Editing Openai/6945f9bd-f198-8008-bb8c-1ab730279e5f (section)

==== A viable nDspace-first GPU system needs four explicit layers, each with its own challenges. ====

===== This does not exist today. =====

You must be able to declare:
* Dimensions
* Independence
* Applicability predicates
* Nullability
* Projection rules

Example (conceptual, not syntax):

<syntaxhighlight>dimension Time        continuous
dimension Jurisdiction discrete
dimension Symmetry    group(D4)
dimension Invocation  boolean

subspace KolamCore:
  requires Symmetry, Invocation
  excludes Jurisdiction

</syntaxhighlight>

====== Current GPU languages (CUDA, GLSL, HLSL): ======
* Assume fixed dimensionality
* Treat dimensions as array indices, not semantics
* Cannot express “non-existence”

This requires a new declarative layer, not a new shader.

===== This compiler must: =====
* Analyze dimensional independence
* Identify null subspaces
* Factor projections
* Generate optimal GPU kernels

In effect, it must:
* Do what humans currently do mentally when optimizing shaders
* But using semantic dimension information

====== - nDspace grows combinatorially ======
* Many dimensions are sparse or latent
* The compiler must avoid generating impossible kernels

This is closer to constraint solving than to compilation.

===== Once dimensions are explicit, kernels can be specialized: =====
* One kernel per active subspace
* No runtime branching
* No unnecessary memory access

But:

====== - Too many subspaces → too many kernels ======
* Requires aggressive subspace collapsing and reuse

This demands:
* Equivalence detection between subspaces
* Projection caching
* Symmetry exploitation

GPUs are fast, but kernel launch overhead is real.

===== Here GPUs are perfectly at home: =====
* nD buffers / tensors
* Sparse masks
* SIMD execution
* Fast projection

This layer is not the bottleneck.

Ironically, GPUs already excel at the final stage—the earlier layers are missing.