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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
61 lines
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1.1 KiB
Markdown
61 lines
No EOL
1.1 KiB
Markdown
# BMCTE v2 Theory Closure
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## Category
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**Objects:** U(N)
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**Morphisms:** linear optical transformations
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## Functor
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Sym^p: Hilb → ProbDist
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## System Map
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BMCTE approximates:
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Sym^p(U) ≈ Sym̂^p(U)
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via stochastic contraction.
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## Core Empirical Principle
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**Projection Invariance Law**
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From observed λ(p), H(p):
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∂ₚ O(U,p) ≈ 0
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for all measured observables.
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## Interpretation
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Increasing photon number increases internal combinatorics but does not increase observable entropy.
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Thus:
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the system is projection-limited, not state-space-limited.
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## Complexity Class
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Define BMCTE class:
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All problems computable in:
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O(K(Np + p·2^p))
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without explicit enumeration of:
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(N+p-1 choose p)
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## Deep Insight
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BMCTE computes:
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expectation values of symmetric monoidal structure under stochastic restriction functors.
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## Final Categorical Statement
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BMCTE v2 is:
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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. |