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.

Theorem 1 (source-fixed all-volume factorized gap).

tfpt research contracts · tfpt research contracts · Research contracts

Let [formula in source] be any finite set of momentum cells, with arbitrary dispersions [formula in source] , and define the graded tensor-product Hamiltonian [formula in source] . Then [formula in source] has a unique product ground state and The same number is the uniform lower edge of canonical one-fermion spectral support.

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

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Source location and explicit evidence links

tex-artefacts/toe_round7_parent_mirror.tex · lines 142 to 154

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.

Complete structured registry How source relations are recorded Knowledge and evidence coverage