TFPT scientific source excerpt
Original repository path: verification/v113_quasifree_kernel.py
Original file SHA-256: a033fe9c292d22b5bbc343aa0d8e352df14a0918e4124fd7596bf7f81e01ff51
Inclusive original lines: 11-38
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000011 |   [I] 1. MAJORANA BOOKKEEPING (exact arithmetic).  Level-1 central
000012 |          charges: c(D5)_1 = 45/9 = 5 = g_car, c(A3)_1 = 15/5 = 3 =
000013 |          N_fam, c(SO(16))_1 = 120/15 = 8, c(E8)_1 = 248/31 = 8.  The
000014 |          carrier net is SO(10)_1 x SO(6)_1 = 10 + 6 = 16 free Majorana
000015 |          fermions, c = 16/2 = 8 -- and the WHOLE extension tower
000016 |          carrier(mu=16) -> SO(16)_1(mu=4) -> E8_1(mu=1) carries the SAME
000017 |          16 free fermions; only the certified glue grows (index steps
000018 |          2 x 2 = 4 = |mu_4|, v89).
000019 |   [I] 2. WICK / PFAFFIAN (the one kernel determines all correlations).
000020 |          In the exact 10-Majorana model (5 slots, integer Jordan-Wigner):
000021 |          ALL 210 vacuum 4-point functions and ALL 210 6-point functions
000022 |          equal the Pfaffian of the single 2-point kernel.  "One scalar
000023 |          2-point kernel" is not a truncation for this net -- it is the
000024 |          complete specification.
000025 |   [I] 3. THE KERNEL IS A CALDERON INVOLUTION OF RANK g.  The 2-point
000026 |          matrix is M = I + iA with A integer, antisymmetric, A^2 = -I;
000027 |          hence P = M/2 is a projection with rank P = 5 = g_car and
000028 |          eps = iA is an involution (eps^2 = 1) whose +/- eigenspaces are
000029 |          the annihilation/creation sides.  At seam level (16 Majoranas)
000030 |          the same construction has rank 8 = rank E8:
000031 |              THE CENTRAL CHARGE IS THE RANK OF THE ONE KERNEL
000032 |          (c = 5 for the carrier block, c = 8 for the seam hull).
000033 |   [I] 4. ONE KERNEL <=> ONE STATE.  The joint kernel of the five
000034 |          annihilators is exactly 1-dimensional: the polarization
000035 |          determines the vacuum uniquely -- kernel => state => (Wick) all
000036 |          correlations.
000037 |   [P] 5. PREMISE MERGE (recorded, not claimed).  QBL's remaining input
000038 |          "single scalar 2-point kernel" = "the seam state is quasi-free"