From 118e85fd3a9bb809fbb3413a978a2a81dbab1edf Mon Sep 17 00:00:00 2001 From: Meta Vens Date: Sun, 4 Oct 2026 07:37:35 +0200 Subject: [PATCH] design.md: the slice returns the final af_snoise arguments; the composition test Co-Authored-By: Claude Sonnet 5.5 --- packages/cultmath/docs/design.md | 14 ++++++++++---- 1 file changed, 10 insertions(+), 4 deletions(-) diff --git a/packages/cultmath/docs/design.md b/packages/cultmath/docs/design.md index fa9f0542..e2e7df14 100644 --- a/packages/cultmath/docs/design.md +++ b/packages/cultmath/docs/design.md @@ -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