents, bifurcation, attractors, fractals

Cluster data using K-Means or DBSCAN

Run ix real-world demo scenarios with optional multi-AI commentary via Octopus. Chains multiple ix MCP tools through curated narratives — chaos detection, governance, FinOps, sprint prediction.

Dynamical systems — inverse kinematics, Lie groups/algebras, neural ODEs

Evolutionary optimization — genetic algorithm, differential evolution

Fractal generation — Takagi curves, space-filling curves, Morton codes

Game theory — Nash equilibria, Shapley value, auctions, evolutionary dynamics

GPU compute via WGPU — cosine similarity, matrix multiply, batch vector search

Formal grammars — weighted CFGs, grammar evolution, constrained generation

Hidden Markov Model analysis — Viterbi, Baum-Welch, forward-backward

Algebraic K-theory for graphs — Grothendieck K0/K1, Mayer-Vietoris sequences

Build ephemeral or persistent ML pipelines — auto-detects task type, selects models, handles preprocessing, evaluation, and caching

Neural networks — trainable transformers with GPU attention, dense layers, backprop, loss functions, positional encodings

Number theory — prime sieving, primality tests, modular arithmetic

Optimize a function using SGD, Adam, PSO, or simulated annealing

DAG pipeline orchestration with parallel execution and caching

Random forest and gradient boosted trees — ensemble classifiers for tabular data

3D rotation operations — quaternions, SLERP, Euler angles, rotation matrices

Search and pathfinding with A*, Q*, MCTS, minimax, BFS/DFS

Hypercomplex algebra — sedenion/octonion multiplication, Cayley-Dickson construction

Signal processing — FFT, filtering, wavelets, Kalman, spectral analysis

Supervised learning — regression, classification, evaluation metrics, cross-validation, confusion matrix, ROC/AUC, SMOTE resampling

Topological data analysis — persistent homology, Betti numbers, point cloud topology

Concrete, runnable examples combining GA music theory tools with ix ML algorithms for chord clustering, harmonic analysis, and scale recommendation

Autonomous belief-revision loop — fuse @ai: annotations + /deep-research claims into the temporal assumption graph and revise the persistent belief log over time

Self-improvement reflex. When the user corrects an approach ("no, don't do that", "we discussed this before", "stop X"), captures the lesson as a permanent project rule appended to CLAUDE.md so the pattern doesn't repeat in this or future sessions. Cherny called this "the most important loop" in his 2026 Sequoia talk.

Capture meaningful session state (current cursor, in-flight work, live hypotheses, open questions, do-NOT-carry-forward, success criteria) to state/digests/latest.md so the next session — including one after auto-compaction — can re-enter without re-discovering context cold. Distinct from /learnings (which captures surprises). Validates against docs/contracts/digest-schema.json.

Deep code review of an IX crate by piping its source into Qwopus-GLM-18B (Qwen3.5 + Opus + GLM distilled frankenmerge). Offline, free, slow, reasoning-heavy.

Compose a chord progression with smooth voice leading — chains ga_generate_progression → ga_voice_leading_pair → ga_search_voicings. Use when the user asks for a progression in a key / style with playable voicings (e.g. "compose ii-V-I in Bb with smooth voicings").

Ask the GA Chatbot music theory questions — grounded voicing answers via real GA+IX MCP tools, no hallucination

Adversarial QA for ga-chatbot — deterministic layers + Octopus judge panel + hexavalent aggregation

Find capabilities across the GuitarAlchemist ecosystem (ix, tars, ga) by domain or keyword

Delegate grammar weighting and evolution tasks across ix (local Rust) and TARS (F# engine)

Combine GA music theory tools with ix ML algorithms for music analysis

Ingest GA trace artifacts, analyze with ix stats, feed results to TARS pattern promotion