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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.

Free scalar: a local repair, then a sharp [formula in source] obstruction.

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It suffices to examine a collinear sector; failure there is failure of a purported universal cubic-lattice identity. Set [formula in source] on a periodic one-dimensional row and write [formula in source] The site energy and link flux [formula in source] obey the exact energy equation [formula in source] The continuum-looking averaged-gradient stress [formula in source] does not obey momentum continuity. An exact sam

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

Source location and explicit evidence links

tex-artefacts/toe_round7_matter_coupling.tex · lines 300 to 382

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.