SHELL-PHASE LAW (Thm 4) — verified table
charge N | #phases | Q(sqrt5) class        | residue value(s)
   1     |   1     | principal (unit)      | 0.777073303
   4     |   1     | principal (square)    | (single)
   5     |   1     | ramified (5)          | (single)
   6     |   0     | inert -> UNREACHABLE   | no seed exists
   9     |   1     | principal (square)    | (single)
  11     |   2     | split (11 = ±1 mod5)  | 0.956482020 / 0.580699392
  16     |   1     | principal (square)    | (single)
  19     |   2     | split (19 = ±1 mod5)  | 0.363813464 / 0.309133276
  20     |   1     | principal (4*5)       | (single)
  25     |   1     | principal (square)    | (single)
  29     |   2     | split (29 = ±1 mod5)  | (two)
  30     |   0     | inert -> UNREACHABLE   | no seed exists
  31     |   2     | split (31 = ±1 mod5)  | 0.158767462 / 0.531503042
  44     |   2     | split (4*11)          | (two)
  55     |   2     | split (5*11)          | (two)
 125     |   1     | principal (5^3)       | (single)

RULE: #phases(N) = number of Z[phi]-orbits of norm N
      = product over primes p|N of: 1 if p=5, 2 if p=±1 mod5, 
        0 if p=±2 mod5 to odd power (N not a norm).
