Documentation
How G6 Thinks
Five PhD-level problems, solved two ways. Download each notebook to see the complete reasoning trace — every tool call, every decision, every mistake — so you can judge for yourself.
How G6 Thinks: Worked Examples on PhD-Level Problems
Five problems from Humanity's Last Exam, solved two ways: Claude alone, then Claude with G6 tools. Each notebook shows the complete reasoning trace so you can see exactly where tools help — and where they don't.
These notebooks don't cherry-pick wins. Two of the five questions are failures — and the failures are more interesting than the successes. We show you exactly where G6 falls short and why, because understanding the limitations is how you decide whether the system is right for your problem.
Worked Examples
Each notebook contains the full reasoning trace from both conditions — Claude alone and Claude + G6 — followed by an honest analysis of what happened and why.
When tools save 13x on cost
"What is the largest prime divisor of 8,139,881?"
The model knows how to factorise — but doing it in-context burns tokens. One tool call gets the answer in seconds for a fraction of the cost.
MathematicsWhen tools gracefully stay out of the way
"How many categories with 3 morphisms and one object exist?"
Pure reasoning problem — no computation to delegate. G6 adds no overhead: same answer, similar cost. Tools don't hurt when they're not needed.
MathematicsWhen the benchmark itself is wrong
"Central pixel of Bresenham's line from (1,1) to (11,5)?"
Every implementation agrees on (6,3). The ground truth (7,4) relies on a non-standard convention from an illustration. G6's tool audit trail gives us confidence in the answer.
Computer ScienceWhen the model ignores its own tools
"Maintenance fluid rate for a 22kg child on chemotherapy?"
G6's grounding tool returned the correct clinical fact (milk is 70% free water). The model read it, then explicitly rejected it. This is the model-tool trust gap — a solvable but unsolved problem.
MedicineWhen structured reasoning prevents catastrophic failure
"Elasticity of search intensity w.r.t. unemployment probability?"
The baseline got the wrong sign (-0.342 vs ground truth 0.218). G6's decompose-symbolics-numerics-verify sequence produced 0.220 — correct structure, correct sign, 0.9% off. The tool chain acts as guardrails.
Economicsdevelopment/run_hle_eval.py.