This "False" value is basically the same as

use Scalar::Util qw/dualvar/;
dualvar(0, '');
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Which stems from the curious fact that a Perl scalar internally has a slot for both a numeric and a string value. By explicitly providing a numeric value, you don't get a warning when used as a number:

$ perl -wE 'say 1 + ""'
Argument "" isn't numeric in addition (+) at -e line 1.
1
$ perl -MScalar::Util=dualvar -wE 'say dualvar(0, "") + 1'
1
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Note that when abused, these dualvars can be very confusing:

$ perl -MScalar::Util=dualvar -E 'my $x = dualvar(42, "23"); say $x; s
+ay $x + 1'
23
43
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Devel::Peek shows that the False value is a wee bit more special than that:

perl -MDevel::Peek -MScalar::Util=dualvar -e 'Dump !1; Dump dualvar(0,
+ "")'
SV = PVNV(0x254ff70) at 0x7409c0
  REFCNT = 2147483647
  FLAGS = (IOK,NOK,POK,READONLY,pIOK,pNOK,pPOK)
  IV = 0
  NV = 0
  PV = 0x254ff50 ""\0
  CUR = 0
  LEN = 8
SV = PVNV(0x2550d90) at 0x2551220
  REFCNT = 1
  FLAGS = (TEMP,IOK,POK,pIOK,pPOK)
  IV = 0
  NV = 0
  PV = 0x255f610 ""\0
  CUR = 0
  LEN = 8
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So it's not only a dualvar, but it's also readonly, and has a very high refcount - it's basically a singleton.