Forging a samurai sword, such as a katana, using Tamahagane steel involves a complex and highly skilled process. While the specific techniques can vary among swordsmiths and schools, here is a general overview of the steps involved in forging a samurai sword with Tamahagane steel:

1. Material Preparation: Tamahagane steel, produced through the smelting process I described earlier, is obtained or acquired. The quality and composition of the Tamahagane steel play a crucial role in the final sword's performance and appearance.
2. Shaping the Blade: The swordsmith begins by carefully shaping the blade's profile. The steel is heated to a malleable state and hammered into a rough shape resembling the final sword. This initial shaping stage is called "kitae-oshi."
3. Folding and Layering: The swordsmith then proceeds to fold the Tamahagane steel multiple times, layering it to eliminate impurities and create a distinct grain pattern. The folding and layering process helps enhance the blade's strength, flexibility, and overall quality. It also contributes to the creation of the visible grain pattern known as "hada."
4. Differential Hardening: One of the critical steps in the forging process is the differential hardening or "yakire" technique. The blade is heated and coated with a heat-resistant clay mixture, leaving the cutting edge exposed while the rest of the blade is covered. The blade is then quenched in water or oil, rapidly cooling the exposed edge, creating extreme hardness, known as the "hamon." The clay coating helps create a distinct line between the hardened edge and the softer, more flexible spine.
5. Tempering and Annealing: After the differential hardening, the sword is tempered to reduce brittleness and improve its overall resilience. The swordsmith carefully heats the blade and lets it cool slowly through a process called "yaki-ire." This tempering process helps balance the blade's hardness and flexibility.
6. Polishing and Finishing: The forged blade is then meticulously polished using different grades of polishing stones to reveal the beautiful grain pattern, hamon, and overall aesthetics of the sword. Skilled artisans employ various techniques to achieve a flawless finish.
7. Mounting and Fitting: Once the blade is completed, it is fitted into a hilt (tsuka) and scabbard (saya) by a specialized artisan. The hilt is wrapped with a handle wrap (tsuka-ito) using traditional methods. Other fittings, such as the guard (tsuba), menuki (handle ornaments), and pommel (kashira), are added to complete the sword's mounting.

The process of forging a samurai sword with Tamahagane steel is a labor-intensive and time-consuming art form that requires a deep understanding of metallurgy, craftsmanship, and tradition. The result is a meticulously crafted weapon that embodies the cultural and historical significance of the samurai and their swords.