I want to ask a question about the answer provided here: https://quant.stackexchange.com/a/35211/61083 . I'm wondering if there is mathematical proof as to why it is working. Meaning if I reprice a vanilla option of strike K, with a stripe of vanillas of strikes ranging from K1 to KN why the gamma would be capped when the option is ATM and close to expiry and not explode.