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