lemmalylisted

# lemmaly — Algorithm-First Proof The model already knows Big-O, hash tables, divide-and-conquer, dynamic programming, sorting, graph algorithms, and amortized analysis. It just does not apply them spontaneously. lemmaly fixes the behavior, not the knowledge. This skill is the gateway. It enforces the hard rules that every other guard in the suite assumes. **Violating the letter of these rules is violating the spirit of the skill.** "Just this once" is how O(n²) ships to production. ## How to use — pick the right skill The suite has four skills. Use this table to route to the right one. When in doubt, **start at lemmaly** — it is the gateway and will tell you when to escalate. | If you are about to… | Use | Why | | --- | --- | --- | | Write *new* code that loops, queries, joins, recurses, or processes a collection | **lemmaly** | Forces complexity + data structure + algorithm family **before** code is written. | | Refactor *existing* code that is already slow, OOMs, times out, or has nested loops / N+1 / repeated work | **complexity-cuts** | Corrective playbook for code that already shipped with bad Big-O. | | Implement an algorithm where the obvious version is subtly wrong (binary search variants, in-place dedup, Boyer–Moore, QuickSelect partition, recursion with accumulators, fixed-point / termination concerns) | **invariant-guard** | Forces writing the function contract + loop invariant before code. The trap is in the contract, not the loop body. | | Work with n ≥ 10