Quantum and numeric runs: QuTiP eigen-decomposition, channel packages, Lindblad shunting, 7-qubit embedding, TDA swarms.
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Deterministic QuTiP eigen-decomposition of C and K on the 125-dimensional Hilbert space. All seven checks pass: dim, ker, Ωc, gap, tensor product, kernel idempotence, Casimir clustering.
Finite-dimensional channel identities: projector-filter complete positivity, QPE circuit, operator certificate. NumPy/SciPy validator; QuTiP runtime is a separate pinned environment.
7+7 qubit embedding |Ψ₄₇⟩ = 47⁻¹ᐟ² Σ |j⟩_S|j⟩_A yields ρ_S = P₄₇/47, rank 47, purity 1/47, S = ln 47 to machine precision.
Open-system coarse-grained 47⊕78 model. Complement-to-kernel shunting identity with a QuTiP destination simulation on the Purple Line.
Commutator residual 3.32e-15, unitarity 6.59e-15, occupancy drift 2.22e-16. Evolution stays inside E₄₇.
Trajectory and spectra-bridge certificates for the topological data swarm lab.
e47_kkp_full_validation.py + report JSON. End-to-end numeric closure of the paradigm checks.