conjecturally

Conjecturally is an adverb used to describe something that is based on conjecture rather than on established proof. It signals that a claim, interpretation, or result is provisional, believed or expected, but not yet demonstrated to be true.

In mathematics, philosophy, and empirical sciences, statements labeled conjectural are supported by evidence, intuition, or partial results but remain unproven. The term serves to warn readers that conclusions may change with new data or arguments. It differs from hypothetical, which relates to imagined scenarios, whereas conjectural refers specifically to the inferential status of a claim.

Etymology: Conjecturally derives from conjecture, from Latin coniectura "a guess" and from conicere "to throw together" (con- "together" + iacere "to throw"), with the adverbial suffix -ally forming conjecturally.

Usage examples: "The conjecturally defined object behaves as expected in simulations." "Conjecturally, the solution extends to a broader class, though a proof is not yet known." In mathematics many conjectures motivate research and some are eventually proved, while others are refuted.

Related terms include conjecture (the noun), conjectural (adjective), as well as hypothetical and hypothesis, in addition to proof and theorem.