generation_torsion_derived

In the Recognition mass formula, a species mass is a sector yardstick times a power of $\varphi$ whose exponent is built from a base rung and a species-dependent integer offset. Generation torsion $\tau$ supplies a global, representation-independent piece of that offset: it depends only on the generation index, not on the particular fermion representation.

At the anchor layer, $\tau$ is defined by cases on the generation index: $\tau(0)=0$, $\tau(1)=E_{\mathrm{passive}}=11$, and $\tau(g)=W=17$ for every $g\ge 2$. The integers 11 and 17 are the passive and active cube-geometry counts carried by the anchor system; the present module only needs their evaluated values.

This file sits in the quarantined mass-comparison layer: it imports PDG 2024 numbers and the $\varphi$-ladder anchor, so it is outside the certified surface. The local goal is a machine-checked side-by-side of RS mass predictions against experiment, not a derivation of the torsion integers from first principles.

One-line term proof: the statement is exactly the content of the upstream anchor lemma tau_values, which evaluates the three match-cases of the generation-torsion definition. No extra algebra or case split is performed here.

Without fixed generation torsion, the $\varphi$-ladder exponents for the three lepton (and quark) generations are not pinned, and the mass-comparison tables in this module cannot be stated. The values 0, 11, 17 are the concrete integers that enter $r_{\mathrm{species}}$ once the sector yardstick and base rung are chosen.

The doc-comment ties the integers to cube geometry (the same geometric source that forces the eight-tick octave and $D=3$ in the T0–T8 chain). Downstream mass checks against PDG 2024 read these equalities as the generation offsets; no further parent theorem is recorded in the graph, so the declaration functions as a named, citable evaluation point inside the verification layer rather than as a lemma inside a longer proof chain.