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design.md: the slice returns the final af_snoise arguments; the composition test

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Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
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Meta Vens 2026-10-04 07:37:35 +02:00
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packages/cultmath/docs/design.md
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@ -787,10 +787,16 @@ centre and variation are the caller's, and a consumer adds them to the slice's
phase takes its own centre; one ball serves when the phases' centres coincide
(warp 0). `NoiseBoundTests.CentredWarpStaysEnclosed` checks 2,000 balls, radius 1e-3 to
500, and fails when `rho` is dropped or halved; `AffineWarpStaysEnclosed` checks
3,000 tile slices of `FogField.Slice` (the owner the affine bound reads: the reach over
which the flow is varied is `|axis| + radius`, and each phase carries its own growth)
and fails when the reach is the ball's radius, a phase's growth is dropped, or `rho`
is halved.
3,000 tile slices of `FogField.Slice`, which returns the final `af_snoise` arguments
(each phase's moved centre and grown radius, the detail's unwarped set, the shared axis),
so the affine bound wires nothing itself: the reach over which the flow is varied is
`|axis| + radius`, each phase carries its own growth, and the gate reads each argument's
reach. It fails when the reach is the ball's radius or the larger of the two, a phase's
growth is dropped or taken from the other phase, the axis or the detail radius is scaled,
or `rho` is halved. `AffineCompositionTightensItsRanges` sees the shared-symbol
composition itself: the bound is exactly the intersection of the affine arithmetic's piece
and the interval composition over the forms' ranges, and the affine piece is the narrower
of the two in at least 35% of the open slices (the piece alone is wider in total).
The deep well is the representative Aetheria case: the camera inside a sun's
bowl, looking across. `DeepWellIsTenBandsDeepAndWide` computes the band `G` from