Co-scientists and agentic scientific claim verifiers are increasingly used to assess claims across the sciences.
Natural-language scientific claims, written for human experts, are often underspecified and so admit several defensible interpretations.
This leads to disagreements with expert labels that cannot be traced to the evidence or the interpretation, and to compute spent on unchecked interpretations.
We introduce Claim Cards to make such interpretations explicit in the reasoning itself.
A Claim Card records a verifier's interpretation as nine fields before evidence gathering, each marked stated, inferred, or default.
To test whether an agent's interpretation can change its verdict, we ran a GPT-5.4 agent five times on each of 60 expert-labeled materials-science and biomedical claims with a card, without one, and with one card frozen across runs (900 runs).
Over 40% of card fields were not marked stated, and a card added about a tenth to a run's GPT-5.4 tokens and time without measurably changing agreement with expert labels.
The agent's own interpretations varied between runs, although within a claim this variation did not measurably track the verdict.
A deliberate change to one field of the frozen card, however, making the quantifier universal or the threshold for support stricter, changed the verdict on about a third of the claims, against about one in seven expected by chance (p < 0.001 for each edit).
On 24 materials-science claims run with computational tools, the stricter threshold also changed what the agent asked those tools to compute.
We therefore argue that verdicts should be reported with their interpretations and that benchmarks could publish the interpretation behind each label.