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

P8 specification and exact integer assembly

P8 specification and exact integer assembly · lines 545–578

Em03-H@8#eq:pulse, Em03-H@8#eq:integerH

The coefficient generator is deterministic; typicality is not asserted. The broad spectral window is not a certified gravitational low-energy window.

Define

b (x) = {exp [- 1/ ((x - 1/4) (3/4 - x))], 0, 1/4 < x < 3/4, otherwise, B_{0} = \int_{0}^{1} b (x) d x > 0,

κ (u) = \frac{π}{2 T B _{0}} b (u / T) .

The pulse is smooth, nonnegative, and has area $π /2$ . At $u / T = 0, 1/4, 1/2, 3/4, 1$ , its cumulative areas are $0, 0, π /4, π /2, π /2$ , by support and reflection symmetry.

With $Γ_{a} = 2 χ_{a}$ , the matrices are signed Gaussian-integer permutations. Hence

H_{4} = \frac{Q _{R} + i Q _{I}}{16773376}, 16773376 = 256 \cdot 65521 = 4 \cdot 4193344.

The coefficient denominator $4193344$ is not the Hamiltonian denominator.

Displayed formulas in this passage

Em03-H@8#eq:pulse · line 560
$κ (u) = \frac{π}{2 T B _{0}} b (u / T) .$
Em03-H@8#eq:integerH · line 570
$H_{4} = \frac{Q _{R} + i Q _{I}}{16773376}, 16773376 = 256 \cdot 65521 = 4 \cdot 4193344.$
unlabeled · line 552
$b (x) = {exp [- 1/ ((x - 1/4) (3/4 - x))], 0, 1/4 < x < 3/4, otherwise, B_{0} = \int_{0}^{1} b (x) d x > 0,$

P8 specification and exact integer assembly

Displayed formulas in this passage

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