TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/e-series-compiler-closure-20261023/THEOREMS.txt
Original file SHA-256: 361450df688c5dc8fa3b8c69ff6a8d0f35156772bee5ec0acab494eb32d3587f
Inclusive original lines: 99-127
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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000099 | 
000100 | The original half-root block B=(16,4) has dimension64. Its family weights
000101 | index the four D5-compatible E6 cuts. For each vertex t there is a literal
000102 | weight projector P_t of rank16 and Q_t=I-P_t of rank48, satisfying
000103 | 
000104 |   P_t P_u=delta_tu P_t,   sum_t P_t=I_B,
000105 |   Q_t B=(16,3),
000106 |   Tr(I_B)/Tr(Q_t)=64/48=4/3=phi_base/c3.
000107 | 
000108 | S4 conjugates the four projectors. All actual D5 and A2 root-step actions
000109 | are verified. In the E6xA2 branching the same48 occurs as
000110 | 
000111 |   (27,3)=(16,3)_1+(10,3)_-2+(1,3)_4,
000112 |   81=48+30+3.
000113 | 
000114 | Every weight in this same block has squared D5 projection5/4 and squared
000115 | A3 projection3/4. Thus48,4/3 and5/4 have one explicit common representation
000116 | dictionary. The trace identity is a structural interpretation of the
000117 | existing seed ratio; it does not introduce a new response law or select a
000118 | tetrahedral vertex. The48 roots missing from an exchanged E7 pair instead
000119 | carry(12,2,2) under D6xA1xA1; their actual Y character rejects the tempting
000120 | identification with three D5 spinors.
000121 | 
000122 | 6. Reproducibility and completion
000123 | 
000124 | Run the existing small exact certificates directly:
000125 | 
000126 |   python3 -B experiments/theory-contracts/e-series-compiler-closure-20261023/field_lift_dictionary.py
000127 |   python3 -B experiments/theory-contracts/e-series-compiler-closure-20261023/cut_dictionary.py