These are all words for a statement that sth is true, although it has not been proved.以上各词均表示未经证实的说法。
claima statement that sth is true, although it has not been proved指声称、宣称、断言
allegation(ratherformal) a public statement that is made without giving proof, accusing sb of doing sth that is wrong or illegal指无证据的说法、指控
assertion(ratherformal) a statement of sth that you strongly believe to be true, although it has not been proved指明确肯定、断言
claim or assertion?用 claim 还是 assertion？
When the point in doubt is a matter of opinion, not fact, use assertion.表示坚持观点而非断言属实，用 assertion：◆She made sweeping claims about the role of women in society.When you are talking about a matter of fact you can use either word; an assertion may be slightly stronger than a claim and it is a more formal word.表示断言属实，两词可以通用。assertion 比 claim 语气稍强，且更正式。