Archive BOSONIC_MONTE_CARLO_PIPELINE_REVIEW.md

archive/2026-07-02/docs/reviews/BOSONIC_MONTE_CARLO_PIPELINE_REVIEW.md

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+# Bosonic Monte Carlo Pipeline — Actionable Review
+
+Source: `/home/allaun/Documents/chatgpt output6222026.md`
+
+## Pipeline Summary
+
+### Critical Boundary (Bosonic ↔ Classical Collapse)
+- **Physics boundary**: N/p² < ϵ → classical regime
+- **For N=2000**: p < √(2000/ϵ) ≈ 4-6 is still physically bosonic
+- **Current implementation**: Switches at p≥5 (algorithmic, not physical)
+
+### Variational Inference Formulation
+Current system implements:
+```
+Q*(p,N) = { Q_bos, p≤4; Q_fact, p≥5 }  // Hard mixture
+```
+This produces:
+- Entropy plateau (~10.8 bits)
+- Runtime collapse at p≥5
+- Loss of correlation structure
+
+### Proposed Fix
+Replace hard switch with continuous interpolation:
+```
+Q(p) = λ(p)Q_bos + (1-λ(p))Q_fact
+λ(p) ~ exp(-p²/N)
+```
+
+## Actionable Reviews
+
+| Issue | Current State | Action Required | Owner |
+|-------|--------------|-----------------|-------|
+| **Regime switching** | Hard threshold p≥5 | Remove if-bloc, unify estimator | Core |
+| **Entropy plateau** | Artificial from mixture collapse | Continuous λ(p) interpolation | Core |
+| **Runtime discontinuity** | O(p) vs O(p!) jump | Single Ryser-based estimator | Core |
+| **No variational continuity** | Discontinuous model change | λ(p) smooth transition | Core |
+| **GPU kernel** | Regime-split kernels | Unified 4-kernel pipeline | Infra |
+| **Category model** | Implicit Sym^p(U) contraction | Extract functor formalism | Formal |
+
+## Implementation Path
+
+### Kernel Pipeline (GPU/Cluster)
+1. **Mode sampler**: O(Np), categorical sampling
+2. **Gather**: M = U[S,:], memory coalescing
+3. **Ryser permanent**: 2^p threads, subset evaluation
+4. **Reduction**: Atomic histogram or segmented buffers
+
+### Complexity
+```
+T(N,p,S) = O(S ⋅ (Np + p²2^p))
+```
+- p ≤ 6: fully tractable (≤2304 samples)
+- No dependence on (p N+p-1)