mathguard — Math-Heavy Optimization for AI Code

lemmaly makes you pick the right classical algorithm. mathguard kicks in when the classical algorithm is already optimal but mathematics gives a better bound — usually by accepting bounded approximation, exploiting structure, or moving to a smarter algebraic space.

The model knows these techniques. It almost never proposes them spontaneously. mathguard fixes that.

Violating the letter of these rules is violating the spirit of the skill. A Bloom filter where the caller assumed exact answers is a production incident, not an optimization.

When to Use This Skill

Use mathguard when:

• Working with large-scale data (n ≥ 10⁶): similarity search, deduplication, top-K / heavy-hitters, streaming analytics, cardinality estimation, embeddings, recommender systems.
• Doing signal/image processing, polynomial or big-integer arithmetic, convolution, graph distance, computational geometry, randomized algorithms.
• The classical O(n log n) is already the floor and you need an asymptotic win (Bloom filter, HyperLogLog, Count-Min Sketch, MinHash/LSH, FFT/NTT, Johnson-Lindenstrauss projection, sweep line, kd-tree/BVH, fast exponentiation, monoid parallel reduction, amortized potential method).
• Loaded after lemmaly has confirmed the classical answer is not enough.