Hidden Structure Research Group
What can an observer never see?
A mathematics program about the limits of observation.
Every observer, whether a person, an animal, an instrument or a machine, sees the world through a filter that can only compare a few things at once. The Observer Limit Program asks what that filter hides for good, proves exactly where the edge lies, and tests what the hidden part does.
Three ideas
Patterns come in sizes
Any pattern across many yes-or-no switches splits cleanly into pieces: single switches, pairs, triples, and so on, up to the whole system at once. Nothing is left over.
Every observer has a depth
An observer that can compare at most a few things at a time sees the small pieces exactly and is blind to the large ones. More data does not help. Only a deeper observer can see them.
The edge is sharp
For a large system, an observer whose depth is below half the system misses almost everything. Above half, almost nothing is hidden. The switch from one to the other gets sharper as systems grow.
How sure are we?
Every result on these pages carries one of five labels, and the labels are not decoration. Proved means proved within the stated mathematical setup, which is a claim about mathematics, not about the physical world.
- ProvedA complete proof exists for the stated setup.
- Proved in a modelExact, but inside a specific model that the program chose and has not yet derived.
- Numerical evidenceStrong computational evidence. Not a theorem.
- OpenUnresolved. Stated so that it can be settled.
- InterpretationWhat a result might mean. Never offered as evidence.
Predictions about a computation are sealed before it is run. Since September 2026, every computed number is logged with a fingerprint of the script that produced it. When something turns out to be wrong, the correction is published, not buried.