TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/ORIGINAL-SEAM-STATE-FLAG-SELECTION.txt
Original file SHA-256: bdbba2dae8386cd94e68663ca3c2291ba652df2de563b1a4e114ffa2af4ec1ee
Inclusive original lines: 117-154
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.

000117 | 4. FULL ORIGINAL NEUTRAL TENSOR DOES NOT REMOVE THE LAST PAIR
000118 | 
000119 | Keep original R_matrix from _native_neutral_branch and, independently, the
000120 | full retained48 root subset. For omitted family(-1,-1,-1), both joint
000121 | stabilizers with the quarter character have native order16/logical order8.
000122 | Their logical action is the independent group
000123 |   <(01),(23),(45)> = C2 x C2 x C2.
000124 | Each of the other three existing omissions gives the same logical action
000125 | and the same three q-orbits {0,1}|{2,3}|{4,5}. We have not chosen an omission
000126 | because it yields a preferred q. No joint fixed q or flag exists.
000127 | 
000128 | The full60 orbit census is six orbits of2, six of4 and three of8. The old
000129 | flag has the exact two-element orbit
000130 |   (4,{0,1}) <-> (5,{0,1}).
000131 | This does NOT prove that an originally specified minimization selects this
000132 | particular two-element orbit among all orbits. It proves that even THIS
000133 | old comparison flag cannot be selected uniquely from these invariant data.
000134 | 
000135 | A concrete full-source witness, in original physical E8 coordinates, is
000136 |   G(x1,x2,x3,x4,x5,x6,x7,x8)
000137 |     =(x3,x4,x1,x2,x5,x6,x7,x8).
000138 | It preserves the E8 lattice, J, v, the retained48 set and AR exactly. It
000139 | therefore fixes the FULL neutral local field T_AR and all its derivatives,
000140 | not merely its C5 compression. The actual induced quartic action is (45).
000141 | Individual lattice lifts exist with the original ordered cocycle and fix
000142 | Omega and the conformal vector. Cocycle sign characters act trivially on
000143 | the neutral oscillator code and Omega; a globally split G31 lift is not
000144 | required and is not asserted. Such unitary field automorphisms preserve
000145 | adjoints, all local products, and vacuum correlations after transporting
000146 | their field arguments. Additional physically fixed insertions or a physical
000147 | Theta would need their own intertwining test; none is silently supplied.
000148 | 
000149 | The two polar operators really differ:
000150 |   ||P(4,{0,1})-P(5,{0,1})||_HS^2
000151 |       =(816-176sqrt6)/625 >0.
000152 | It is not a redundant labelling of the same operator. Equal vacuum Gram
000153 | does not identify these two subspaces.
000154 |