TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/QUARTER-TOWER-HIGGS-INVERSE-PROOF.txt
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000117 | 4b. Connection to the existing full invariant Higgs marginal
000118 | R057 already proves, under its EXPLICIT constant-H weak-invariant positive
000119 | marginal premise, H=sqrt(u)xi with Haar xi onS3 independent ofu.
000120 | This is NOT a new Haar measure choice and is NOT inferred from the tower.
000121 | R057 covariance/field-identification assumptions are retained when invoked;
000122 | the moment-free radial theorem above does not depend on those assumptions.
000123 | Adding precisely that existing premise, the uniquely recovered radial mu
000124 | therefore determines the ENTIRE constant-H marginal. Given the original
000125 | conditional whole fermionic word functional W_A(H), including its actual
000126 | Majorana/Pfaffian/charge/grading conventions, every finite original word is
000127 |  omega(A)=int dmu(u) int_(S3) W_A(sqrt(u)xi) dHaar(xi). (12b)
000128 | Thus one given nonzero original quark Yukawa channel's whole tower fixes
000129 | all these conditional matter responses in this same class. It does not
000130 | supply other boson/geometry joint conditionals, field-local H(x) or an E8
000131 | physical carrier map. Angle-dependent conditional words are NOT fixed if
000132 | R057's invariance premise is omitted. No new96 independent physical CAR
000133 | fields or alternative Majorana prescription is introduced by this corollary.
000134 | This is why two-point information across the WHOLE constrained family can
000135 | identify a NONquasifree mixture, while Wick of averaged two-point entries
000136 | still gives incorrect higher words. Fixed-triplet and whole-tower inputs
000137 | are different information, so R062's finite ambiguity is preserved.
000138 | The unchanged original charged-lepton Yukawa channel is used as a direct
000139 | cross-channel diagnostic after reconstructing one shared radial law.
000140 | 
000141 | 5. Finite automatic reader, not an arbitrary physical completion
000142 | A real multipoint Schur recursion provides target intervals from finite
000143 | tower values. Start S0(z)=(F(z)-1)/(F(z)+1). At a sample p_k let
000144 |  c_k=S_k(p_k), b_k(z)=(z-p_k)/(z+p_k), and
000145 |  S_(k+1)(z)=(S_k(z)-c_k)/[(1-c_k S_k(z))b_k(z)].       (13)
000146 | Schwarz-Pick ensures |S_(k+1)|<=1 for consistent analytic source data.
000147 | For real targetq use terminal S_N(q) in[-1,1], then recurse backwards
000148 |  S_k(q)=(c_k+b_k(q)S_(k+1)(q))/(1+c_k b_k(q)S_(k+1)(q)). (14)
000149 | Endpoints, with ordering after each real Mobius map, give a certified
000150 | analytic-class interval. Intersect the resulting F interval with
000151 | 0<=F(q)<=tanh(ell q) for the original mixture. Zero pivots and |c_k|=1
000152 | are handled by the terminating constant-Schur case; the diagnostic code
000153 | uses only strict interior data. Numerical reconstruction needs sufficient
000154 | precision; an uncertified floating interval is not a rigorous enclosure.
000155 | This reader takes ACTUAL source answers as input. It does not generate them.
000156 | A positive-real finite Pick matrix is a necessary consistency test:
000157 |  K_ij=(F(p_i)+F(p_j))/(p_i+p_j)>=0 as a MATRIX.       (15)
000158 | From(3) it is a Gram sum with two features p/(p²+a),sqrt(a)/(p²+a).
000159 | This test ALONE is not sufficient for the special Higgs mixture class.
000160 | The recovered Stieltjes measure must also admit(10) with nonnegative nu
000161 | of total mass1 and original support; these are real additional conditions.
000162 | 
000163 | 6. First original-source assignment test
000164 | For any p>0, t_p(u) is strictly decreasing in finiteu wheny>0.
000165 | Thus bar_t(p)=t_p(0) under a positive common law forces mu=delta0.
000166 | In particular the original zero-H elliptic right tower cannot AT THE SAME
000167 | TIME be the integrated source of a nontrivial positive H mixture in this
000168 | unchanged marked-field/ell/Y dictionary. This is a precise obstruction to
000169 | that SAME-source assignment, not a TFPT no-go or an imposed master equation.
000170 | The primitive free seam source before H integration remains allowed.
000171 | The actually given free covariance is replayed at2/4/8 quarter samples
000172 | under this EXPLICIT marked-field identity candidate; that identity is not
000173 | a derived physical carrier map. Nontrivial original carrier/field/source
000174 | transport can change the relevant
000175 | integrated observable; it must be derived, not silently set to the identity.