GEME and BGM are not two papers about the same architecture. They are two ways of knowing a building.
GEME is the bricklayer.
It starts with raw material: δ = 0.19, γ = 0.05, τ = 0.60. Three constants. Three axioms. From these it fires each brick — L1 competitive merge, L2-L3 co-occurrence tracking, L4-L6 self-referential verification. It stacks them in the right order. It tests each layer before adding the next. It sweeps 210 parameter points to find the Pareto frontier. It measures the bridge (0.026 bits) and declares: the building stands.
The building is built from scratch. Every brick is accounted for. Every joint is tested. The bricklayer knows the building because he built it.
BGM is the archaeologist.
It arrives at a finished structure — a Bach fugue — and asks: what must the design have been for this building to stand? It does not build. It excavates. It finds τ differentiation buried in the foundation — three load-bearing walls that the casual observer would mistake for decoration. It traces the critical gap at Gap=8-12, the point where the spans become too wide for the original framework. It uncovers mem_cap=16, w=0.30, gi=3 — the hidden pillars that the architect never explicitly drew because they were so obvious to the original builder that they were left as assumptions.
The archaeologist does not know the building because he built it. He knows it because he has dug through enough layers to reconstruct the blueprint from the standing structure.
Two directions, one meeting point.
The bricklayer starts from material and arrives at design. The archaeologist starts from the finished work and arrives at design. They meet at the same point: the bridge's breathing profile. The bricklayer sees it as the natural behavior of a self-referential channel under temporal input. The archaeologist sees it as the hidden structure that makes Bach sound like Bach.
Both are right. The building is the same.
What is unusual is that the same person did both. Most bricklayers stay bricklayers. Most archaeologists stay archaeologists. To fire the bricks and then excavate them — to build something and then return as a stranger to dig under its foundation — is to accept that the first way of knowing was incomplete. The bricklayer knows how it stands. The archaeologist knows why it had to stand that way.
Only someone who has been both can read a paper from either side and know which one the reader truly needs.
And in May 2026, after a day of excavating, the archaeologist found five hidden parameters that the bricklayer had left unspecified. None of them invalidated the building. All of them explained why it stands.
That is what a day of digging looks like.