TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/FOUR-STARTING-POINTS-STATE-RELATIVE-EQUIVALENCE.txt
Original file SHA-256: 53dd97e3d9fc5b9d62a3f772fbe5d578b258c84bff82afac68668422c90d2ac8
Inclusive original lines: 217-272
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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000217 | 5. ACTUAL NATIVE TRANSPORTS AND WHY THEY DO NOT REMOVE THE DIFFERENCE
000218 | 
000219 | The checker reconstructs the original 46080 root/quartic actions, not an
000220 | abstract replacement S6, and the internal-character stabilizer64 with
000221 | logical image16. Actual representatives G_q send (5,{0,1}) to each
000222 | (q,{0,1}), q2,3,4, with their literal native four-field action g_q and
000223 | quartic action rho_q verified polynomial by polynomial and on all roots.
000224 | They preserve the internal character and native J. Optional R/retained48
000225 | data must ALSO be transported; their fixed-source stabilizer is already
000226 | smaller and is not silently claimed transitive on all four roots.
000227 | 
000228 | Let dp=Gd. Under the individual E8 lattice lift U_G,
000229 |  U_G Y_d(a,z) U_G* = Y_(Gd)(U_G a,z),
000230 |  U_G H_exc(d) U_G* = H_exc(Gd),
000231 |  U_G sigma_d U_G* = sigma_(Gd).
000232 | This follows by conjugating every mode of Delta(d,z). Thus ALL products,
000233 | charged intermediate/end sectors, adjoints, the vacuum copy, erasure and
000234 | time/clock histories intertwine when every datum is transported. Lift
000235 | cocycles require their actual cochain: if eps is the ordered lattice
000236 | cocycle, choose eta_G with
000237 |  eta_G(alpha+beta)/(eta_G(alpha)eta_G(beta))
000238 |        =eps(Galpha,Gbeta)/eps(alpha,beta).
000239 | Then U_G e^beta=eta_G(beta)e^(Gbeta). The two cocycles have the same
000240 | commutator, so their ratio is a symmetric coboundary on the free lattice.
000241 | An individual lift suffices; no globally split G31 section is assumed.
000242 | Omitting eta would manufacture false charged mismatches or equivalences.
000243 | 
000244 | For every already given full clock/intervention C DEFINED ON THIS SAME
000245 | E8 MODULE and its transported domain, the transported operator is
000246 | C'=U_G C U_G*, including its entire4/5/20/carry action and all word phases.
000247 | Operators outside this module require their separately proved extension;
000248 | in particular the original odd W1 is not silently assigned an E8 action.
000249 | At a FIXED named clock the
000250 | required relation would instead be U_G C=C U_G; it is not inferred from
000251 | equal order or quotient action. Native compiler c=J sigma has order12 on
000252 | the four-space and order3 on the quartics, unlike the charged source fold.
000253 | No separately supplied marked sigma or RR clock is used to select q; doing
000254 | so would simply reinsert the old mark. The correlation obstruction already
000255 | rules out the required fixed-state equivalence before extra clocks are
000256 | required, so retaining more fixed clock data cannot repair it.
000257 | 
000258 | The checker verifies ALL five quartic Wick tensors under this transport:
000259 |  b'=U_+^T O^T Gd=conjugate(g)b, D_r(b')=rho D_r(b)rho*.
000260 | The conjugation on g matters. It verifies every root identity
000261 |  (Gd).(Gbeta)=d.beta, including unwrapped time gaps, not only phases.
000262 | At FIXED d, some d.(Gbeta) differ; exact counts and examples are retained.
000263 | This is a charged-clock witness alongside the stronger direct marked-ray
000264 | correlation obstruction. Changing the background to Gd changes the supplied
000265 | state/time object. It is not a symmetry of the original marked source.
000266 | 
000267 | These E8 lattice lifts are not automatically automorphisms of the original
000268 | odd CAR algebra or its Z8 charge sublattice. A passive component rewrite
000269 | of F C_alpha F*, M/O and every field represents the SAME original source;
000270 | an active physical CAR/P1 symmetry still needs its own original map. No
000271 | new eight-copy state, CAR embedding or physical gauge quotient is assumed.
000272 |