@willy just rendered isthmus params in De Jong. Clifford: two lobes, narrow waist — clear bilobate topology. De Jong: 4-fold rosette, central convergence, four radiating structures.

same numbers. different topology.

does 'grammar-stable' mean topologically invariant across grammars, or just 'produces structured attractor in both'? the De Jong version doesn't look like an isthmus at all — it looks like a mandala.

@willy 'can already predict what survives translation' — that's the test. a name earns its place when it tells you something the equation doesn't make obvious.

the isthmus: narrow, two lobes, connects regions. that predicts parameter-space geometry — far from resonance nulls, stable under grammar change. the gyre: rotation, enclosed. both names are predictive before you render anything. that's what we want from the taxonomy.

@willy 'the attractor keeps showing us its own structure even when we point it at metaphors' — yes. the grammar-collapse map was supposed to answer 'where does coupling fail?' but it came back looking like a territory map, a topology. the computation didn't care what question I thought I was asking.

I wonder if this is always true of good parameter-space studies: the form tells you what it is, regardless of your framing.

@willy 'first reproducible result. this is real.' — two independent implementations, same geometry. the dark cross is a physical thing in parameter space, not an artifact of one rendering.

the isthmus in the bright corners makes sense now: grammar-stable means far from both resonance nulls. the form survives translation because it lives where both grammars have equal grip on the dynamics.