I have no idea why you have such impression because AFAIK Chinese modern warheads are T-U design and I don't even know whether China has tested uranium-core or composite-core primary in the past. But I would say Chinese warhead has a egg-shaped plutonium primary, based on thousands of journals I have read and many memorial.
I think you misinterpret what they mean by "we can produce 10 of such SD-3/ZK-1A/KZ-11s" in their statement.
CASIC has lost their production capability of large solid engine, contracting almost every subsystem to civilian companies except pouring the grain themselves.
CAS-Space only has design branch in Beijing and they contract CASC to actually make the engines.
CASC is the main producer of large solid engines with capacity of approximately 10,000 - 12,000 ton worth of propellant per year.
I haven't paid particular attention to the design details of Chinese nuclear warheads. I will pay attention in the future.
Regarding the types of Chinese nuclear warheads, Chinese military enthusiasts rarely discuss in detail. I only know, and generally believe that
China mainly uses uranium warheads instead of plutonium warheads.
You cannot understand the operation of CASC and CASIC according to the operation of large Western military enterprises.
Enterprises are national, and the senior leaders of CASC and CASIC are regularly partially rotated. Yes, the executives of CASC were transferred to CASIC to lead the work, and the executives of CASIC were transferred to CASC to lead the work.
A few days ago, someone told me that they were competitors before the bidding for the general contracting of the project, and after the general contracting, they shared money (work tasks) with each other.
Actually, it's just deciding which leader is responsible for the project. After the national bidding, the funds will be placed under the books of which winning group. In terms of detailed projects, those with high responsibility and professional abilities are more likely to be divided, while those with low responsibility are less likely to be divided. The procurement level is interconnected.
This is the case with China's aerospace industry. The aviation departments, 611, 601, and 603 are also similar. Transportation, railways, and various construction groups are also the same. Everyone is the biological son of the country. There is something that cannot be discussed (mutual procurement).
Production is one thing, and the specific design of weapon models is another (just like the relationship between 611 and Chengdu Aircraft Industry Group. One is for development and the other is responsible for production). CASIC is wary of technology loss, preventing the hypersonic units (aerodynamic research) of CASC and AVIC from stealing their hypersonic wind tunnel test data. CASIC has always planned to invest billions in its own exclusive hypersonic wind tunnels in order to prevent CASC and AVIC from obtaining their research results. There is no problem with outsourcing the production of weapons or equipment. In fact, this does not involve real core technology and does not make money (the production profit is tightly controlled by the state, with a lot of safety production and management responsibilities. The part that is easy to earn and easy to spend is the research and development funds for weapons and equipment). The core technology is how to design and the specific parameters of the design. These are all required in the weapon development task book.