Sukemune of the Ko- is recorded as a son of Norimune, the founder of the Fukuoka , and as one of the smiths who served in the rota of Go-Toba-in. The published sources state that 「助宗は則宗の子で御番鍛冶の一人として知られるが、その遺例は極めて少なく」 (Sukemune is known as a son of Norimune and one of the , but his surviving works are extremely few), and until the 1990s the only signed works accepted with confidence were a at Matsugasaki Shrine in Yonezawa, an Important Cultural Property handed down from Uesugi Kagekatsu, and a in the Tokyo National Museum. His record now comprises two Important Cultural Properties and two blades.
The sources place him within a group whose manner they define against its neighbours: 「同派の作風は古備前に比してやや丁子が目立って整い、映りが鮮明となるが、鎌倉中期のものに見るような絢爛たる丁子乱れの作風とは趣をかなり異にしている」 (compared with , the group's is somewhat more prominent and orderly and the clearer, yet the feeling differs considerably from the splendid of mid- work). The Matsugasaki , 77.8 cm with a , is recorded with forging and a .
The designated in 1998 came to light only recently, and its signature differs in hand from the two older examples; the sources nonetheless find it 「いかにも古朴で雅味があり」 (truly archaic, simple and elegant) and 「古一文字以外には紛れることのない古様にして格調高い作品である」 (an old-style work of high dignity that could not be mistaken for anything but Ko-). It is , narrow, with a high , and a ; the is mixed with with a vivid , and the is in character with small irregularities, , slight below the , fine and . It is accompanied by an iron mounting thought to be contemporary with the blade, and it was long kept as a sacred treasure of the Izuo Hachiman Shrine in Higashi-Yoshino, Nara, with storage boxes made in Shōhō 3 (1646) and Kaei 6 (1853).
The designated in 1994 is , slender with a high and a , its with and . The is in character with small and , and , -dominant with adhering well, and the sources judge that 「総じて技巧味が目だたぬ穏やかな乱れとなり、古一文字の特徴がよく表示されている」 (overall the irregular temper is quiet, without conspicuous artifice, and shows the features of Ko- well). Its breaks off at the shortening and is read as having stated that the blade was a shortened Sukemune, so that 「所伝は充分に首肯し得るものである」 (the traditional attribution can be fully accepted).
The second Important Cultural Property, a 70.0 cm held by the Corporation of Osaka, is recorded with forging and a -, a fuller than the restrained temper the sources describe for the Ko- blades above.