Manuscript Em03-H@8 · Em03-H-v8.tex · proposition · 91e9e3bd

Proposition: Exact assembly invariants

P8 specification and exact integer assembly · lines 579–603 · proof included or linked

Em03-H@8#prop:assembly

The exact matrices satisfy

Q_{R}^{T} = Q_{R}, Q_{I}^{T} = - Q_{I},

zero even–odd blocks, and

tr (H_{4}) = 0, tr (H_{4}^{2}) = 16 r \sum J_{r}^{2} .

Equivalently,

ij \sum (Q_{R, ij}^{2} + Q_{I, ij}^{2}) = 256 r \sum (2 a_{r} - 65521)^{2} .

Proof. Hermiticity and parity give the matrix symmetries and blocks. Quartic Clifford monomials are trace orthogonal and square to $I /16$ . The boundary dimension is $256$ . Substitute the rational denominators to obtain the integer identity.

Displayed formulas in this passage

unlabeled · line 582
$Q_{R}^{T} = Q_{R}, Q_{I}^{T} = - Q_{I},$
unlabeled · line 587
$tr (H_{4}) = 0, tr (H_{4}^{2}) = 16 r \sum J_{r}^{2} .$
unlabeled · line 592
$ij \sum (Q_{R, ij}^{2} + Q_{I, ij}^{2}) = 256 r \sum (2 a_{r} - 65521)^{2} .$

Proposition: Exact assembly invariants

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