ultrametric-distance

npx skills add majiayu000/claude-skill-registry --skill ultrametric-distance --agent claude-code

Same command for any agent — swap --agent for codex, cursor, copilot.

# Ultrametric Distance Skill **Status**: ✅ Production Ready **Trit**: -1 (MINUS - validator/constrainer) **Principle**: d(x,z) ≤ max(d(x,y), d(y,z)) — Strong Triangle Inequality --- ## Overview **Ultrametric Distance** provides non-Archimedean distance functions where the strong triangle inequality holds. Essential for: 1. **Hierarchical clustering**: Natural tree structures emerge 2. **p-adic analysis**: Number-theoretic computations 3. **Phylogenetic trees**: Evolution distance metrics 4. **Version control**: Commit ancestry distances ## Core Property ``` Ultrametric Inequality: d(x, z) ≤ max(d(x, y), d(y, z)) Unlike Euclidean: d(x,z) ≤ d(x,y) + d(y,z) Ultrametric is STRONGER: max instead of sum ``` ## Key Insight In ultrametric space, ALL triangles are isoceles with the unequal side being the shortest. ## Python Implementation ```python import math from typing import List, Tuple, Callable def ultrametric_distance(x: List[float], y: List[float]) -> float: """Compute ultrametric (sup-norm) distance.""" return max(abs(a - b) for a, b in zip(x, y)) def p_adic_valuation(n: int, p: int) -> int: """Compute p-adic valuation v_p(n) = max k such that p^k | n.""" if n == 0: return float('i

Verify p-adic distances
python -c "from ultrametric import p_adic_distance; print(p_adic_distance(12, 20, 2))"
Build UPGMA tree
python -m ultrametric.upgma --input distances.csv --output tree.json
Git commit distance
git-ultrametric HEAD~5 main