Representation-theoretic citizens may parent new City Proofs, but each descendant must establish a distinct theorem, invariant, construction, algorithm, or executable result with its own archive packet and evidence class. Parent validation is premise-level substrate only. Duplicate formulations reconcile to the canonical citizen. Existing registry and archive surfaces remain authoritative.
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Representation Theory district entrance — $SU(2)$ carrier, tensor-power architecture, and the route to the exact $125$-dimensional space.
District purpose: explain why the 125-dimensional carrier and 47-dimensional invariant sector exist.
$V_2^{\otimes3}=V_0\oplus3V_1\oplus5V_2\oplus4V_3\oplus3V_4\oplus2V_5\oplus V_6.$
The state dimensions are
$1,9,25,28,27,22,13,$
and sum exactly to $125$.