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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.

CROSS: the sufficient one-sided theorem.

tfpt research contracts · Research contracts

Let [formula in source] be the unitary fractional shift with entries [formula in source] , let [formula in source] restrict to [formula in source] , [formula in source] , [formula in source] , [formula in source] and [formula in source] . Crucially [formula in source] . For the finite unitary overlap [formula in source] and [formula in source] , the source identity is [formula in source] Hence [formula in source] . P

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

Source location and explicit evidence links

tex-artefacts/toe_round4_proofs.tex · lines 143 to 174

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.