TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/joint-native-algebra-selection-20261016/CONFORMAL-HISTORY-AND-ERASURE-CARRY.txt
Original file SHA-256: 8a50ef4c3621005d39ecaa93f38fa1d06f6c32f46c57e138fadcebb49c0ab184
Inclusive original lines: 103-172
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.

000103 | 4. Actual erasure across a higher geometric excursion
000104 | ----------------------------------------------------
000105 | The ORIGINAL erasure is not a Virasoro intertwiner: it lowers conformal
000106 | weight by1, and its complete Ward rule follows from(1):
000107 | 
000108 |   [L_m,a_a]=-bar u_a(m+1).                                    (5)
000109 | 
000110 | For m=-1 the right side is a neutral zero mode and vanishes. The first
000111 | new term is at m=-2:
000112 | 
000113 |   a_a L_-2 f_i=L_-2 g_(i,a)+t_(i,a),
000114 |   t_(i,a)=bar u_a(-1) f_i.                                    (6)
000115 | 
000116 | No coefficient, coupling or field identification is chosen in(5)-(6).
000117 | The t vectors are orthonormal20 of conformal weight5. The source gives
000118 | 
000119 |   L1 t=0,    L2 t=g,    L_m t=0 for m>=3.                       (7)
000120 | 
000121 | Hence t is not yet primary. Isolate its component in the EXISTING
000122 | level2 descendants of the h3 erasure primary g. The original Virasoro
000123 | Gram and the overlap vector are
000124 | 
000125 |   Gram(L_-2g,L_-1^2g)=[[16,18],[18,84]],
000126 |   (<L_-2g,t>,<L_-1^2g,t>)=(1,0).                              (8)
000127 | 
000128 | The exact inverse Gram fixes coefficients (7/85,-3/170). Thus
000129 | 
000130 |   r_(i,a)=t_(i,a)-(7/85)L_-2g_(i,a)
000131 |                     +(3/170)L_-1^2g_(i,a),                   (9)
000132 |   L0 r=5r,       L_m r=0 for ALL m>0,
000133 |   <r_(i,a),r_(j,b)>=(78/85) delta_ij delta_ab.                 (10)
000134 | 
000135 | This is a forced20-dimensional nonzero primary carry at weight5, obtained
000136 | from the SAME original code, canonical stress and erasure. It is uniquely
000137 | the orthogonal primary remainder of(6) relative to the given erasure
000138 | descendant block; it is NOT a classification of every weight5 primary.
000139 | The orthogonal decomposition is mathematical, never a performed projection.
000140 | State-field correspondence supplies the associated original neutral source
000141 | fields; no physical Higgs/fermion assignment is inferred.
000142 | 
000143 | The entire first Ward output has Gram
000144 | 
000145 |   Gram(a_a L_-2 f_i)=19 I20.                                  (11)
000146 | 
000147 | Indeed16+1+2=19 from(6),(8). The primary carry has Gram78/85 I20.
000148 | Tracing over the4 erased labels gives respectively76 I5 and312/85 I5.
000149 | Even retaining this required carry therefore does not by its unweighted
000150 | returned Gram distinguish a logical2-plane or3-plane. No fitted probe weights
000151 | or additional selection rule are introduced to make it do so.
000152 | 
000153 | 5. Actual native sector action, not a matching dimension
000154 | --------------------------------------------------------
000155 | For every original native G31 event, the already checked f and g transform
000156 | as rho5 and rho5 tensor bar rho4. The creation field bar u_a(-1) carries
000157 | bar rho4, so t carries exactly rho5 tensor bar rho4. The canonical stress
000158 | commutes with the original lattice isometries; equations(9) therefore
000159 | intertwine the SAME20 representation, with its original source normalization.
000160 | 
000161 | The checker independently substitutes the actual native reflection lifts
000162 | at original ray IDs1,21,32 into the full Fock polynomials and verifies all60
000163 | carry intertwining identities. These are the SAME existing event lifts in
000164 | operator_checker.py; no fitting, relabeling or a new finite-group census.
000165 | The all-native covariance also follows algebraically from this construction.
000166 | 
000167 | The two native20 copies have different conformal weights3 and5. They must
000168 | not be equated as states, and neither is the charged E8 F20 block.
000169 | The corresponding joint Virasoro/native source subspaces are copies of
000170 | M_(8,1) tensor V4, M_(8,4) tensor C5, M_(8,3) tensor V20 and
000171 | the newly forced M_(8,5) tensor V20. These are infinite graded source
000172 | cycles, not a new finite physical state space or a particle census.