All Skills

Lower Big-O on existing code via a one-transformation-at-a-time playbook with verify-revert-stop. For new code use lemmaly; for math-level wins escalate to mathguard.

Correctness-first: forces writing the function contract, loop invariant, termination argument, and edge cases BEFORE code. Catches Boyer-Moore, leftmost binary search, QuickSelect traps.

Algorithm-first discipline: state Big-O, data structure, and algorithm family BEFORE writing loops, queries, or recursion. Catches O(n^2), N+1, and brute-force defaults.

Math-heavy escalation for n >= 10^6 — Bloom, HyperLogLog, Count-Min, MinHash/LSH, FFT, JL projection, sweep line. Use when classical O(n log n) is the floor and approximate or math wins.