Supposed, supposititious, suppositious, reputed, putative, purported, conjectural, hypothetical can mean accepted or advanced as true, real, or in accordance with the facts on the basis of less than conclusive evidence.
All imply a measure of doubt of what is asserted and may serve as a disclaimer of responsibility for the assertion.
Supposed is likely to imply rather general or common acceptance of what is asserted, though suggesting the presence of uncertainty or conflicting evidence or the likelihood of error.
Supposititious occasionally comes close to supposed , but usually it carries distinct and positive suggestions of fraudulence or spuriousness.
Suppositious is used chiefly to imply that a belief or assertion is based on theory or on a postulate or hypothesis, and lacks factual support.
Reputed , putative , and purported imply a basis in tradition or in popular belief.
Reputed in itself is usually a thoroughly neutral word, but can be strongly colored by context.
Putative describes something that is commonly or generally accepted but about which the describer reserves certain doubts. In its common legal use it applies to a thing or person that may be subject to proof that it is not what it is generally accepted to be; thus, a putative marriage is one duly formalized but to a greater or less degree invalid because of some impediment (as consanguinity).
Purported may differ little from reputed and putative , but especially in its common journalistic use the word tends to stress the writer’s disclaimer of responsibility for the matter asserted (compare alleged under ADDUCE ) and may approach rumored in meaning.
Conjectural implies inference from incomplete or defective evidence, and what is so described is offered as a possibility or likelihood but not as a fact.
Hypothetical describes someone or something (as a principle, a situation, or a question) that is invented or put forward as possibly true or as likely to be true in the main if not in detail, or as the tentative basis for continuing an argument or investigation.