Reasoning:
- Detailed-balance / crossing logic: the amplitude connecting the parton initial state to the black-hole state is the same object that connects the black-hole state back to partons. A nonzero production cross-section therefore implies a nonzero decay width into the same channel; for a TeV-scale object with gravitational-strength couplings this width makes the lifetime extremely short.
- The only escape for single production would be a new conserved quantum number carried by the hole but not by the partons — impossible, since it was made from exactly those partons.
- Pair production of black holes carrying new, opposite conserved quantum numbers changes nothing material: only the ground state is guaranteed stable, and any normal matter (quarks, gluons, leptons) subsequently accreted is immediately re-radiated, so even such a relic cannot grow.
- Both this argument and Hawking evaporation remain valid in the extra-dimensional models invoked for LHC black-hole production; stability therefore requires violating quantum mechanics (production-decay link) and/or general relativity (Hawking radiation).
Validity verdict (step 6)
Reconstruction: premises = quantum mechanics (unitarity/crossing) applies to the produced object; it was made singly from ordinary partons. Load-bearing step traced: the amplitude for partons → BH is the same analytic object as BH → partons, so nonzero production implies nonzero decay width into the same channel; a selection rule forbidding decay would need a conserved number the partons lack, impossible for an object built from exactly those partons. The width → short lifetime step is order-of-magnitude but sound for TeV-scale gravitational coupling. The pair-production caveat is handled (only the ground state protected, accreted matter re-radiated). Conclusion correctly framed as: stability would require violating QM itself.