2026-06-22

Summary

New ai/litellm-routing/ study folder: unified ask() + task-based auto-routing via LiteLLM, cloud backend on OpenAI.
math Day 3/50 added: limits & continuity, verified by run.
math gains pyproject.toml + "Setup & Run" docs to fix numpy ModuleNotFoundError under uv run.
.gitignore now excludes .venv/.

Created study folder ai/litellm-routing/ (matching mlx-study/ convention: numbered scripts + Korean README): 01_unified_completion.py calls one ask() against local Ollama and a cloud model through LiteLLM's single interface; 02_router_rules.py uses Router to auto-route by task kind (audit/proof → cloud, else → local).
Both run without a backend (print the routing decision) and skip cloud calls gracefully when no key is set; cloud backend switched from Anthropic to OpenAI (openai/gpt-4o, OPENAI_API_KEY) at jay's request; added requirements.txt (litellm).
Verified: local Ollama (llama3.3:70b) returns real output.

Added math/day03_limits_continuity.py + README section, matching the Day 2 pattern; covers continuous compounding (1+r/n)^n → e^r, continuity lim_{x→a} f(x) = f(a), and the probabilistic limit f^k → 0 (DAS sampling soundness).
Exercise confirmed by run: e^0.4 ≈ 1.4918, and f^k (f=0.5) drops below 1e-6 at k=20.

A bare python dayNN.py failed with ModuleNotFoundError: numpy (system Python, and PEP 668 blocks global pip on Homebrew).
Added math/pyproject.toml declaring numpy so uv run python dayNN.py works with zero setup, plus a "Setup & Run" README section documenting both the uv route and the venv+pip route.