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What is this? A multi-layer visualization of the chess-spectral encoding of the position. Pick a channel; toggle layers independently to dissect the field; combine with bot strategies to experiment with play.
1. Hover overlay (Channel dropdown)
When you click a piece, each legal destination is tinted by the post-move signature on the chosen channel. Bright = more positional shake-up.
- A1 default
- Orbit projection — overall complexity.
- STD4_X / Y / Z / W
- Coordinate-residuals along each axis. Signed; pairs naturally with the Signed-mode color ramp below.
- FIB_SYM_1 / 2 / 3, FA_PAWN_W / Y, FD_DIAG
- Slower nonlinear channels; full re-encode per destination.
2. Board-signature display modes (Board signature dropdown + checkboxes)
The same channel renders into multiple visual layers — toggle any combination:
- Volumetric cloud (default when channel ≠ off)
- Translucent BoxGeometry per cell, scale + color modulated by intensity.
- Tint board cells by channel M11.3.6
- Paints the chess-board surface itself with the channel's color. Replaces the white/black checker pattern visually. Pieces stay readable on top.
- Smooth isosurface shells M11.3.1
- Marching-cubes nested shells at 50/75/90th-percentile thresholds — translucent rainbow contour-plot look.
- Dot plot (sphere per cell) M11.9
- Discrete sphere markers instead of overlapping cloud. Good when you want to see EVERY cell without blending.
- Mark local maxima
- Small white spheres at each strict local max (face-neighbor test in 4D). The peaks of the field.
3. Statistics options
- Log scale (log1p)
- Compress heavy-tailed channels via
sign(x)·log1p(|x|).
- Signed (diverging) color mode
- Blue → white → red ramp; height tracks
|value|. Best for STD4_X/Y/Z/W.
4. Filter tools — narrow what you look at
- Slice axis + value M11.3.8
- Pin one lattice axis to a value. Slider supports fractional values (0.5 step) — adjacent slabs blend at weight (1 − dist) for smooth scrubbing.
- Threshold
- Hide cells below a normalized intensity. Sweeps "percentile shells".
- Clip sphere M11.3.2
- Hide cells outside a 4D ball around the lattice center, the brightest peak, or a console-set pin. Soft 10% falloff. Stacks AND with slice + threshold.
5. Streamline filaments
Field lines through the active board-signature channel. Default seeding stride-tiles the lattice; topology mode replaces it with Morse–Smale extraction.
- Topology mode (Morse–Smale) M11.2
- Lines emanate from each critical point along Hessian eigenvectors, integrated in
sign(λ)·∇φ. Red = ascending (toward peaks). Blue = descending (toward pits). The visible lines ARE the topological 1-skeleton.
6. Phase-operator commutator M12
Click a piece, tick "Commutator [P_A, P_B]", choose two piece types. Yellow tetrahedrons appear on cells in (A∘B)(o) Δ (B∘A)(o) — where the order of piece-move composition matters. Discrete analog of gauge-theory's Fμν = [Dμ, Dν]. Same piece both sides → empty (idempotent).
7. Camera + layout
- ⤺ Align view to flow M11.3.3
- Tween the camera along the dominant Hessian eigenvector at the most prominent critical point.
- Hide chess boards / Stack height slider
- Boards-off + compressed-stack gives a clean "spectral cloud" view. Both reach the cloud / filaments / pieces independently.
- Arc layout M11.0.1
- URL flag
?layout=arc: line of W-columns gently bends in 120° instead of stretching linearly. Boards stay parallel; only their centers follow the arc.
8. Bot strategies (Bot Strategy card on left panel) M13.1, M13.2
Each side picks a decision matrix independently. Try ``smart`` vs ``random`` to see how much edge alpha-beta search has; ``aggressive`` vs ``defensive`` for stylistic contrast. Live-switchable mid-game. URL flags ?botWhite=NAME&botBlack=NAME.
9. Game I/O M11.6, M11.6.1
Export game (JSON) writes chess-spectral's JSONL fixture format + a moves array. Load game (JSON) reads the same back — replays each move so the live state matches.
What it all describes: the Morse–Smale complex of one chosen scalar field on the 8⁴ lattice. The cloud / tinted boards / shells / dots are the field; the white spheres are its peaks; the red/blue filaments are the curves connecting peaks, pits, and saddles. The yellow tetrahedrons are where two piece operators DON'T commute. Filtering and clipping let you isolate slabs, percentile shells, or 4D balls. Together they give a verbal-only description even with aphantasia: "at every red endpoint a peak; at every blue endpoint a pit; where colors cross, a saddle; yellow markers show where piece-pair order matters; the cloud is everywhere; the slicers/clipper hide everything except the slab/shell/ball I'm looking at."
4D CHESS