electron_Z_value
plain-language theorem explainer
The lemma fixes the Z-value for the electron at exactly 1332 under the Recognition Science mass ladder. Workers deriving forced fermion masses from T8 ledger quantization cite it as the base computational step for the electron rung. The proof is a direct term reduction that unfolds the sector, tilde-charge, and Z definitions then normalizes the arithmetic.
Claim. The Z-value assigned to the electron equals 1332, where for any lepton fermion with tilde charge $q = -6$ the Z-value is defined by $Z = q^2 + q^4$.
background
The module T9 Necessity proves that the electron mass formula is forced from T8 ledger quantization together with the geometric constants obtained earlier. The Z-value function ZOf maps each fermion to an integer that indexes its rung on the phi-ladder mass formula. For leptons the definition reduces to $Z = q^2 + q^4$ where $q$ is the tilde charge supplied by tildeQ; the electron is the lepton constructor with tildeQ equal to -6 and sector lepton.
proof idea
The term proof applies simp to unfold ZOf, tildeQ, and sectorOf, then invokes norm_num to evaluate the resulting integer expression 36 + 1296.
why it matters
This supplies the concrete Z = 1332 that enters the electron mass formula yardstick * phi^(rung - 8 + gap(Z)) inside the T9 necessity argument. It therefore closes the base case for the lightest charged lepton under the eight-tick octave and D = 3 framework. No downstream uses are recorded yet.
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