TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/ORIGINAL-ORDERED-CURRENT-KERNEL-AND-SEAM-GRADING.txt
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Inclusive original lines: 162-207
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000162 | 5. Original charged seam acts on the full density/geometric field products
000163 | 
000164 | Use the already derived internal charged character v=(0^5,1/2^3).
000165 | The SAME original M gives t=M^T v=(1/2,1/4,0,-1/4)^2. Its one-particle
000166 | CAR phases are [-1,i,1,-i]^2, or u_r=-i^(-r). Therefore EXACTLY
000167 |  t_v J_m t_v^-1=i^m J_m,
000168 |  t_v Lcal_m^alpha t_v^-1=i^m Lcal_m^alpha.
000169 | Products carry the total Fourier degree, with all OPE/contact terms;
000170 | the central terms have total degree0, so the character respects them.
000171 | 
000172 | The known global identity is retained on EVERY charge sector:
000173 |  t_v=exp(-4pi iK_alpha) exp(i pi(1+alpha/2)Q)=(-1)^Q W_alpha^-1,
000174 |  W_alpha=exp(4pi iK_alpha)exp(-i pi alpha Q/2).
000175 | Indeed, with original residue charges p and oscillator level N,
000176 |  t.p-[-2K_alpha+(1/2+alpha/4)Q]
000177 |    =2N+sum_k p_k^2-Q+sum_(k=4..7)p_k is integer.
000178 | Odd CAR parity must NOT be deleted on the full CAR; it disappears only on
000179 | the even source. The internal order4 character is still not the original
000180 | charged quarter holonomy. Its time/charge relation does not physically
000181 | compensate that holonomy or prove a newly autonomous clock.
000182 | 
000183 | 6. Complete seam-graded energy response does not yield a sharp3+2
000184 | 
000185 | Use ALL actual positive-mode density response matrices G_m, m=1,...,32,
000186 | already independently computed on the full five inputs, both quarters.
000187 | The original seam fixes four characters, without fitting a profile:
000188 |  G_rho=sum_(1<=m<=32,m=rho mod4) G_m, rho=0,1,2,3.
000189 | Exactly sum_rho G_rho=32 B4, with B4 the ACTUAL source input metric.
000190 | All four G_rho are positive definite (rank5) in BOTH quarters, independently
000191 | checked by exact Gaussian-rational Sylvester minors. So for the normalized
000192 | mathematical response effects E_rho=(32B4)^-1/2 G_rho (32B4)^-1/2,
000193 |  0<E_rho<I, sum E_rho=I.
000194 | Every nonempty proper coarsening also lies strictly between0 andI. In
000195 | particular deck-even G0+G2 and deck-odd G1+G3 both have rank5. This is an
000196 | energy-response decomposition, NOT an executed POVM or filtering rule.
000197 | The exact common commutant of (32B4)^-1 G_rho has dimension1 overQ(i).
000198 | Thus no common reducing3+2 input-spectrum is hidden in these four forms.
000199 | 
000200 | EXCLUSION SCOPE: only a sharp deterministic character/deck input-sector
000201 | reading, and a common reducing spectral split of this complete response
000202 | decomposition. There is NO new axiom that a physical mark must commute
000203 | with every response; no exclusion of all nonlinear intrinsic event
000204 | relations, other full-field histories, admissibility rules or P1. The
000205 | existing original global event-label pair, intrinsic six rays and60 flags
000206 | are retained. The original physical q/S and polar3+2 selection remain open.
000207 |