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CONSOLIDATED VALIDATION DELTA · 2026-08-19
The current correction-aware authority is Revised E47 Multi-Branch Formalism — Consolidated Validation with Drive machine ledger.
Operator distinction: the product-cycle Laplacian $L_{C_5^3}$ retains its rank-one constant kernel. The newly audited twist Laplacian $L_{\mathrm{twist}}=\sum_g[I-\tfrac12(U_g+U_g^T)]$ is a different operator and has rank-10 kernel. Its generated action has 10 site orbits of sizes $8,24,12,24,24,6,8,12,6,1$, and $\ker L_{\mathrm{twist}}=\operatorname{Ran}P_{\mathrm{orbit}}$.
Correction propagation: the 14-qubit filter at $t=0.01$ is not a high-fidelity kernel projection; the seeded run crosses $1-F<10^{-14}$ at about $t=4.151$. The original Hodge example was not a chain complex because edge $(0,2)$ was absent; the repaired complex has $\partial_1\partial_2=0$ and $\beta_1=1$. The Newton-Mean $\kappa=0.376$ point remains locally stable, while the prior global interval classification is superseded by the supplied multiplier’s $0<\kappa<1$ range on the stated branch.
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TIGHTENING RECONCILIATION · 2026-08-14
Canonical Civic Kernel–Projector Drive authority: formal constitution and validation monograph, bound to this existing Python Validation surface under sync key CIVIC-KERNEL-PROJECTOR-NOTION-PY with hash 1b6219bb01d87494191e7f7208efd2e50386b0eb9d17062a8307fe1f8383448c.
Canonical E47 quantum-operation Python witness: e47_channel_validation_corrected.py, bound under E47-QOP-PYTHON-20260728 with hash adacbc0294afc94d5a839dd90daebcf461d97f776a9c29cc51980994d6ba6058. This is an executable witness and does not by itself promote any physical or hardware claim.
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Python validation is normalized to the exact Casimir construction rather than a synthetic rank-prescribed operator.
$$ K=(C-6I)(C-30I),\qquad K^2\ge0 $$
$$ \ker K=5V_2\oplus2V_5,\qquad \dim\ker K=47 $$
$$ P_{47}(C)=\frac{C(C-2I)(C-12I)(C-20I)(C-31I)(C-42I)}{1814400} $$
$$ \varepsilon_*=\frac1{99144},\qquad \rho_\perp=\frac{15}{17} $$
Required checks: decomposition sum 125; nullity 47; projector rank 47; $P^2=P$; $P^\dagger=P$; $KP=0$; corrected polynomial values $(0,0,1,0,0,1,0)$; nonzero $K^2$ spectrum $\{11664,12544,19600,32400,186624\}$; convergence of $(I-\varepsilon_*K^2)^n$ to $P_{47}$.
Rejected validator language: a script that inserts 47 zero eigenvalues and gap 0.00631 by construction is a synthetic control, not a reconstruction of the canonical E47 Casimir operator.
Drive monograph · Python · Certificate
Validated finite-dimensional theorem:
$$ \rho_*=\frac{Pe^{-\beta H}P}{\operatorname{Tr}(Pe^{-\beta H})},\qquad [P,H]=0. $$
The Python witness verifies projector, support, positivity, normalization, free-energy decomposition, uniqueness, 200 feasible random states, and a noncommuting negative control. Maximum free-energy identity residual: $2.22\times10^{-15}$. Certificate: PGT-E47-20260731 · PASS · E0+E1.
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Canonical finite-dimensional result: $V=V_2^{\otimes3}$, $\dim V=125$, $K=(C-6I)(C-30I)$, $\ker K=E_6\oplus E_{30}$, and $\dim\ker K=25+22=47$. The corrected projector is $P_{47}=P_6+P_{30}$.
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