allR0Assignments

This module turns the O1 yardstick discussion into an explicit finite search. One starts from four candidate $B_{\mathrm{pow}}$ values and four candidate $r_0$ values, enumerates all sector-to-value assignments by permutation, and filters by the structural constraints used in the yardstick argument. Under those constraints the valid sets collapse to singletons for both $B_{\mathrm{pow}}$ and $r_0$.

An $R_0$-assignment is a four-tuple of integers (lepton, up, down, electroweak). Upstream, the canonical $r_0$ offsets are not free parameters: they are derived from wallpaper and cube geometry ($W=17$ wallpaper groups, passive edge count $E_{\mathrm{passive}}=11$, total cube edges $12$), giving the sector formulas lepton $4W-6$, up $2W+A$, down $E_{\mathrm{total}}-W$, electroweak $3W+4$.

The present definition is the unfiltered enumeration step for the $r_0$ side of that search: every permutation of the candidate pool, optionally packed into an assignment record.

Definitional, not a proof. Take the list of all permutations of the $r_0$ value pool, then filterMap through the optional packing function that turns a four-element integer list into an $R_0$-assignment (or fails). The result is exactly the raw choice set of size $4!=24$, later confirmed by native decision.

This list is the domain for the $r_0$ half of the O1 combinatorial collapse. Downstream, validR0Assignments filters it by the structural constraints; all_r0_assignments_count pins its length at 24; and r0_constraints_force_canonical shows that any member of the list satisfying the principle constraints equals the canonical assignment. Together these close the claim that the yardstick $r_0$ choice set is a singleton under the structural sum and role constraints, matching the geometric derivation of the sector offsets from wallpaper groups and the cube edge count.