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Question
When may a proof obligation move from a thick reconstruction to its thin limit?
What the note explains
A theorem proving that hypotheses imply a conclusion does not also prove that the intended physical system satisfies those hypotheses. The latter requires its own model certificate.
Example
Suppose a limiting theorem assumes a diagram of positive-thickness objects. It can analyze their limit only after those objects and comparison arrows have been supplied; the limit cannot create its missing inputs.
What the approach gains
The dependency framework locates the exact stage that owns each obligation. It helps distinguish a legitimate limiting task from an unresolved finite-thickness construction hidden behind a later paper reference.
Reading route
Read the abstract and Sections 1–2, then follow the dependency-category and cut-criterion discussion. Use the application as an obligation map, with each witness restricted to its certified domain.
Scope and limits
The note does not discharge the model-specific Yang–Mills obligations, construct the thin net, or prove a mass gap. “Paper IV will handle it” is valid only when the transferred task is actually a limiting obligation.