Beginning of the Mid antiquity:

History of Manchuria is in the names. Hae Mo-su (解慕漱) established Northern Buyeo in the southern Manchuria . Hae Mo (解慕) is PSMCs of Gae-ma (蓋馬: 蓋; gài gě hé音合; hé gě). Su(漱) meant a person ran away leader (澣) who settled in the (醫巫閭山, 鮮卑山, 黑[hēi] hēi hè/흐어/해山, 富山) nearby the Old Capital(舊都, 骨都, 訖升骨城).
The King Bi丕 was killed in the Old Capital in the west of Liao River. Wie Man (魏滿) came back to north and settled in the old capital where the King Bi had been killed . Wie Man is Hae Mo-su had two sons; Hae Buru and Jumong (解夫婁與朱蒙) from different mother. Jumong settled in the east of Liao River and built the Goguryeo . Hae Buru (解扶婁/解夫婁; 86 – 48 BCE) means Hae from the Buyeo.
The Spring and Autumn Annals(春秋傳) has the phrase “附𡝤”, Korean scriptures; Samguk yusa and Tongsa Chŏryo(東史節要) interpreted as Buyeo that Buru is the son of Dangun . Hae Buru is mythical king Geumwa (金蛙), moved the capital eastward, had seven sons. His first son is Daeso (帶素; 60 BC – 22 AD) who was killed in the battle against Goguryeo . Whereabout the other sons of Hae Buru are unknown.
The logogram “Wa蛙 in 金蛙” appears in the Zhuangzi(莊子 外篇) and Xunzi (荀子 正論) as metaphorical description related to the mystical leader “河伯”, the maternal ancestor of Goguryeo .
Hae Buru descendants were recorded as Buyeo (扶餘, 百濟王扶餘) meaning helpful Buyeo people to the southerners by Chen Shou. The other sons of king Geumwa had moved down to south through the waterway, where their ancestor Wie Man used to govern (真番朝鮮, 滿潘汗為界, 遼東郡番汗縣) along the coastal region, known as Michuhol (彌鄒忽) of Baekjae (伯濟) which has meaning ten families lead by the first son.
Although they revealed the source of information as “魏略曰, 古典記 and 壇君記云” which came from the Bamboo Scripts unearthed in 279, history of Baekjae in the continent was concealed.

Southwestern Boundary of Joseon in Manchuria:
The Gutal in the Ya valley was in dispute between Xiongnu and Dong-hu. The Ancient Cliff dwellings (古崖居遺趾) in the north of Beijing appears to be the Gutal . It was the same place where the son No-Kwan (盧綰子, 亞谷侯) was appointed as the King of Dong Hu and remained as the western boundary of Old Joseon under the King Bi written in the Biography of Zhao family . The title Earl(侯) had been carried on till the beginning of Emperor Wu. It was recorded as Ya valley(亞谷) in Shiji, but Village of bandit (惡谷)in the Book of Han. The King of Gutal (甌脫王) was captured by the southern power around 80 BC . it shouldn’t be far away from the Beijing vicinity.
New Emperor of Qin chose the best geographic terrain to protect Dong Hu (朝鮮胡) invasion . They named it as the Pei Creek(浿水), which is the small creek, Shihe Creek(大石河) passing through the Shan-hai Pass in the southwestern shore of Balhae Bay . Han built the frontier fortress by the Pei Creek. Distal segment of Pei Creek passing through lots of gravel spread out to the sea. The Great historian named the Pei Creek as Eonsu(衍水; meaning spill over), where the Yan Crown Prince Dan (太子丹) committed suicide. Hence, the Eonsu(衍水) got the nick name as the Crown prince river (太子河).

Han army had caught the King of Gutal, chased out the Xiongnu, and arrived at the shore of Bohai bay where the Great Wall of Qin ended and retuned. Sima Qia name the place as “臨翰海” meaning arrived at the Hahn-he . The capital (都王險) of King Ugeo (右渠) shouldn’t be too far away from the Pei creek and Liekou (洌口) in Liaodong where Han Navy disembarked. Liekou (洌口; meaning entrance to the Liek river) is the current Luan River(灤河) in the south of Shanhai Pass.
Yet, Chinese scriptures tempered the original location of Pei Creek to the east of current Liao River. They implanted the PSMCs of Pae “浿 to 沛” and applied [nick name Crown prince river] into the south of Liaoyang City (梁貊部落), where the high officer known as Pae-ja(沛者) of Goguryeo .
As they shuffling around, all the names such as “遼東, 浿水, 王險城 =王儉城” around the eastern end of the Great wall had been relocated to the east of Liao River. As a result, they created out of common sense, the Great Wall passing over the Liao River in the middle of southern Manchuria.
By looking over the record of various battle against Xiàng yǔ (項羽) and Xiongnu and Han era census, the Han Lelang county (樂浪郡, 낭랑, Nang-nang by Korean) included most southwestern part of Old Joseon (戰國時燕國)territory extending to (薊, 無終) the east of Beijing region . The Shiji and Book of Han have the word Yang-pyeong(襄平) in the Tianjin municipality where Gonsun Yuan established power base and captured.