TFPT scientific source excerpt Original repository path: experiments/theory-contracts/recursive-mirrored-source-20261103/ADMISSIBILITY-AND-MEASURE-REVIEW.txt Original file SHA-256: de2ccd65bc3070d969182a62e274e219595cdcb77db7c7d3a282699f45c2171e Inclusive original lines: 66-180 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. 000066 | 000067 | 2. Original radial field, with all coefficients and angular directions 000068 | --------------------------------------------------------------------- 000069 | The original full96 constructor is 000070 | D_F=full_D(Yu,Yd,Ye,Ynu,MR)=D_Y+D_M, 000071 | D_Y=full_D(Yu,Yd,Ye,Ynu,0), 000072 | D_M=full_D(0,0,0,0,MR). 000073 | For the actual common Higgs field H in C2, r=|H|, its exact source identity 000074 | is Phi(H)=V(q(H)/r)[r D_Y+D_M]V(q(H)/r)* for r>0. 000075 | The full quaternion acts on every left weak doublet and conjugately on 000076 | antiparticles; Majorana right-singlet entries are unchanged. Thus the 000077 | source contains a whole noncompact coefficient space, not just a radial 000078 | ray chosen as a substitute for the original field. 000079 | 000080 | [OMITTED: non-scientific conversation or execution metadata] 000081 | [OMITTED: non-scientific conversation or execution metadata] 000082 | [OMITTED: non-scientific conversation or execution metadata] 000083 | [OMITTED: non-scientific conversation or execution metadata] 000084 | [OMITTED: non-scientific conversation or execution metadata] 000085 | [OMITTED: non-scientific conversation or execution metadata] 000086 | [OMITTED: non-scientific conversation or execution metadata] 000087 | [OMITTED: non-scientific conversation or execution metadata] 000088 | [OMITTED: non-scientific conversation or execution metadata] 000089 | 000090 | [OMITTED: non-scientific conversation or execution metadata] 000091 | [OMITTED: non-scientific conversation or execution metadata] 000092 | [OMITTED: non-scientific conversation or execution metadata] 000093 | [OMITTED: non-scientific conversation or execution metadata] 000094 | [OMITTED: non-scientific conversation or execution metadata] 000095 | [OMITTED: non-scientific conversation or execution metadata] 000096 | [OMITTED: non-scientific conversation or execution metadata] 000097 | [OMITTED: non-scientific conversation or execution metadata] 000098 | [OMITTED: non-scientific conversation or execution metadata] 000099 | 000100 | Finite coefficient theorem. Suppose the actual supplied four Yukawas 000101 | are invertible, and put y_min=min_f s_min(Y_f)>0. The actual original 000102 | full96 D_Y has s_min(D_Y)=y_min. For any bounded other coefficient A(b), 000103 | ||A(b)||<=M, and any original Higgs angular direction n, 000104 | s_min(r D_Y(n)+A(b))>=r y_min-M. (2) 000105 | Here D_Y(n) is the actual unitary quaternion orbit, not a new matrix. 000106 | Equation(2) is the triangle inequality applied to every unit vector. 000107 | Thus the high gap is identity in this coefficient chart for every 000108 | r>(M+epsilon_adm/2)/y_min, uniformly over the entire allowed angular 000109 | family and bounded nonradial backgrounds. Singular supplied Yukawas 000110 | are not silently perturbed to make this theorem apply. 000111 | 000112 | Stronger original smooth-circle theorem, with all modes and couplings. 000113 | Use exactly FINITE-COUPLED.txt:10-48: 000114 | A=-i partial_theta+a(theta), 000115 | Phi_r(theta)=r L(H0(theta))+D_M, 000116 | h_r=A gamma_F-i gamma_F Phi_r, 000117 | h_r^2=A^2+Phi_r^2-i[A,Phi_r]. 000118 | Take any actual C1-bounded field tube of H0 and a for which 000119 | inf_theta |H0(theta)|>=kappa>0. This can be an OPEN neighborhood of a 000120 | nonvanishing field in any actual finite smooth coefficient regulator; 000121 | nonconstant field directions and nonzero gauge connections are retained. 