TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-HEAT-PROOF.txt
Original file SHA-256: 5904d71d3b9cc978ef5025b86a43931db227d7ee9e87d894384f844b10f1d805
Inclusive original lines: 131-200
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.

000131 |  Y2=Tr3(3Yu*Yu+3Yd*Yd+Ye*Ye+Ynu*Ynu),
000132 |  Y4=Tr3(3(Yu*Yu)²+3(Yd*Yd)²+(Ye*Ye)²+(Ynu*Ynu)²),
000133 |  T=Tr3(Ynu*Ynu MR MR*)=||Ynu MR||_HS²>=0.             (4)
000134 | Here * is adjoint. No family matrices are assumed commuting. A,B>0 for
000135 | nonzero Y, C>=0 because C=||DY DM||_HS².
000136 | 
000137 | The whole original block proof, using the left rotation R028, gives
000138 |  Tr96(Phi²-DM²)=A u,
000139 |  Tr96(Phi⁴-DM⁴)=B u²+4C u,
000140 |  Tr96(dPhi dPhi)=A |dH|².                             (5)
000141 | In radial coordinates Phi=rDY+DM. Every word with an odd count of DY has
000142 | zero trace by the original chirality/slot paths. DM DY DM=0, so the six
000143 | quartic mixed words reduce cyclically to four DY² DM² words, giving4C.
000144 | Polarizing the exact quadratic identity for arbitrary four real H
000145 | coordinates gives Tr(L_a L_b)=A delta_ab, proving the derivative identity
000146 | also for nonconstant H with the supplied fixed Y and constant MR.
000147 | For gauge-covariant derivatives use the actual gauge intertwiner and
000148 | covariantly constant invariant MR. Varying MR would add its own terms.
000149 | 
000150 | The first extra spacetime realization is explicitly the STANDARD product
000151 |  D=-i gamma^mu nabla_mu tensorI96+gamma5 tensorPhi(H),
000152 | with spin4, Euclidean Clifford algebra and a fixed local spin connection.
000153 | It is used as a conditional consumer of the given original finite map,
000154 | not claimed to be a derivation of the primitive-to-geometric spacetime map.
000155 | In a flat chart D²=-partial²+Phi²-i gamma^mu gamma5 partial_muPhi.
000156 | The same curvature convention yields
000157 |  E=-R/4-Phi²+i gamma^mu gamma5 nabla_muPhi.
000158 | The derivative term has spin trace zero, and its square has spin trace
000159 | 4 delta_mu,nu times the internal derivative product, hence POSITIVE kinetic.
000160 | Keeping the H-dependent bulk terms and integrating total derivatives for
000161 | interior changes gives
000162 |  a2_H=-A u/(4pi²),
000163 |  a4_H=A |DH|²/(8pi²)+B u²/(8pi²)+C u/(2pi²)
000164 |                          +A R u/(48pi²).             (6)
000165 | Spin4 has been traced separately from internal96. These spectral traces
000166 | do not introduce96 independent physical Grassmann fermions. An actual
000167 | uniform trace weight w multiplies A,B,C together. A source with a distinct
000168 | projection/trace must be evaluated in its own contract, not fitted here.
000169 | 
000170 | For the SAME two-residue combination c chi²a2+d a4, d>0, A>0,
000171 |  Z=d A/(8pi²), Hcan=sqrt(Z)H,
000172 |  mu_can²=2(c/d)chi²-4C/A-R/6,
000173 |  lambda_can=8pi² B/(d A²).                            (7)
000174 | These are the coefficients of V=-mu_can²|Hcan|²+lambda_can|Hcan|⁴,
000175 | NOT a calculated physical pole mass or full connected H covariance.
000176 | At R=0 the negative quadratic condition is c chi² A>2d C. Positive c is
000177 | necessary, not sufficient. For printed c=-6,d=1 the local coefficient is
000178 | positive for every nonzero given Y and every symmetric MR, since C>=0.
000179 | Keeping only a sign change to c=+6 is a candidate convention comparison,
000180 | not an original selection, and it leaves the independent factor6 problem
000181 | of section2 untouched. Its R sign and common Wick map must also agree.
000182 | 
000183 | 5. Big picture and next actual origin arrow
000184 | Equation(6) connects the given Yukawas to kinetic normalization, quartic
000185 | strength and the positive neutrino/Majorana mass correction. They are
000186 | moments of ONE operator, not independently tunable Higgs coefficients.
000187 | One field normalization cannot turn TrPhi⁴ into (TrPhi²)² or remove T/Y2.
000188 | Do not reinterpret the printed scalar (Phi*Phi)² as a96er matrix trace.
000189 | The full96 finite source and scalar geometric Erel need an actual map.
000190 | 
000191 | R030 rejects the literal SAME local heat producer for the printed linear
000192 | mass and curvature coefficients, with the explicit scope in sections1-3.
000193 | R031 evaluates the whole finite original class through a conditional4D
000194 | consumer with no new Y fitting. Neither closes F1 or the common original
000195 | field/state/time/reflection/RP/measure problem. The next step is the actual
000196 | primitive H insertion into Dgeo+Brel, its admissible compression and bound
000197 | reference, and the resulting principal symbol/endomorphism and scale map.
000198 | It must explain the ratio or identify the different original coefficient,
000199 | before using that weight for the full dynamical H/source integration.
000200 | No extra free counterterm, Gamma_H, or independent Higgs model is allowed.