Five quinary citizens are now present in the canonical Citizenship Roll:
QMET-C01 · v_5(125)=3, |125|_5=1/125QMET-C02 · v_5(47)=0, |47|_5=1QMET-C03 · |S_5|=120=440_5, 125-120=5=10_5QMET-C04 · local bijection d=5b+qQMET-C05 · 125-state label multiplicities 12 or 13The formal bridge is restored. The current script’s missing label-to-P_{47} conversion, explicit S_5/Petersen representation, and 5-adic dynamical operator remain build and proof targets. Implementation incompleteness is not mathematical disproof, and exact cardinality identities do not themselves derive the E47 projector.
Canonical source: Theoretical Modular Mathematics And Pyramid Construction.
Revision C preserves the independent three-digit quinary carrier $\{0,1,2,3,4\}^3$ with 125 states and separates it from the four-tier Base-5 display register, which has cardinality $5^4=625$. The packing bijection $\pi(x,y,z)=25x+5y+z$ remains exhaustively verified over all 125 triples. Certificate TMP-PC-20260728-RC strengthens the executable lineage without altering the independent spectral reason for selecting 47.
The Quinary Metabolism formalism is restored to its proper constructive status.
The current script demonstrates two verified components:
The script does not yet encode the explicit operator that maps those labels to the E47 projector. This is an implementation omission only. It does not negate, reject, or under-credential the mathematical bridge.
The corrected conversion chain is
$$ \text{quinary carrier} \longrightarrow \text{bi-quinary labeling} \longrightarrow \text{explicit selector/operator to be encoded} \longrightarrow P_{47} \longrightarrow E_{47}. $$