TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/FULL-SOURCE-HULL-AND-QUARTIC-OPE.txt
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Inclusive original lines: 229-265
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000229 | 8. Original3+2 comparison, source symmetries and exterior memory
000230 | 
000231 | The six axes give fifteen rank2 planes by pairing simplex vertices. No
000232 | pair is selected. Compare ALL15 with the actual original polar P2 only
000233 | after reconstruction. None is that P2; exact minimum squared HS distance
000234 |  min ||P2-P_pair||²=(21-6sqrt6)/25>0.
000235 | The earlier marked-plane exclusion is thereby recovered from the actual
000236 | local OPE geometry, not discarded. Simply calling one of these planes
000237 | the physical two-sector would replace the original mark.
000238 | 
000239 | The full current algebra is affine E8 at level1, with irreducible vacuum
000240 | module V_E8. Its horizontal E8 is a covariance/VOA-automorphism symmetry,
000241 | not the commutant of every field or a derived physical gauge group.
000242 | The first horizontal grades are1,248,1+248+3875. The grade2 remainder
000243 | has lattice weight multiplicities1 at all2160 norm4 vectors,7 at240
000244 | roots and35 at0; all2400 nonhighest Freudenthal recurrences are checked.
000245 | The character in section3 determines the higher finite decompositions.
000246 | The code's full endpoint algebra M5 has no intrinsic3+2 superselection.
000247 | 
000248 | For invariant complete exterior data and fully contracted LINEAR
000249 | code-to-code response/memory kernels K, native covariance implies
000250 |  K rho5(g)=rho5(g)K, hence K=k I5 by the actual irreducible native action.
000251 | Keeping every exterior state does not evade this statement. It is NOT
000252 | a claim that all covariant density-matrix channels, open outcome tensors,
000253 | noninvariant source preparations or spontaneous branches are trivial.
000254 | The uncontracted OPE tensors above contain precisely such nontrivial
000255 | relational information. Their scalar full contraction loses it.
000256 | 
000257 | For a specified full operator L and observer split P,Q only used in
000258 | analysis, K=PLP,B=QLP,D=QLQ give the existing exact exterior memory
000259 |  M_(n+1)=K M_n+sum_(j=0)^(n-1)B*D^(n-1-j)B M_j.
000260 | Where the selfadjoint resolvent is defined, the equivalent Feshbach form is
000261 |  P(z-L)^(-1)P=[z-K-B*(z-D)^(-1)B]^(-1).
000262 | Neither formula selects L, a physical history or a state. The prior
000263 | 35/44 leakage and rank10 Hankel statements remain for their exact
000264 | single-beta source process, not every E8 history. Do not insert P as
000265 | a measurement after each step and do not build a new free10D model.