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fix(research): remove Direction F (OISC CMYK) — references abandoned infrastructure

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Direction F referenced FPGA/NIICore/FAMM/CMYK/Tang Nano 9K hardware
that is no longer part of SilverSight. Removed entirely.

Directions A-E remain as the active research directions for the
Sidon-Sofa Coloring problem.
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docs/research/SIDON_SOFA_COLORING.md
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@ -665,46 +665,6 @@ and the chromatic number of Γ_γ (combinatorics).
Question: Does a longer braid word → higher chromatic number?
Is there a braid invariant that bounds χ from below?
### Direction F: Hardware Coloring Filter (OISC CMYK)
The SilverSight infrastructure includes a **Blitter6502OISC** — a SUBLEQ
one-instruction CPU on Tang Nano 9K FPGA with Q16_16 fixed-point LUT
arithmetic, connected via **Tailscale mesh** to Provider-Nixos (EPYC
bare metal). A 4-gate CMYK filter designed on this substrate maps
directly onto the conflict graph chromatic number computation.
**The mapping:**
| CMYK Gate | SUBLEQ operation | What it computes |
|-----------|-----------------|------------------|
| C (Cyan) | SUBLEQ on x-coords | ‖γ(t_a)pᵢ − γ(t_b)pⱼ‖_x in Q16_16 |
| M (Magenta) | SUBLEQ on y-coords | ‖γ(t_a)pᵢ − γ(t_b)pⱼ‖_y in Q16_16 |
| Y (Yellow) | SUBLEQ on distance² | d² = dx² + dy² − 1 (conflict iff ≤ 0) |
| K (Key) | SUBLEQ on color ID | assigns color class (1..χ) to t_a |
Each gate is one SUBLEQ subtract-and-branch: subtract, branch if result
≤ 0. This is exactly one unit-distance check in Q16_16 fixed-point:
Y-gate: SUBLEQ(Q16_16_MUL(dx,dx) + Q16_16_MUL(dy,dy), Q16_16_ONE)
→ branch if ≤ 0 means d² ≤ 1 → CONFLICT → assign different color
**4 gates = 4 colors.** A CMYK filter with χ = 4 tests the boundary
below de Grey's lower bound (5 ≤ χ(ℝ²)). If the 4-gate filter rejects
all colorings of Γ_γ^T, this gives a hardware proof that χ(Γ_γ^T) ≥ 5.
**Hardware parallelism.** The FPGA evaluates all n(n−1)/2 pairwise
distances simultaneously (one SUBLEQ per pair per time-step pair),
giving O(1) latency per conflict graph evaluation at fixed (n, m).
**Compute pipeline:**
- FPGA (Tang Nano 9K): conflict graph construction + greedy coloring
- Provider-Nixos (EPYC): shape optimization over A*(n, χ) landscape
- Tailscale mesh: distribute (n, χ) parameter sweep across nodes
Question: Can the 4-gate CMYK filter on SUBLEQ hardware prove
χ(Γ_γ^T) ≥ 5 for Gerver's sofa at n = 13, m = 100?
Infrastructure: Blitter6502OISC + Q16_16 LUT + Tailscale mesh
---
## 8. Why This Problem Is Structurally Rich