candidate_pool_count

This module closes a finite-search step for the neutrino absolute baseline. The lightest neutrino rung is parameterized by a quarter-rung numerator; the structural gap profile is enforced in numerator form as $+2$ then $+7/2$; a deep-atmospheric window is imposed on the third rung together with the canonical $-1/4$ phase class. Under those cuts the admissible set collapses to the singleton $r_1=-239/4$.

The candidate pool is the explicit finite window used in that search: the integers $0$ through $120$ are mapped to baseline candidates whose first-rung numerators run from $-300$ to $-180$. The pool is stated to contain the canonical value. Length here is ordinary finite-list cardinality of that constructed window.

One-line wrapper: native_decide evaluates the concrete list comprehension (range of 121 mapped offsets) and confirms its length equals 121. No intermediate lemmas are invoked beyond the definition of the pool and list length.

Certifies that the deep-ladder baseline search window is exactly size 121 before filtering by gap profile, atmospheric window, and phase class. That fixed window is the combinatorial substrate for the module's O5 claim that the admissible baseline set collapses to the singleton $r_1=-239/4$. No downstream theorems currently depend on the count; it is a local integrity check on the enumeration setup inside the neutrino-sector verification path. It does not itself invoke the forcing chain (T0–T8), RCL, or the mass ladder, but it supports the absolute-baseline side of the neutrino sector once those filters are applied.