[abhishekcpp007]

_save_integral only checked the upper bound, so any int below -2**31 went down the 4-byte INT/LONG opcode path and struct.pack("!i", i) raised a bare struct.error. Positive values above 2**31 - 1 were already routed through LONGINT/LONGLONG, so 2**40 round-tripped and -2**40 did not.

>>> import execnet
>>> execnet.loads(execnet.dumps(2**40))
1099511627776
>>> execnet.loads(execnet.dumps(-2**40))
struct.error: 'i' format requires -2147483648 <= number <= 2147483647

Over a gateway the same thing shows up as a RemoteError ending in _write_int4 ... struct.error from channel.send(-2**40), while channel.send(2**40) arrives fine. A negative nanosecond timestamp or a hash value gets there easily.

The fix adds FOUR_BYTE_INT_MIN and checks both bounds in _save_integral, so anything outside the 4-byte range takes the string-backed long path. _write_int4 now rejects values below the minimum with DumpError, the library's own exception, instead of leaking struct.error. The wire format is unchanged: load_longint already does int(s) and handles the sign, so an old receiver reads the new output.

Tests: 2**31, -(2**31) - 1, 10**30 and -(10**30) join the TestSerializeAPI matrix in testing/test_basics.py (dumps/loads, mmap and BytesIO), and test_negative_long in testing/test_serializer.py mirrors test_long for the cross-interpreter path.

Verified in a python:3.12 container (pip install pytest -e ., gevent/eventlet deselected):

• this branch: 479 passed, 125 skipped, 6 xfailed, 11 xpassed, plus the 5 test_remote_exec_module_is_removed variants that also fail on unmodified main when run together (they depend on a cached remote module, which testing: Drop cached remote module in test_remote_exec_module_is_removed #442 addresses)
• the new tests against main's src: 7 failed (struct.error on every negative case)