08 — CLUE/2.0 Recursive Bell Closure & LION Heterogeneous (NPU / GPU / CPU / APU) Invariant Miner
Ticket Lineage: Root(TKT-8001) -> ... -> TKT-10208 -> TKT-10209
Target Hardware Node: lion (AMD Ryzen AI 9 HX 370 w/ Radeon 890M + AMD XDNA 2 RyzenAI-npu4)
Executable Engine: /opt/mev-engine/clue_2_0_lion_miner/clue_2_0_lion_heterogeneous_miner.py (libclue2_avx512.so)
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1. Recursive Development: From CLUE/1.0 to CLUE/2.0
In CLUE/1.0, the Canonical First-Appearance Relabeler $\pi_{\text{first}}^{(1)}$ maps a length-4 window of 4-symbol market states ($4^4 = 256$ words) into one of $B_4 = 15$ Canonical Bell Orbits (0000 .. 0123).
In CLUE/2.0 (Recursive Hierarchical Quotient), we observe that the stream of Level-1 Bell orbit tokens $c_1^{(1)}, c_2^{(1)}, \dots, c_T^{(1)} \in \mathcal{B}_4$ is itself a discrete symbolic sequence over an alphabet of size $M_1 = 15$. Applying the first-appearance quotient map $C_*^{(r)}$ recursively across $r = 1, 2, 3$ time scales yields a profound algebraic closure property:
Theorem 5.1 (Recursive Bell Closure Theorem)
Let $\Sigma^{(r-1)}$ be an alphabet of size $M_{r-1} \ge 4$. Because any length-4 window $W^{(r-1)} = (x_0, x_1, x_2, x_3) \in (\Sigma^{(r-1)})^4$ can contain at most $4$ distinct elements ($d \in \{1, 2, 3, 4\}$), its equality partition under $\pi_{\text{first}}^{(r)}$ is canonically isomorphic to one of the exact same $B_4 = 15$ Bell orbits $\mathcal{B}_4 = \{b_0, \dots, b_{14}\}$ at every recursion level $r \ge 1$:
| Recursion Level $r$ | Time Horizon | Input Alphabet Size $M_{r-1}$ | Input Word Space $M_{r-1}^4$ | Output Canonical Quotient $\mathcal{B}_4$ | Single-Level Compression Ratio |
| :--- | :--- | :--- | :--- | :--- | :--- |
| **Level 1 ($C_*^{(1)}$ Micro-Orbit) | 4 bars | $M_0 = 4$ | $4^4 = 256$ words | $15$ Bell Orbits | 17.07x** |
| **Level 2 ($C_*^{(2)}$ Meso-Orbit) | 16 bars | $M_1 = 15$ | $15^4 = 50,625$ meta-words | $15$ Bell Meta-Orbits | 3,375.00x** |
| **Level 3 ($C_*^{(3)}$ Macro-Orbit) | 64 bars | $M_2 = 15$ | $15^4 = 50,625$ hyper-words | $15$ Bell Hyper-Orbits | 3,375.00x** |
| Joint 3-Level Hierarchy | 64-bar tree | Raw $4^{64}$ paths | $\approx 3.40 \times 10^{38}$ paths | $15^3 = 3,375$ Joint States | Hierarchical Closure |
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2. Theorem 5.2 (General-$M$ Multi-Scale Telescoping Identity)
For uniform strings of length $4$ over any alphabet of size $M \ge 4$, the cardinality of a canonical Bell orbit $b \in \mathcal{B}_4$ having $d(b) \in \{1, 2, 3, 4\}$ distinct symbols is the falling factorial:
$$\left|\mathcal{O}_M(b)\right| = (M)_{d(b)} = \frac{M!}{(M - d(b))!}$$
Summing across the $B_4 = 15$ orbits grouped by Stirling numbers of the second kind $\left\{\begin{matrix}4\\d\end{matrix}\right\} \in \{1, 7, 6, 1\}$ for $M = 15$:
$$1\times(15)_1 + 7\times(15)_2 + 6\times(15)_3 + 1\times(15)_4 = 15 + 1,470 + 16,380 + 32,760 = 50,625 = 15^4$$
And the Multi-Scale Shannon Entropy Telescoping Identity holds with 0.000000000000000 bits residual error at every recursion level:
$$\log_2\!\left(M^4\right) = H\!\left(C_*^{(r)}(W)\right) + \mathbb{E}\!\left[\log_2 (M)_{d(W)}\right]$$
$$8.0000000000\text{ bits} = 3.4594316186\text{ bits} + 4.5405683814\text{ bits} \quad (\text{Error} = 0.0)$$
$$15.6275618918\text{ bits} = 2.3694738050\text{ bits} + 13.2580880868\text{ bits} \quad (\text{Error} = 0.0)$$
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3. 4-Unit Heterogeneous Hardware Acceleration on LION
lion is equipped with an AMD Ryzen AI 9 HX 370 w/ Radeon 890M (Strix Halo) and an AMD XDNA 2 NPU (RyzenAI-npu4). The CLUE/2.0 miner coordinates all 4 hardware subsystems in a single pipeline:
| Compute Unit | Hardware Device on lion | Kernel / Driver Binding | Role in CLUE/2.0 Recursive Invariant Miner |
| :--- | :--- | :--- | :--- |
| 1. CPU (AVX-512 + OpenMP) | AMD Ryzen AI 9 HX 370 (12C / 24T, avx512f/bw/vl/vnni/bf16/vpopcntdq) | Native C++20 libclue2_avx512.so (g++ -O3 -march=native -fopenmp) | Exhaustive $50,625$-word Bell closure proof, 3-level recursive encoding, and 24-thread $N=2,000$ permutation null tests (Gate 3) |
| 2. APU (Unified Memory) | Strix Halo 121.5 GB LPDDR5x Unified Fabric | /dev/shm/clue2_apu_unified_tensor.bin (mmap Zero-Copy Ring) | Zero-copy shared physical memory pages between C++20 AVX-512 buffers and PyTorch / ONNXRuntime tensors (data_ptr parity verified) |
| 3. GPU (Radeon 890M) | AMD Radeon 890M (RDNA 3.5, 16 SIMDs, 2,900 MHz) | /dev/kfd + /dev/dri/renderD128 + PyTorch Vectorized Tensors | Batched 6,750-state histogramming, Walk-Forward Sharpe (Gate 1), and 2.0x Execution Friction stress grids (Gate 2) |
| 4. NPU (RyzenAI-npu4) | AMD XDNA 2 NPU (PCIe 16.0 GT/s x16, 0x17f0) + Local Ollama | /dev/accel/accel0 + onnxruntime + qwen2:1.5b / nemotron-3-nano-4b | Neural structural stability scoring ($\mathcal{S}_{\text{NPU}} \in [0, 1]$) + Rule 16 autonomous regime synthesis |
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