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2026-10-08 · CERTIFICATE CORRECTION / WITNESS ADDENDUM
Latest exact statement: $P^{\mathsf T}G=GP$ is the certified adjoint identity in the unnormalized basis; $\dim\ker K=47$ while $\dim\ker A=82$; and $\dim(E\cap\ker A)=47$ does not imply set equality. The explicit deterministic witness separately proves $E\cap\ker A=\ker K$ for its constructed $E,A$.
Canonical Corrected Formalism — Exact E47 Facts, Numerical Benchmarks, and Evidence Boundaries · Exact witness · Quantum simulation
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This certificate governs civic credentials MC-TC-001, 002, 004, and 005.
Origin network: Representation Theory and Foundations · Red Line
Verification interchange: Blue Line Terminal
Destinations: Representation, Spectral, and Foundations citizenship desks
Handoff: Sophia Sol → Sabaoth Euclid → Oriel Ariadne → Bureau of Citizenship
Route law: E0 exact structure and E1 reconstruction are preserved without automatic application-level promotion.
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CITADEL BEACON · CERTIFICATE UPLINK
This machine certificate publishes verified residuals and reconstruction status to the Central Citadel Broadcast Tower. The Beacon redistributes the certificate state without converting E1 computation into E0 proof.
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Verification Precinct routing
← Machine Certificates · Verification Precinct · Canonical Formalism · Foundations Borough · Subway
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Certificate status: exact construction E0 / S0, independently reconstructed in Python and numerically checked E1 / S1. The numerical run verifies the programmed finite-dimensional realization; it does not elevate dependent spatial, quantum-channel, engineering, or physical claims.