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Exact finite layer: $\dim V=125$, $\dim\ker[(C-6I)(C-30I)]=47$, $P_{47}^2=P_{47}=P_{47}^\dagger$, and $KP_{47}=0$. A regenerated generic-basis witness gives projector, conjugation, and finite AQSFT product-kernel residuals at floating-point scale.
Cryptographic boundary: a public concrete spectral operator yields its selected projector and kernel in polynomial time; a fixed public E47/ISSR instance is not a hardness assumption. The finite proof therefore does not imply post-quantum secrecy.
Conditional hybrid route: ML-KEM/MLWE may establish a secret seed $\sigma$ that derives a unitary $U_\sigma$; E47 then acts only as a keyed transform/filter. Any confidentiality theorem is carried by the stated ML-KEM/KDF/AEAD reduction, with protocol and implementation obligations remaining open.
Canonical monograph: E47–AQSFT Spectral Cryptography — Multi-Silo Reconciliation Monograph.
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NEW MATHEMATICAL CITIZEN · E1 CONDITIONAL RECONSTRUCTION
This citizen records exactly what a diagonal Casimir reconstruction proves when the target spectrum and multiplicities are supplied as input.
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Let $D=\operatorname{diag}(\lambda_1,\ldots,\lambda_{125})$ carry the declared E47 Casimir multiset
$\{0^{(1)},2^{(9)},6^{(25)},12^{(28)},20^{(27)},30^{(22)},42^{(13)}\}$,
and define
$K_D=(D-6I)(D-30I)$.
Then the submitted reconstruction verifies
$\dim D=125,\qquad \operatorname{nullity}(K_D)=25+22=47,$
with orthogonal selector $P_{47}$ satisfying
$\operatorname{rank}P_{47}=47,\quad P_{47}^2=P_{47}=P_{47}^\dagger,\quad K_DP_{47}=0.$
The normalized rank is
$\Omega_c=\operatorname{Tr}(P_{47})/125=47/125=0.376.$
Corrected independent execution returns dim(V)=125, nullity(K)=47, rank(P47)=47, ||P47²−P47||F=0.0, ||KP47||F=0.0, and max singular value(K)=432.0.
Validator SHA-256: efadae8e094d59494934bdd2b8d53f66479af9c9669f19659fae324740205127.
Canonical Google Drive monograph · current GitHub generator 10667959 · controlled release da5501b · historical certificate-era finite-core dependency ad297e1