TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-admissible-source-closure-20261025/REWEIGHTING-REVIEW.txt
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Inclusive original lines: 126-154
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000126 | 3. Alpha-dependent measures
000127 | ----------------------------
000128 | 
000129 | If the measures vary with alpha, first transport each sector to a fixed
000130 | reference space and write
000131 | 
000132 |   d mu_(r,alpha)=w_r(alpha,x) d mu_(r,*),       r=s,0.
000133 | 
000134 | Let
000135 | 
000136 |   sigma_r(alpha,x)=partial_alpha log w_r(alpha,x)       (13)
000137 | 
000138 | be the measure score. Under the usual differentiation and integrability
000139 | hypotheses,
000140 | 
000141 |   partial_alpha log R
000142 |     =-<partial_alpha S_s^0>_s+<sigma_s>_s
000143 |      +<partial_alpha S_0^0>_0-<sigma_0>_0.              (14)
000144 | 
000145 | Equation (14), rather than (12), is the complete Ward test. Moving domains,
000146 | gauge-fixing Jacobians and determinant normalizations must be included in the
000147 | scores after pullback. The archived exponential remains exact if the right
000148 | side of (14) vanishes. Measure compatibility alone means the ratio is
000149 | well-defined; cancellation still has to be stated or proved.
000150 | 
000151 | 4. Smallest decisive countercheck of the omitted condition
000152 | -----------------------------------------------------------
000153 | 
000154 | Take one configuration in each sector, with unit counting measure, and set