Question: Who were the two parties fighting in the war where Kajiwara Heima served as karō?

Context paragraphs:
Two-party system: A two-party system is a party system where two major political parties dominate the government.  One of the two parties typically holds a majority in the legislature and is usually referred to as the "majority" or "governing party" while the other is the "minority" or "opposition party".  Around the world, the term has different senses.  For example, in the United States, Jamaica, and Malta, the sense of "two party system" describes an arrangement in which all or nearly all elected officials belong to one of the only two major parties, and third parties rarely win any seats in the legislature.  In such arrangements, two-party systems are thought to result from various factors like winner takes all election rules.  In such systems, while chances for third party candidates winning election to major national office are remote, it is possible for groups within the larger parties, or in opposition to one or both of them, to exert influence on the two major parties.  In contrast, in the United Kingdom and Australia and in other parliamentary systems and elsewhere, the term "two-party system" is sometimes used to indicate an arrangement in which two major parties dominate elections but in which there are viable third parties which do win seats in the legislature, and in which the two major parties exert proportionately greater influence than their percentage of votes would suggest.

Self-enforcing agreement: A self-enforcing agreement is an agreement or contract between two parties that is enforced only by those two parties; a third party cannot enforce or interfere with the agreement.  This agreement stands so long the parties believe the agreement is mutually beneficial and the agreement is not breached by either party.

Boshin War: The Boshin War (戊辰戦争 , Boshin Sensō , "War of the Year of the Yang Earth Dragon") , sometimes known as the Japanese Revolution, was a civil war in Japan, fought from 1868 to 1869 between forces of the ruling Tokugawa shogunate and those seeking to return political power to the Imperial Court.

Communist Party of Nepal (Unity Centre–Masal): Communist Party of Nepal (Unity Centre–Masal) (Nepali: नेपाल कम्युनिष्ट पार्टी (एकताकेन्द्र–मसाल) ) was an underground communist political party in Nepal.  CPN(UC–M) was formed in 2002 through the merger of Communist Party of Nepal (Unity Centre) and Communist Party of Nepal (Masal).  The merger of the two parties was announced at a public meeting on April 22, 2002 by the general secretaries of the two parties, Ram Singh Shris of CPN(Masal) and Narayan Kaji Shrestha (Prakash) of CPN(UC).  The CPN(UC–M) adhered to Marxism–Leninism–Mao Zedong Thought as its ideological basis.  The founding general secretary of CPN(UC–M) was Mohan Bikram Singh.  The two electoral mass fronts of the two parties merged into Janamorcha Nepal.  The Janamorcha Nepal joined the Seven Party Alliance and took active part in the 2006 Loktantra Andolan.

Kajiwara Heima: Kajiwara Heima (梶原 平馬 , 1842? -1889) was a Japanese samurai of the late Edo period who was a retainer of the Aizu domain.  He served as a "karō" in the Aizu administration, and supervised political affairs during the Boshin War, also attending to matters of arms procurement.  After the war, he went to Nemuro, and died there.  His grave in Nemuro was recently rediscovered.

Yamakawa Futaba: Yamakawa Futaba (山川 二葉 ) (1844 – November 14, 1909) was a Japanese educator of the early Meiji era.  Born in Aizu, she was the sister of the "karō", Yamakawa Hiroshi; her other siblings included physicist Yamakawa Kenjirō and Meiji-era social figure Ōyama Sutematsu.  Futaba took part in the defense of Tsuruga Castle in the Boshin War (1868-9).  She was also briefly married to Kajiwara Heima, another Aizu "karō".

Mise of Lewes: The Mise of Lewes was a settlement made on 14 May 1264 between King Henry III of England and his rebellious barons, led by Simon de Montfort.  The settlement was made on the day of the Battle of Lewes, one of the two major battles of the Second Barons' War.  The conflict between king and magnates was caused by dissatisfaction with the influence of foreigners at court and Henry's high level and new methods of taxation.  In 1258 Henry was forced to accept the Provisions of Oxford, which essentially left royal government in the hands of a council of magnates, but this document went through a long series of revocations and reinstatements.  In 1263, as the country was on the brink of civil war, the two parties agreed to submit the matter to arbitration by the French king Louis IX.  Louis was a firm believer in the royal prerogative, and decided clearly in favour of Henry.  The outcome was unacceptable for the rebellious barons, and war between the two parties broke out almost immediately.

Trusted third party: In cryptography, a trusted third party (TTP) is an entity which facilitates interactions between two parties who both trust the third party; the Third Party reviews all critical transaction communications between the parties, based on the ease of creating fraudulent digital content.  In TTP models, the relying parties use this trust to secure their own interactions.  TTPs are common in any number of commercial transactions and in cryptographic digital transactions as well as cryptographic protocols, for example, a certificate authority (CA) would issue a digital identity certificate to one of the two parties in the next example.  The CA then becomes the Trusted-Third-Party to that certificates issuance.  Likewise transactions that need a third party recordation would also need a third-party repository service of some kind or another.

Relay attack: A relay attack in computer security is a type of hacking technique related to man-in-the-middle and replay attacks.  In a classic man-in-the-middle attack, an attacker intercepts and manipulates communications between two parties initiated by one of the parties.  In a classic relay attack, communication with both parties is initiated by the attacker who then merely relays messages between the two parties without manipulating them or even necessarily reading them.

Unite the Right: The Unite the Right movement was a Canadian political movement which existed from around 1996 to 2003.  The movement came into being when it became clear that neither of Canada's two main right-of-centre political parties, the Reform Party of Canada/Canadian Alliance (CA) and the Progressive Conservative Party of Canada (PC), was independently capable of defeating the governing Liberal Party.  The objective of the movement, therefore, was to merge the two parties into a single party (or, if this was not possible, to find a power-sharing arrangement between the two parties).  The goal of uniting the right was accomplished in December 2003 with the formation of the Conservative Party of Canada.

Supporting paragraphs: Kajiwara Heima Boshin War
Answer: Tokugawa shogunate and those seeking to return political power to the Imperial Court