TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/seam-joint-conjugation-20261015/PROOF.txt
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Inclusive original lines: 153-187
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000153 | 5. THE MARKING IS TRANSPORTED, AND CANNOT BE REPAIRED AT FIXED TIME
000154 | 
000155 | Let P5 project onto coordinates {1,2,3,4,5} and P3 onto {6,7,8}, as in the
000156 | existing dictionary. O transports them to P5' on {1,2,4,5,6} and P3' on {3,7,8}.
000157 | Exactly 24/40 D5 roots stay in the old D5, and 16 leave it. Of the D3 roots,
000158 | 4/12 stay and 8 leave. This says which embedding moves, not that E8 is lost.
000159 | 
000160 | There is NO orthogonal correction T simultaneously satisfying
000161 |     T d_beta=d_beta,    T P5' T^-1=P5.
000162 | Indeed those equalities require ||P5' d_beta||^2=||P5 d_beta||^2. But
000163 |     beta=1/4: fixed 129/256, transported 137/256;
000164 |     beta=3/4: fixed 137/256, transported 129/256.
000165 | The family norms are respectively 41/256 versus 33/256, and vice versa.
000166 | This proves the obstruction for the whole orthogonal class, hence every Weyl
000167 | correction, without a GPU search. It is scoped to the fixed folded d and marked
000168 | D5+A3. Nonlinear/dynamical dictionaries or a different original source are
000169 | not ruled out. Old module symmetries that preserved an unshifted norm do not
000170 | automatically preserve this quarter-dependent physical time.
000171 | 
000172 | There IS a parameter-free covariant completion from a GIVEN initial marking:
000173 |     P5_beta=O P5_alpha O^-1,  P3_beta=O P3_alpha O^-1,
000174 |     y_beta=O y_alpha,   k_beta(p)=k_alpha(O^-1 p).
000175 | Here k_alpha is the original given Z4 character. Its neutral-root second moment
000176 | M0=16P5+8P3 transports to O M0 O^-1. Therefore the same previously proved
000177 | formula P5=(M0-8I)/8 reconstructs precisely the transported projector; no new
000178 | independent projector or fitted phase is required. The 3+2 color/weak subspaces
000179 | transport in the same way. O^2=I makes the lattice/marking transport coherent.
000180 | On operators, H_y -> H_(Oy), so the transported state and observable retain
000181 | the same expectation. Retaining the old y instead would describe a different
000182 | comparison. A second-quarter coordinate choice can make charge labels appear
000183 | as simple negation, but does not turn the result into a symmetry of fixed M.
000184 | 
000185 | This reduces the joint problem to the origin of ONE marked source realization,
000186 | rather than independent choices of two markings, two vacua and two times.
000187 | It is a derived relation between supplied data, not a P1 selection theorem.