The maximum of FriCASIssues is not really maximal.

)abbrev package MYSINT FriCASIssues
FriCASIssues : Public == Private
  where
    Public == IntegerNumberSystem with
      max : () -> %
      mymax : () -> %
      mymax2 : () -> %
    Private  == SingleInteger add
      mymax() == max() + 1
      mymax2() == mymax() + 1

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1558850444918824065-25px001.spad
      using old system compiler.
   MYSINT abbreviates package FriCASIssues 
------------------------------------------------------------------------
   initializing NRLIB MYSINT for FriCASIssues 
   compiling into NRLIB MYSINT 
   compiling exported mymax : () -> $
Time: 0.03 SEC.

   compiling exported mymax2 : () -> $
Time: 0 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |FriCASIssues| REDEFINED

;;;     ***       |FriCASIssues| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor FriCASIssues
      Time: 0.03 seconds

(|RealConstant|)    extends 
(|ConvertibleTo| (|DoubleFloat|))    but not 
(|ConvertibleTo| (|String|)) --------------non extending category----------------------
.. FriCASIssues of cat 
(|Join| (|IntegerNumberSystem|)
        (CATEGORY |domain| (SIGNATURE |max| ($)) (SIGNATURE |mymax| ($))
         (SIGNATURE |mymax2| ($))))   has no 
(|ConvertibleTo| (|String|))    finalizing NRLIB MYSINT 
   Processing FriCASIssues for Browser database:
--->-->FriCASIssues(constructor): Not documented!!!!
--->-->FriCASIssues((max (%))): Not documented!!!!
--->-->FriCASIssues((mymax (%))): Not documented!!!!
--->-->FriCASIssues((mymax2 (%))): Not documented!!!!
--->-->FriCASIssues(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MYSINT.NRLIB/MYSINT.lsp" (written 04 APR 2022 07:25:58 PM):

; /var/aw/var/LatexWiki/MYSINT.NRLIB/MYSINT.fasl written
; compilation finished in 0:00:00.014
------------------------------------------------------------------------
   FriCASIssues is now explicitly exposed in frame initial 
   FriCASIssues will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYSINT.NRLIB/MYSINT

a: FriCASIssues := max()$FriCASIssues

(1)

m: FriCASIssues := mymax()

   >> System error:
   The value 4611686018427387904 is not of type FIXNUM.

On my 32 bit system I get

FriCASIssues := mymax()

(1) - 2147483648 Type: FriCASIssues (2) -> m2: FriCASIssues := mymax2()

(2) - 2147483647 Type: FriCASIssues (3) -> (2^31, 2^32, 2^63, 2^64)

(3) [2147483648,4294967296,9223372036854775808,18446744073709551616]? Type: Tuple PositiveInteger? (4) -> b: FriCASIssues := 2^63-1

(4) - 1 Type: FriCASIssues (5) -> c: FriCASIssues := b+1

(5) 0 Type: FriCASIssues " title=" (1) -> )co aaa.spad

(1) -> m: FriCASIssues := mymax()

(1) - 2147483648 Type: FriCASIssues (2) -> m2: FriCASIssues := mymax2()

(2) - 2147483647 Type: FriCASIssues (3) -> (2^31, 2^32, 2^63, 2^64)

(3) [2147483648,4294967296,9223372036854775808,18446744073709551616]? Type: Tuple PositiveInteger? (4) -> b: FriCASIssues := 2^63-1

(4) - 1 Type: FriCASIssues (5) -> c: FriCASIssues := b+1

(5) 0 Type: FriCASIssues " class="equation" src="images/5463052088287443490-16.0px.png" align="bottom" Style="vertical-align:text-bottom" width="560" height="420"/>

Concerning the results: I guess they are due to different Lisp implementations. SBCL used here by default is rather strict in error checking. AFAIK Clisp does not care, it produces "correct" results. With other (unsafe) settings in SBCL or with some other Lisp one can get silent corruption possibly leading to crash.