Manuscript Hawk02-C@2 · Hawk02-C.tex · section · bb332d66

Reported saved arrays

Reported diagnostics and arithmetic-aware interpretation › Reported saved arrays · lines 2371–2421

The detailed summary reports these keys and shapes. The binary arrays have not been independently inspected.

Key	Shape	Reported dtype
`H_reference`	$(25, 25)$	`float64`
`H_finite`	$(9, 9)$	`float64`
`psi_reference`	$(25,)$	`complex128`
`psi_finite`	$(9,)$	`complex128`
`W_reference`	$(147, 2)$	`complex128`
`W_finite`	$(147, 2)$	`complex128`
`collected_embedding`	$(17, 2)$	`complex128`
`joint_residual_embedding`	$(99, 2)$	`complex128`

The dimensions follow from

1 + 24 d = 49, (d + 1) 49 = 147,

1 + 8 d = 17, (d + 1) [1 + (24 - 8) d] = 99.

The split matrix, constructed but not saved under a separate key, has shape $(99 \cdot 17, 2) = (1683, 2)$ . Both it and the $(147, 2)$ matrix are rectangular isometries in exact arithmetic.

For the exact finite Hamiltonians,

H^{[24]}_{F} = 273, H^{[8]}_{F} = 97 .

Their finite diagonal and hopping entries are exactly the declared $3$ and $1$ . These structural facts do not certify floating-point propagation errors.

The summary's high-index coefficients include magnitudes near floating-point precision. Such entries are not resolved physical tail measurements. The complete analytical tail bounds remain separate.

Displayed formulas in this passage

unlabeled · line 2395
$1 + 24 d = 49, (d + 1) 49 = 147,$
unlabeled · line 2398
$1 + 8 d = 17, (d + 1) [1 + (24 - 8) d] = 99.$
unlabeled · line 2408
$H^{[24]}_{F} = 273, H^{[8]}_{F} = 97 .$