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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.

Proof.

tfpt research contracts · tfpt research contracts · Research contracts

For [formula in source] , differentiation of minimum and substitution gives [formula in source] . The other empty/full eigenstate costs at least [formula in source] , and the [formula in source] sector also costs at least [formula in source] , so neither undercuts tensor product and energies add. Any state orthogonal to the product ground excites at least one cell, proving the same bound independently of [formula in

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 155 to 175

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

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.