TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/check_det16_source.py
Original file SHA-256: 0511dddb7d2c1f634014e2ba7e7227aa9ed20c8aafeccb05b6bec15d9727a0a0
Inclusive original lines: 60-138
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000060 |     for selection in itertools.product((0,1),repeat=len(spans)):
000061 |         term=I; weight=1.0
000062 |         for idx,(span,selected) in enumerate(zip(spans,selection)):
000063 |             aa=math.exp(-2*span)
000064 |             weight*=(-math.expm1(-2*span)) if selected else aa
000065 |             if selected: term=term@P
000066 |             if idx<len(ops): term=term@ops[idx]
000067 |         result+=weight*trace(term)
000068 |     return result
000069 | 
000070 | 
000071 | def zcomplex(value): return [float(value.real),float(value.imag)]
000072 | 
000073 | 
000074 | def apply_word(letters,state):
000075 |     """Apply left-to-right written CAR word to one bit state, right first."""
000076 |     amplitude=1
000077 |     for mode,dagger in reversed(letters):
000078 |         occupied=(state>>mode)&1
000079 |         if occupied==int(dagger): return None,0
000080 |         if (state & ((1<<mode)-1)).bit_count()&1: amplitude=-amplitude
000081 |         state ^= 1<<mode
000082 |     return state,amplitude
000083 | 
000084 | 
000085 | def word_fock_trace(letters):
000086 |     modes=sorted({mode for mode,_ in letters})
000087 |     # Each mode's initial bit is forced by the first right-to-left action.
000088 |     bits={}
000089 |     for mode,dagger in reversed(letters):
000090 |         if mode not in bits: bits[mode]=0 if dagger else 1
000091 |     state=sum(bit<<mode for mode,bit in bits.items())
000092 |     end,sign=apply_word(letters,state)
000093 |     return 0 if end != state else sign*(1<<(16-len(modes)))
000094 | 
000095 | 
000096 | def word_phi(letters):
000097 |     value=0j
000098 |     for state,ket in ((0,1),(D-1,np.exp(1j*phi))):
000099 |         end,sign=apply_word(letters,state)
000100 |         if end==0: value+=sign*ket/2
000101 |         elif end==D-1: value+=sign*ket*np.exp(-1j*phi)/2
000102 |     return value
000103 | 
000104 | 
000105 | def word_renewal(letters,spans):
000106 |     """Unnormalized trace via cyclic rank-one renewal, polynomial work."""
000107 |     k=len(letters)
000108 |     if any(not isinstance(letter,(tuple,list)) or len(letter)!=2
000109 |            or type(letter[0]) is not int or not 0<=letter[0]<16
000110 |            or type(letter[1]) is not bool for letter in letters):
000111 |         raise ValueError('letters require mode 0..15 as int and dagger as bool')
000112 |     if len(spans)!=k+1 or any(type(t) not in (int,float) or not math.isfinite(t) or t<0 for t in spans):
000113 |         raise ValueError('one finite nonnegative interval around each word boundary required')
000114 |     beta=sum(spans)
000115 |     if not math.isfinite(beta): raise ValueError('total interval must be finite')
000116 |     if not k: return D*math.exp(-2*beta)-math.expm1(-2*beta)
000117 |     delta=[spans[0]+spans[-1]]+spans[1:-1]
000118 |     doubled=letters+letters
000119 |     @lru_cache(maxsize=None)
000120 |     def edge(i,j):
000121 |         b=-math.expm1(-2*delta[i%k])
000122 |         a=math.exp(-2*sum(delta[r%k] for r in range(i+1,j)))
000123 |         return b*a*word_phi(doubled[i:j])
000124 |     result=math.exp(-2*beta)*word_fock_trace(letters)
000125 |     for anchor in range(k):
000126 |         dp={anchor:1+0j}
000127 |         for j in range(anchor+1,k):
000128 |             dp[j]=sum(dp[h]*edge(h,j) for h in range(anchor,j))
000129 |         result+=sum(dp[h]*edge(h,anchor+k) for h in range(anchor,k))
000130 |     return result
000131 | 
000132 | 
000133 | def main():
000134 |     initialize_native_controls()
000135 |     require(P.nnz==4 and close(trace(P),1),'native projector support or trace')
000136 |     require((P@P-P).nnz==0 or max(abs((P@P-P).data))<1e-14,'projector identity')
000137 |     require(close(P[D-1,0],np.exp(1j*phi)/2),'native projector phase')
000138 |     require(close(omegad[D-1,0],1),'native determinant creation sign')