Skip to main content

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.

Full-reference theorem and proof.

tfpt research contracts · Research contracts

Let [formula in source] be the sum of moduli before cancellation, resolved into elementary hopping words, initial charge profiles and scalar integrals. Then Every elementary hop changes the complete profile, hence [formula in source] . Scalar spectral Jensen gives [formula in source] . Pinching [formula in source] into its charge blocks [formula in source] contracts the Schatten [formula in source] norm, so [formula

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

Source location and explicit evidence links

tex-artefacts/toe_round27_full_reference.tex · lines 66 to 113

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.