step_sum
plain-language theorem explainer
The definition aggregates the four generation step values 13, 11, 6, and 8 into one natural number. Mass modelers working on sector-dependent torsion cite this sum when checking consistency with the N3 = 55 partition constraint. It is introduced as a direct arithmetic expression to support the equality theorem that follows.
Claim. The sum of the four sector step values is defined as $13 + 11 + 6 + 8$.
background
The SDGT Forcing module establishes that sector-dependent generation torsion is forced by three constraints: the partition of N3 = 55 into overlapping consecutive-pair spans, lepton uniqueness requiring only the pair summing to 17 in the middle position, and charge asymmetry forcing unequal end spans. The four step values {13, 11, 6, 8} are the Q3 cell counts for up quarks {13, 11}, leptons {11, 6}, and down quarks {6, 8}. This definition supplies their plain sum for use in the partition calculation, where the overlapping version expands to a + 2b + 2c + d.
proof idea
This declaration is a direct definition that computes the arithmetic sum of the four step values 13, 11, 6, and 8. No lemmas or tactics are applied.
why it matters
This definition feeds the theorem step_sum_eq that confirms the sum equals 38, closing the partition constraint inside the SDGT Forcing theorem. It helps establish the unique assignment of steps to up quarks, leptons, and down quarks under charge asymmetry. The module doc notes that why these specific counts appear as generation steps remains open.
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