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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
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BMCTE v2 Theory Closure
Category
Objects: U(N)
Morphisms: linear optical transformations
Functor
Sym^p: Hilb → ProbDist
System Map
BMCTE approximates:
Sym^p(U) ≈ Sym̂^p(U)
via stochastic contraction.
Core Empirical Principle
Projection Invariance Law
From observed λ(p), H(p):
∂ₚ O(U,p) ≈ 0
for all measured observables.
Interpretation
Increasing photon number increases internal combinatorics but does not increase observable entropy.
Thus:
the system is projection-limited, not state-space-limited.
Complexity Class
Define BMCTE class:
All problems computable in:
O(K(Np + p·2^p))
without explicit enumeration of:
(N+p-1 choose p)
Deep Insight
BMCTE computes:
expectation values of symmetric monoidal structure under stochastic restriction functors.
Final Categorical Statement
BMCTE v2 is:
a stochastic natural transformation of the symmetric power functor over U(N), evaluated via Monte Carlo contraction of induced submatrices, operating in a regime-stable observable manifold where entropy is invariant under photon scaling.