Crux-Lab

Proof Forge

Patterns, proofs, programs.

A public notebook of mathematical and algorithmic problem solving.
This site focuses on how ideas are found: brute force, pattern spotting, conjectures, proofs, and compact code checks.

[!NOTE] Polished notes shall be displayed here. Detailed raw solve logs, dead ends, and full research notes are kept private. Contact admin for access


Start Here

If you are new to the site, these are the best entry points:


What this is

This is not just an answer archive.

It is a growing lab of:


Current Themes

Pattern spotting

Small cases, brute force experiments, and output structure.

Conjecture making

Turning observations into precise guesses worth testing.

Proof tools

Modular arithmetic, factorization, parity, symmetry, discriminants, invariants, and bounds.

Computation as support

Tiny checkers used to confirm, explore, or narrow the search.


[!TIP] Use these notes as high yield concept boosters.


Learning Style

My typical solve loop looks like this:

```mermaid flowchart LR A[Try small cases] –> B[Spot a pattern] B –> C[Make a conjecture] C –> D[Try to break it] D –> E[Find the mechanism] E –> F[Prove or compute]