Verification in Theo
Theo supports two different forms of verification. Citation Verification checks whether published evidence supports written claims. Derivation Verification checks the mathematical steps and dependencies inside a physics derivation. They answer different questions, and neither replaces expert scientific review.
Two verification workflows
Citation Verification checks whether references are real, whether their metadata is accurate, and whether each cited paper supports, contradicts, or provides insufficient evidence for the associated claim.
Derivation Verification uses the FirstPrinciples Step Level Verification Pipeline for Machine Generated Reasoning service to evaluate a structured mathematical derivation step by step. It is designed to identify where a derivation is supported, where executable evidence shows a problem, and where the system cannot safely decide. It is automatically executed after a call to the math phase.
How Theo checks a derivation
The step level verifier is a deterministic, non-LLM verification service. It does not require a reference solution. Instead, it converts the derivation into an executable dependency record and checks whether each step follows safely from its stated inputs.
Structure the reasoning — Record declared symbols, physical dimensions, semantic roles, assumptions, typed steps, claims, substitutions, and explicit parent steps.
Validate the basis — Check that dependencies are complete and acyclic, symbols are declared, dimensions are usable, assumptions are enforceable, and the stated domain can support a meaningful test.
Select one appropriate check — Choose a verification procedure from the structure of the step, such as dimensional analysis, substitution, algebraic identity, solve-and-back-substitute, reduction, manipulation, or approximation-order checking.
Return inspectable evidence — Record a verdict for each supported step together with the check used, an explanation, coverage information, and the relevant dependency context.
Understanding Verification Results
The Verification phase examines a mathematical derivation step by step using the checks applicable to each step. These may include symbolic comparisons, numerical tests, dimensional analysis, and checks that a conclusion follows from the steps it cites.
Verification helps identify issues and clarify which parts of a derivation could be assessed. It is not a formal proof or a guarantee that the assumptions, physical model, or final conclusion are correct.
Overall Verification Verdict
The verdict shown for the Verification phase summarizes both the verifier’s findings and how much of the derivation it could assess.
Verified
Every assessable step passed the verifier’s applicable checks.
Some structural steps, such as starting assumptions and declarations of method, may not be independently verified and are not necessarily included in the verification count. A numerical check provides evidence across the tested values but is not the same as a symbolic proof. Expand the step-level results to see which checks were performed.
Issues Found
The verifier found a potential issue in one or more highlighted steps. A dispute does not necessarily mean the step is wrong; notation, units, missing context, or verifier limitations may affect the check. Review the step-level explanation before changing the result.
Partially Verified
The verifier confirmed one or more assessable steps but could not make a reliable determination on the remaining steps. No assessed step produced an issue, but verification coverage is incomplete. Review the unadjudicated steps before relying on the result.
Verification Incomplete
The verifier could not make a reliable determination on any assessable step. This does not mean the answer is correct or incorrect; it means the current verifier could not assess it with confidence.
How the Overall Verdict Is Determined
If one or more steps are disputed, the overall verdict is Issues Found.
If every assessable step passes its applicable checks, the verdict is Verified.
If some assessable steps pass and others cannot be adjudicated, the verdict is Partially Verified.
If the verifier cannot reliably adjudicate any assessable step, the verdict is Verification Incomplete.
Starting assumptions and method steps that cannot be independently assessed are generally excluded from the verification count. However, an issue that can be established directly, for example, a dimensional inconsistency in a starting equation, may still affect the overall verdict.
Understanding Step-Level Results
Expand a step to see what the verifier checked, the evidence it found, and any limitations that prevented a determination.
Correct
The step passed the verifier’s applicable checks.
The explanation may indicate that:
The result follows exactly through symbolic substitution.
A closed-form expression satisfies the cited equations.
Coefficient matching establishes the relationship.
The step agrees numerically across independently sampled values.
When the result is based on numerical testing, it is evidence that the step is consistent with the cited equations over the tested values, not a symbolic proof.
Disputed
The verifier found evidence that the step may be incorrect or may not follow from the steps it cites. Read the expanded explanation before changing the derivation.
A disputed step can represent two different situations:
Incorrect as written: The step contains an issue that can be identified directly, such as the two sides of an equation having inconsistent dimensions.
Does not follow from the cited steps: The result may still be correct, but the cited steps do not establish it. This can occur when a necessary intermediate step was not cited, two steps use different names for the same quantity, relevant context is missing, or the claim itself is incorrect.
Unadjudicated
The verifier could not reliably determine whether the step is correct. The expanded explanation describes why the check could not be completed.
This may occur when the step depends on information the verifier cannot evaluate confidently, such as nonlinear elimination, unconstrained quantities, unevaluated functions or integrals, ambiguous solutions, insufficient premises, or missing equations.
An unadjudicated result should not be interpreted as either confirmation or rejection of the step.
Root
A root step is a starting assumption, known definition, established law, or other statement from which the derivation begins. Because it does not follow from an earlier step, the verifier generally cannot independently confirm it.
The verifier may still detect properties of the equation itself, such as a dimensional inconsistency.
Method
A method step introduces an approach, notation, substitution, or standardized technique rather than a mathematical claim the verifier can independently adjudicate. The equations produced by the method are checked in subsequent steps.
Interpreting Verification Carefully
Verification results should be treated as structured assistance for reviewing a derivation—not as a replacement for scientific judgment.
When reviewing a result:
Start with the overall verdict to understand the findings and coverage.
Expand disputed and unadjudicated steps to read the specific explanation.
Check whether the correct assumptions, definitions, units, and preceding steps were provided.
Revise the derivation or its citations when relevant, and run Verification again.
Independently review important conclusions, especially when verification is partial, incomplete, or based on numerical evidence.
Limits and current availability
Citation Verification is available as a user-facing phase for suitable reports and uploaded documents.
Step Level Verification is currently implemented as an automatic add on to math phase, Sage, Mathematica and OpenAI based Math executions can produce a structured trace for automatic verification. Availability depends on workspace configuration.
The verification path currently applies to supported structured physics and mathematics derivations. Some mathematical objects, ambiguous branches, unsupported operations, or unsafe inputs may be left unadjudicated or may prevent verification.
If Theo does not display or explicitly report a result, do not assume that the verifier ran. A model explanation, a Sage or Mathematica computation, and a verification verdict are different kinds of evidence.
Verification is an additional research control, not a substitute for checking assumptions, reviewing the derivation, reproducing the computation, or obtaining expert review for consequential work.