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Find the original argument.

Search the paper sections, open their original context and follow the checks they actually cite. The knowledge atlas explains the result; this library locates its source.

An exact local repair boundary.

tfpt research contracts · tfpt research contracts · Research contracts

The following repair is included to make the result actionable, not to present a new source claim. On a bond let It obeys [formula in source] . For the flavour-diagonal hopping [formula in source] with unit coefficient, [formula in source] exactly. Therefore On a graph of maximum degree [formula in source] , replacing ordinary hopping by its projected version yields For the newly chosen periodic-1D bond analogue [for

Opening source excerpt. Formulas and the full argument remain in the original document.

Source location and explicit evidence links

tex-artefacts/toe_round7_parent_mirror.tex · lines 298 to 345

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

No explicit verification citation is attached to this section in the registry.

What this source index covers

The public registry includes 116 document views, 6,693 section records and 985 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.