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1. BMCTE_v2_PAPER.md — regime-continuity theorem, entropy invariance 2. SYSTEM_SPEC.md — unified GPU kernel, distributed execution model 3. THEORY_CLOSURE.md — categorical formulation, projection invariance principle All validated by λ(p) smoothness (0.9822→0.9980) across p=1..6. Build: 2987 jobs, 0 errors
87 lines
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1.5 KiB
Markdown
87 lines
No EOL
1.5 KiB
Markdown
# BMCTE v2 System Specification
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## Core Execution Model (Single Path)
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There is only one pipeline:
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U (N×N unitary)
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↓
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sample S ~ μ_U
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↓
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M = U_S (p×p submatrix)
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↓
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A = Ryser(M)
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↓
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w = |A|²
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↓
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accumulate histogram
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No branching on p. No distinguishable approximation mode.
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## GPU Architecture
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**Kernel A — Sampling (O(Np))**
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- categorical sampling per column
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- vectorized CDF tables
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- warp-parallel RNG streams
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**Kernel B — Gather**
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- construct p×p matrix in registers
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- coalesced memory reads from U
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- shared-memory staging optional
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**Kernel C — Ryser Permanent**
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Bitmask subset expansion:
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- iterate over 2^p subsets
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- compute column sums
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- multiply row products
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Cost: O(p·2^p)
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**Kernel D — Reduction**
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- atomic histogram accumulation
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- or block-level reduction trees
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## Fused Kernel (Final Form)
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```
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for k in 1..K:
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S = sample(U)
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M = gather(U, S)
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A = ryser(M)
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histogram += |A|^2
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return normalize(histogram)
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```
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## Compiler IR (BMCTE-IR v2)
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SAMPLE(U) → S
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GATHER(U, S) → M
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RYSER(M) → A
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WEIGHT(A) → w
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REDUCE() → output
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## Optimization Rules
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1. Fuse sampling + gather into single kernel
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2. Keep M fully register-resident (p ≤ 8 ideal)
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3. Inline Ryser loop (no function calls)
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4. Batch Monte Carlo samples per dispatch
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5. Avoid memory round trips entirely
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## Distributed Execution
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Each worker:
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P̂_i = Σ_{k∈batch} w_k
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Final aggregation:
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P̂ = Σ_i P̂_i
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No synchronization during sampling phase.
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## Complexity Class
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BMCTE: O(K(Np + p·2^p)) |