The phrase "asserted only when" is correct and usable in written English.
It can be used in contexts where a statement or claim is made under specific conditions or circumstances.
Example: "The theory is asserted only when sufficient evidence is presented to support it."
Alternatives: "claimed solely when" or "stated exclusively when".
It is asserted that only when commonly available sources of information are eliminated is the subject forced to rely on assumptions.
The forced feedings, Guantánamo and Justice Department officials have asserted, occur only when a detainee's hunger strike poses a major health risk.
Thus just as mathematicians will assert P only when they have decided that P holds by proving it, they may assert P ∨ Q only when they either can produce a proof of P or else produce one of Q. Classical logic gets round this by widening the interpretation of disjunction: it interprets P ∨ Q as ¬ ¬P∧¬Q), or in other words, "it is contradictory that both P and Q be false".
In 1882, when she was four months short of two years, medical knowledge could assert only "acute congestion of the stomach and brain," though later speculation proposes meningitis or scarlet fever.
Even his colour asserts only itself.
Some analysts have asserted that it is only when the health needs of migrants are addressed would the host countries be able to support the health of the country as a whole [ 14].
Echoing the Laozi (Chapter 18), Ji Kang asserts that it is only when the "great Dao" fell into disuse that is, when selfishness and strife rendered natural, prereflective kindness out of the ordinary that benevolence and righteousness came to be treasured as acquired, remedial virtues.
Direct observations, which were not quantified, asserted that pecking was performed only when the birds were present in the zone.
During this short period of Whig administration, the king allowed his ministers to discuss (abortively) peace with Napoleon and to abolish the slave trade; he asserted himself and forced their resignation only when they dared to propose some amelioration of the laws against Roman Catholics.
A distinct lack of solidarity, a nearly genetic inability to regard neighbors' points of view, resulted in uncontrollable, fairly non-stop, gruesomely bloody western range wars in the post-Civil War decades, abating only when federal authority asserted itself and created...rules...rules
