[Rafael-SOWNet]

abs(x * ln(x)) at 0 was NaN, the claim that the limit does not exist, and it was unevaluated from each side. The limit is 0 from both sides. The expression is real on both sides, and from the left |x|·|ln|x| + iπ| tends to 0 too.

The modulus took its argument's limit as the descent reads it, and the descent reads x * ln(x) as 0 · (-oo), which is NaN. 2.6.0 gives the same results.

Now, where that reading has no value, the modulus asks its argument's whole limit and takes the modulus of a value. It does this through AsTheWholeLimit, as a quotient already does: one level deep, and not under a limit budget.

On the two-sided convention (#2365): x * ln(x) and x^x stay NaN at 0, because neither has real values to the left. The tests pin both. A modulus of them does have real values on both sides, since |x^x| is |x|^x to the left of 0. So under the same convention abs(x^x) has a limit there, and it is now 1.

Input, at 0	2.6.0 and master	Now
abs(x * ln(x))	NaN; unevaluated from each side	0
abs(sin(x) * ln(x))	NaN	0
abs(x^2 * ln(x))	NaN	0
abs(x^x)	NaN	1

Measured

• limitcheck at DEPTH=3 on 21 seeds (14 to 51), master against this branch: 20 more rows compared, across 8 seeds. 10 "NaN where the values settle" findings are answered. Each takes the modulus of something that holds a power like x^x at 0, for example abs(x^x), abs(sinh(x^x)) and abs(x + 1 - x^x). No row moved to another value.
• The new tests fail on master: the three zero rows. The NaN rows pass on both.
• Suite: 18994 passed, 0 failed. AOT passed. BoundCheck, RootCheck, CasBench, PropCheck, SimpSweep, RuleCheck, CanonCheck and Confluence are clean.

Found while checking #2371. Recorded in BREAKING-CHANGES.md.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 83.33333% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 86.76%. Comparing base (598dae9) to head (4246612).

Files with missing lines	Patch %	Lines
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	83.33%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2372      +/-   ##
==========================================
- Coverage   86.77%   86.76%   -0.01%     
==========================================
  Files         312      312              
  Lines       68908    68911       +3     
  Branches    20081    20082       +1     
==========================================
- Hits        59798    59794       -4     
- Misses       4912     4917       +5     
- Partials     4198     4200       +2     

Flag	Coverage Δ
cpp	37.77% <ø> (ø)
csharp	87.31% <83.33%> (-0.01%)	⬇️
fsharp	32.97% <ø> (ø)
interactive	40.72% <ø> (ø)

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Files with missing lines	Coverage Δ
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs	74.83% <83.33%> (+0.59%)	⬆️

... and 6 files with indirect coverage changes

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