previewNatArray
plain-language theorem explainer
A utility converts the first few natural numbers from an array into a bracketed comma-separated string for diagnostic output. It is called inside the J-monotone certificate reporter to display a truncated view of deltaJ values. The body is a direct functional implementation that truncates the list, maps to strings, joins them, and adds an ellipsis when needed.
Claim. For an array $a$ of natural numbers and optional limit $l=4$, the function returns the string $``[`` ++$ (intercalate $``,'' $ (map toString (take $l$ (toList $a$)))) $++$ ellipsis $++ ``]``$, where ellipsis is appended precisely when the array length exceeds $l$.
background
The LNALReports module produces human-readable status strings for LNAL compiler outputs and certificates in the URC adapter layer. The listed upstream results supply map (which applies a function to a Measurement while preserving its window and uncertainty) and toList (which extracts the canonical triple of lepton mass ratios). These belong to the surrounding module context rather than the body of this definition itself.
proof idea
The definition converts the input array to a list, truncates to the limit, maps each entry to its decimal string, and joins the results with commas. It then checks the original array length to decide whether to append an ellipsis before wrapping the whole expression in brackets. No lemmas are invoked; the steps are standard library operations on List and String.
why it matters
The definition is invoked by jmonotone_report to embed a readable preview of deltaJ arrays inside certificate status messages. Those arrays arise from the J-cost function whose uniqueness is stated at T5 of the forcing chain. It supplies only display scaffolding and touches no open Recognition Science question.
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