Park the CultMath tape campaign: interval-pruned field evaluation, option c

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/cultmath-tape-target.md

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+# CultMath tapes: interval-pruned field evaluation on CPU and GPU
+
+Status: **parked**, 2026-10-02. The operator wants Asura working first. This
+note records the direction so it can be picked up without re-deriving it. It is
+not a cut map: no Imagination pass has run, and nothing here is ruled except
+that the campaign exists and waits.
+
+## Intent
+
+Evaluate large implicit fields, meaning deeply nested CSG trees of brushes with
+thousands of nodes, cheaply enough to mesh at many levels of detail and to
+raymarch. The operator's words (2026-10-02): "I would love to design a space
+station out of a grammar of nested brushes, and have the ability to
+automatically mesh it at multiple levels of detail so I can get arbitrarily
+close to its tiny details without melting my GPU."
+
+GameCult has no deep CSG trees today because nothing could evaluate them
+cheaply. The capability comes first, and the content follows.
+
+## Prior art
+
+[Fidget](https://www.mattkeeter.com/projects/fidget/) by Matt Keeter
+(MPL-2.0, Rust, v0.5.1 on 2026-09-27; repo `mkeeter/fidget`).
+- It compiles an expression to a register-allocated bytecode tape.
+- It evaluates that tape as points, SIMD batches, intervals, and forward-mode
+  gradients.
+- The central trick is interval evaluation over a region. When it proves that
+  one operand of a `min` or `max` always wins, the tape for that region is
+  rewritten without the other branch. In the project's example, the tape
+  shrinks from 254 clauses to about 20 at pixel level.
+- `fidget-jit` targets x86-64 and AArch64.
+- `fidget-wgpu` has a WGSL tape interpreter, interval ops and tape
+  simplification on the GPU (`interval_ops.wgsl`, `tape_interpreter.wgsl`,
+  `tape_simplify.wgsl`).
+- `fidget-mesh` implements Manifold Dual Contouring. It is known to be weak on
+  thin features.
+- Halfspace is the IDE codesigned with `fidget-wgpu` (Rust, egui and wgpu,
+  MPL-2.0).
+
+## Chosen shape (option c)
+
+The ideas are ported into CultLib and owned here. Fidget is not a dependency.
+Unity renders HLSL on its own graphics backend, so `fidget-wgpu` cannot run
+inside it.
+
+Three options were weighed on 2026-10-02:
+
+| Option | What it is | Trade |
+|---|---|---|
+| a | Fidget as a Rust native plugin in Unity | Fastest demo; costs per-platform native builds, an FFI boundary, and an upstream that warns of breaking changes |
+| b | Offline bake with a Rust tool; ship meshes | Simplest; the baked depth caps how close a viewer can get |
+| c | CultLib owns tape, interval and pruning in C# and HLSL | Most coherent end state; the largest code liability we would own |
+
+The operator parked (c). An (a) spike to validate authoring and LOD behaviour
+before owning code was suggested but not ruled.
+
+Sketch, to be replaced by the target pass:
+
+1. **CultMath `interval`** in C# and HLSL with parity tests:
+   - arithmetic, `min`/`max`, `smin`, `sqrt`, `clamp` and `smoothstep`;
+   - interval or Lipschitz bounds for every CultMath noise primitive.
+
+   This step needs no tape. It stands alone, and is the first cut to take even
+   if the rest stays parked.
+2. **Tape**: an expression graph lowered to bytecode, with point, interval and
+   gradient evaluators in C#. Gradients reuse CultMath's analytic-gradient
+   primitives, which Asura cut 2a built.
+3. **Pruning**: per-region tape simplification driven by interval results.
+4. **HLSL interpreter** for the same bytecode, with interval ops and pruning.
+   Fidget's MPL-2.0 WGSL is the reference. MPL code keeps its own MPL-headed
+   files, as Phacelle does.
+5. **Meshing**: an octree of chunks, dual contouring for hard-surface creases,
+   and seams stitched between LOD levels. GameCult.Geometry's surface nets
+   comes from Asura Cut 2.
+
+## Truth and lowerings
+
+The field is data: a typed CultCache document holding the expanded tree. A
+generator, such as a brush grammar, expands into that document, and everything
+downstream caches it. The CPU evaluator, the HLSL interpreter, the mesher and
+collision are all lowerings of that one document. This is how "one
+implementation of the field" survives having both CPU and GPU evaluators.
+Asura's invariant 2 had to forbid CPU evaluation because its field is HLSL
+source.
+
+## Known consumers
+
+- **Aetheria volumetric raymarching** (clouds, nebulae). Step 1 alone gives it
+  empty-space skipping. Coverage and shape terms carry the culling, because
+  detail octaves only bound to ±amplitude.
+  - Prerequisite: Aetheria's shaders must use CultMath noise, not their own
+    copies. That is already owed at Aetheria's CultMath pin bump (see the Asura
+    cut map, snoise release follow-ups).
+- **Space stations from a brush grammar**, meshed in LOD chunks around the
+  camera. This is a separate project with its own target. This campaign
+  supplies its evaluator.
+- Asura does not need this campaign. Its field is noise-dominated, and its
+  `A_max` shell and band-limiting already give the cheap culling.
+
+## Open before unparking
+
+- Run the (a) spike first, or go straight to (c)?
+- Pick the interval representation (plain intervals or affine arithmetic) and
+  the noise bound strategy.
+- Choose the bytecode register model for the HLSL interpreter, given GPU
+  register pressure.
+- Decide whether the brush-grammar station project lives in Aetheria or in
+  its own repo.