Drive derivation: Kartikeya Operator — First-Principles Derivation and Machine Validation is now bound as corroborating provenance for the existing finite-dimensional Kartekeya/E47 operator family.
Independent reconstruction from the stated recipe under Python 3.13.5, NumPy 2.3.5, complex128 reproduces the Casimir spectrum and multiplicities, μ=18, σ²=144, the positive Q=K² spectrum, rank(P47)=47, and the five-factor spectral closure. Rerun diagnostics: ||P−P_eig||F=1.71e−11, ||P²−P||F=1.71e−11, ||KP||F=7.38e−9, ||QP||F=3.19e−6 for the direct floating-point product implementation.
Evidence boundary: the Drive document states that an accompanying program, JSON certificate, and compressed NumPy archive exist, but none was located in accessible Drive search. The document also omits issuance package/library versions, datatype, declared norms/tolerances, recorded residual outputs, and an immutable result hash or commit. It therefore strengthens reconstruction provenance but does not close the E1 package audit or change the existing Correction-routed status.
The visual and documentary Kartekeya formalism is normalized to the current finite-dimensional E47 certificate spine.
$$ \mathcal H=V_2^{\otimes3},\qquad \dim\mathcal H=125 $$
$$ \mathcal H\cong V_0\oplus3V_1\oplus5V_2\oplus4V_3\oplus3V_4\oplus2V_5\oplus V_6 $$
$$ C=(J^{\mathrm{tot}})^2,\qquad K=(C-6I)(C-30I) $$
$$ E_{47}=\ker K=5V_2\oplus2V_5,\qquad \dim E_{47}=47,\qquad \Omega_c=\frac{47}{125}=0.376 $$
$$ P_{47}=P_6+P_{30} $$
$$ P_{47}(C)=\frac{C(C-2I)(C-12I)(C-20I)(C-31I)(C-42I)}{1814400} $$
$$ \Gamma_\varepsilon=I-\varepsilon K^2,\qquad 0<\varepsilon<\frac1{93312} $$
$$ \varepsilon_=\frac1{99144},\qquad q_\perp=\frac{15}{17},\qquad \Gamma_{\varepsilon_}^n x_0\to P_{47}x_0 $$
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Visual correction rule. Any plate using $I-\varepsilon K$ as a positive-step contraction is superseded by $I-\varepsilon K^2$. Any full-projector polynomial containing $C-30I$ is superseded because it annihilates the selected $30$ eigenspace. Hardware, vacuum, mass-gap, cosmology, biological, or fabrication claims require separate bridge certificates and do not inherit finite-dimensional E47 certification.
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Uniqueness normalization: $(C-6I)(C-30I)$ is the unique monic quadratic of minimal degree with roots exactly $6$ and $30$; arbitrary nonzero scalar multiples have the same kernel.
Canonical spectral data: $\sigma(C)=\{0,2,6,12,20,30,42\}$ and the nonzero $K^2$ spectrum is $\{11664,12544,19600,32400,186624\}$.
