GPT-5.5 vs Claude Opus 4.7: I Tested Both So You Don’t Have To (Honest Verdict)
May 20, 2026
Rick Ross ft Drake – Aston Martin Music (1950’s Soul Version)
May 20, 2026
By C. Rich
Imagine a perfect rectangular box, like a brick, but magical. Its three faces are all perfect right triangles (so each face satisfies the Pythagorean theorem), and even the long diagonal through the whole brick is also a perfect integer length. Sounds simple, right? Just three numbers a, b, and c where every possible sum of squares works out to another perfect square. That’s the Perfect Cuboid. Mathematicians have been hunting for one for over 300 years. We’ve found plenty of “almost” versions, called Euler bricks, where the three faces work but the space diagonal refuses to cooperate. No one has ever found a single example where all four conditions are satisfied at once. And despite computers searching trillions of possibilities and clever mathematicians throwing every trick in the book at it, the damn thing remains stubbornly hidden… or possibly nonexistent.
So, I decided to try something a little different. Instead of attacking the equations head-on with bigger computers or fancier number theory, I stepped way back and asked a more philosophical (but surprisingly practical) question: What if the problem isn’t just about finding the right numbers, what if we’re starting from the wrong kind of mathematical universe? I built something with the C. Rich Mash System that we call the Garden, a tiny, perfectly symmetric mathematical cosmos based on the 24-cell, one of the most beautiful and symmetric objects in four-dimensional geometry. Inside this Garden, we defined the very first possible “distinction” (a thing called a flag with a tiny order-2 symmetry leftover), then let it propagate according to strict internal rules, tracking both Gaussian integer orientations and 2-adic valuations as we went. We tested it against real Euler bricks. We watched how flat local corners behaved when forced to spread across the exceptional geometry of the 24-cell. We measured phase shifts, valuation drops, and holonomy. We ran the numbers honestly, corrected our own mistakes along the way, and let the code speak without forcing a dramatic conclusion.
The result?
The geometry looked right back at us and chose total, quiet compliance. As our connection traveled along hundreds of global paths through the 4D lattice, it didn’t catastrophically crash or twist into chaotic knots. It slid through the gears smoothly, gently absorbing the arithmetic shifts with only rare, minor ripples. By forcing our code to speak with absolute scientific honesty, we proved that the 24-cell is far too cooperative to be the blunt geometric cage that kills the perfect cuboid. The mystery successfully evaded our finite net, slipping back out into the infinite landscape of continuous number theory. We didn’t solve the century-old problem, but we did something just as electric: we built a brand-new computational bridge between abstract geometry and hard arithmetic, proving that even when the universe refuses to give up its secrets, it will always reward a deeper, more disciplined way of looking at the ground beneath our feet.
The Perfect Cuboid problem is one of those delightfully stubborn math puzzles that sounds simple until you try to solve it. Imagine building a rectangular box where every edge, every face diagonal, and the long diagonal through the center all land on whole numbers. That means not only do the three side lengths have to fit together neatly, but the diagonals on each face and the space diagonal have to fit perfectly too. We know examples called Euler bricks, where the edges and face diagonals are integers, but the final step, making the space diagonal an integer too, has never been found. So, the problem sits there like a nearly finished jigsaw puzzle with one last piece missing, and nobody knows whether that piece exists at all.
What we did was try to look at that missing-piece problem from a very unusual angle. Instead of attacking it only with ordinary number theory, we built a kind of geometric “laboratory” using the 24-cell, a highly symmetric object from four-dimensional geometry. Think of it as a very elegant cage made of 24 vertices, 96 edges, and 96 triangular faces, with 576 little incidence patterns inside it. Then we tried to place a simple arithmetic signal on that structure using Gaussian integers and a four-state phase rule, sort of like tracking whether the math stayed aligned or twisted as it moved around. We tested it on several known Euler bricks, including the famous one with side lengths 44, 117, and 240, and watched to see whether the pattern broke in a dramatic way. It didn’t. The signal stayed mostly flat, with only small, rare flickers linked to 2-adic behavior, which means the geometry was surprisingly cooperative rather than hostile.
So, the honest result is this: our method did not solve the Perfect Cuboid problem, but it did tell us something important. It suggests that the obstruction, if it exists, is not a simple “the geometry falls apart” kind of problem. The 24-cell was too well-behaved for that. In plain language, the puzzle is deeper than a visible crack in the structure; if there is a reason perfect cuboids don’t exist, it probably lives in subtler arithmetic layers, not in an obvious geometric twist. That’s useful because good science is not just about finding the answer you hoped for, it’s about learning what kinds of answers are not there. The Garden is surprisingly friendly. Local corners stay nice and flat. The geometry absorbs the cubic structure without throwing a tantrum. The rare glitches we saw were mild and tied to 2-adic behavior rather than some grand cosmic “no” sign. In other words, the 24-cell didn’t slam the door on the Perfect Cuboid; it politely showed us that if there’s an obstruction, it’s deeper and subtler than this particular geometric lens can see.
So, the hunt continues, but now with a new kind of map. We didn’t solve the Perfect Cuboid (yet), but we built a genuine pre-geometric laboratory where philosophy, geometry, and computation can actually talk to each other without anyone shouting. And honestly? That feels like real progress. The Garden is planted. The first distinctions have been made. The rest of the universe, and whatever secrets the Perfect Cuboid still holds, will have to reveal itself one honest computation at a time. And that is just how I built Cosmological Pangaea.
