TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-collar-multifield-20261016/boundary_operation_response.py
Original file SHA-256: e0be5a934fee1fd72b830d620b4e7bd73781eb85bec035e876d07c86f9f627f3
Inclusive original lines: 1-89
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | """Two-face source response, not an assumed local quantum instrument.
000002 | 
000003 | All rational values are read from the already specified quarter-circle
000004 | product collar, alpha=1/4 and ell=4 log 2. Infinite-shift formulas are checked
000005 | coefficientwise, without truncating the shift to a finite/cyclic matrix.
000006 | """
000007 | import json
000008 | import sys
000009 | from pathlib import Path
000010 | import sympy as s
000011 | 
000012 | 
000013 | def ratio(n):
000014 |     return s.Rational(2)**(-(4*n+1))
000015 | 
000016 | 
000017 | def occupation_chart(n):
000018 |     return 1/(1+ratio(n)**2)
000019 | 
000020 | 
000021 | def graph(n):
000022 |     r=ratio(n)
000023 |     return s.Matrix([[1,r],[r,r*r]])/(1+r*r)
000024 | 
000025 | 
000026 | def exact_check():
000027 |     p=s.diag(1,0)
000028 |     rows=[]
000029 |     for n in range(-3,4):
000030 |         r=ratio(n); a=occupation_chart(n); g=graph(n)
000031 |         j=s.Matrix([1,r])/s.sqrt(1+r*r)
000032 |         null=s.Matrix([-r,1])/s.sqrt(1+r*r)
000033 |         assert g*g == g and g.T == g
000034 |         assert s.simplify(j*j.T-g) == s.zeros(2)
000035 |         assert g*null == s.zeros(2,1)
000036 |         leak=s.simplify((null.T*p*g*p*null)[0])
000037 |         assert leak == a*(1-a) and leak > 0
000038 |         m=graph(n+1)
000039 |         # diag(U,U) has identity 2x2 block from mode n to n+1.
000040 |         assert m != g  # it fails to commute with the fixed graph.
000041 |         block=s.simplify((s.Matrix([1,ratio(n+1)]).T /
000042 |                           s.sqrt(1+ratio(n+1)**2)*p*j)[0])
000043 |         assert s.simplify(block-s.sqrt(a*occupation_chart(n+1))) == 0
000044 |         forward=a*occupation_chart(n+1)
000045 |         backward=a*occupation_chart(n-1)
000046 |         comm=s.factor(forward-backward)
000047 |         assert comm > 0
000048 |         rows.append({'n':n,'a':str(a),'Lstar_L':str(forward),
000049 |                      'L_Lstar':str(backward),'commutator':str(comm),
000050 |                      'null_vector_face_mask_norm_squared':str(leak)})
000051 |     # Fixed-graph facewise unitary classification, linear intertwiner space:
000052 |     # the diagonal graph blocks force U0 to preserve each B eigenspace;
000053 |     # nonzero offdiagonal graph block then forces U1=U0. Check both simple
000054 |     # spectrum (complex dimension 3) and a double degeneracy (dimension 5).
000055 |     from sympy import linear_eq_to_matrix
000056 |     dimensions=[]
000057 |     for modes in [(-1,0,1),(0,0,1)]:
000058 |         aa=s.diag(*(occupation_chart(n) for n in modes))
000059 |         cc=s.diag(*(ratio(n)*occupation_chart(n) for n in modes))
000060 |         gg=aa.row_join(cc).col_join(cc.row_join(s.eye(3)-aa))
000061 |         variables=s.symbols('x:18')
000062 |         u0=s.Matrix(3,3,variables[:9]);u1=s.Matrix(3,3,variables[9:])
000063 |         ss=s.diag(u0,u1)
000064 |         coeff,_=linear_eq_to_matrix(list(ss*gg-gg*ss),variables)
000065 |         dim=18-coeff.rank();dimensions.append(dim)
000066 |         assert dim==(3 if len(set(modes))==3 else 5)
000067 |     a0=occupation_chart(0);a1=occupation_chart(1)
000068 |     w0=s.sqrt(a0*a1)
000069 |     # xi=(e0+e1)/sqrt2. This is a coherent boundary-vector comparison,
000070 |     # not a physically source-prepared quantum state claim.
000071 |     overlap=w0/2
000072 |     return {'verdict':'NONCOMMUTING_GEOMETRIC_RESPONSE_DERIVED_PHYSICAL_OPERATION_OPEN',
000073 |             'alpha':'1/4','ell':'4 log 2','mode_checks':rows,
000074 |             'coherent_overlap_I_L_on_two_mode_boundary_vector':str(overlap),
000075 |             'coherent_overlap_I_iL':str(s.I*overlap),
000076 |             'fixed_graph_intertwiner_dimensions_simple_degenerate':dimensions,
000077 |             'raw_face_mask_descends_to_G_quotient':False,
000078 |             'compressed_response_descends':True,
000079 |             'physical_local_instrument_derived':False,
000080 |             'physical_state_preparation_derived':False,
000081 |             'raw_P1_source_selected':False,
000082 |             'internal_carrier_or_coupling_assumed':False}
000083 | 
000084 | 
000085 | if __name__=='__main__':
000086 |     result=exact_check()
000087 |     target=Path(sys.argv[1]) if len(sys.argv)>1 else Path(__file__).with_name('boundary_operation_response_results.json')
000088 |     target.write_text(json.dumps(result,indent=2)+'\n')
000089 |     print(json.dumps(result,indent=2))