000122 | No constant-field, zero-connection or zero-measure slice is used. 000123 | The quaternion identity gives pointwise s_min L(H0)>=kappa y_min. 000124 | Let ||D_M||<=M on the actual fixed or bounded Majorana inputs. Then for 000125 | r kappa y_min>=M, 000126 | Phi_r^2 >= (r kappa y_min-M)^2 I. 000127 | The whole commutator is a bounded multiplication operator, 000128 | [A,Phi_r]=-i r partial_theta L(H0) 000129 | +r[a,L(H0)]+[a,D_M]. 000130 | On that same tube there are finite constants C1,C0 with 000131 | ||[A,Phi_r]||<=r C1+C0. 000132 | Since A^2>=0, the ORIGINAL full operator satisfies, as a quadratic form, 000133 | h_r^2 >= [(r kappa y_min-M)^2-r C1-C0] I. (3) 000134 | The right side tends+infinity uniformly on the entire tube. This retains 000135 | ALL circle frequencies and the actual gauge/Higgs/Majorana coupling. 000136 | Therefore a high-gap selector applied to this actual h_r^2 becomes 000137 | identity beyond a finite radius. It cannot supply compact radial support 000138 | in this declared whole source class. 000139 | 000140 | Scope: (2)-(3) are exact original-branch operator estimates. Using them 000141 | for the primitive P_gap requires the actual D_adm-to-this-chart map, 000142 | with its original P_str and domain. No such universal identity is 000143 | asserted. Structural topological factors are not replaced by Fock parity, 000144 | nor is P_adm set to identity globally. Positive rescaling preserves the 000145 | original seam parity and determinant bundle class; the concrete action 000146 | of any additional whole selector must still be carried by its real map. 000147 | 000148 | [OMITTED: non-scientific conversation or execution metadata] 000149 | [OMITTED: non-scientific conversation or execution metadata] 000150 | [OMITTED: non-scientific conversation or execution metadata] 000151 | [OMITTED: non-scientific conversation or execution metadata] 000152 | [OMITTED: non-scientific conversation or execution metadata] 000153 | [OMITTED: non-scientific conversation or execution metadata] 000154 | [OMITTED: non-scientific conversation or execution metadata] 000155 | 000156 | [OMITTED: non-scientific conversation or execution metadata] 000157 | [OMITTED: non-scientific conversation or execution metadata] 000158 | [OMITTED: non-scientific conversation or execution metadata] 000159 | [OMITTED: non-scientific conversation or execution metadata] 000160 | [OMITTED: non-scientific conversation or execution metadata] 000161 | [OMITTED: non-scientific conversation or execution metadata] 000162 | [OMITTED: non-scientific conversation or execution metadata] 000163 | 000164 | [OMITTED: non-scientific conversation or execution metadata] 000165 | [OMITTED: non-scientific conversation or execution metadata] 000166 | [OMITTED: non-scientific conversation or execution metadata] 000167 | [OMITTED: non-scientific conversation or execution metadata] 000168 | [OMITTED: non-scientific conversation or execution metadata] 000169 | 000170 | [OMITTED: non-scientific conversation or execution metadata] 000171 | [OMITTED: non-scientific conversation or execution metadata] 000172 | [OMITTED: non-scientific conversation or execution metadata] 000173 | [OMITTED: non-scientific conversation or execution metadata] 000174 | [OMITTED: non-scientific conversation or execution metadata] 000175 | [OMITTED: non-scientific conversation or execution metadata] 000176 | 000177 | [OMITTED: non-scientific conversation or execution metadata] 000178 | [OMITTED: non-scientific conversation or execution metadata] 000179 | [OMITTED: non-scientific conversation or execution metadata] 000180 | [OMITTED: non-scientific conversation or execution metadata]