Verifiable reward: A reward signal derived from an outcome, execution, proof state, trace, or other artifact that can be checked with reasonable reliability.
Verifier: The mechanism that performs that check, whether symbolic, executable, formal, learned, or hybrid.
Reward signal: The scalar or graded feedback that learning actually sees after verification.
Interface: The part of the task exposed to checking, such as a final answer, a program, a proof state, a citation set, or an environment trajectory.
Outcome verifier: A checker that scores a completed solution rather than its intermediate steps.
Process reward: A reward signal attached to intermediate reasoning, subgoals, or partial traces rather than only the final artifact.
Programmatic verifier: A rule-based checker implemented through deterministic logic, execution, or formal constraints.
Learned verifier: A model-based judge that predicts correctness, quality, or consistency.
Verifier stack: A layered pipeline that combines multiple checks before producing a reward or decision.
Signal quality: How informative, stable, and hard to game the reward is for the capability of interest.
C.2 Evaluation, reporting, and robustness terms
Base model and checkpoint: The starting policy and exact checkpoint used before RLVR or test-time intervention.
RLVR model and checkpoint: The trained policy and exact checkpoint whose improvement is being claimed.
Training verifier: The verifier whose score is used as reward during RLVR.
Evaluation verifier: The verifier or benchmark grader used to report results after training.
Independent audit verifier: A separate checker, judge, harness, or human audit path used to test whether the policy overfit the training verifier.
Audit suite: A held-out set of checks, examples, adversarial probes, or human review items used to test the verifier itself.
High-reward tail: The region of outputs selected by best-of-\(N\), search, or gradient optimization because the verifier scores them highly.
pass@1: Single-sample policy quality under the specified decoding setup.
pass@\(N\): Policy plus sampling; the probability that at least one of \(N\) samples passes the checker.
Search-guided score: A system-level score that includes active test-time control, reranking, verifier-guided search, or tool-mediated exploration.
Generation budget: The number of samples, tokens, tool calls, search steps, or other generation-side work used to produce the answer.
Verification budget: The number or cost of tests, judge calls, proof checks, environment runs, or other verifier-side work used to score or select the answer.
Hidden-test status: Whether the policy trained against the same tests being reported, and whether a separate hidden or independent suite was used.
Contamination audit: Checks for prompt, answer, partial-prompt, trace, and test leakage across pretraining, SFT, preference data, RL data, and synthetic data construction.
Regression tax: Calibration, abstention, refusal, safety, instruction-following, latency, or cost regressions paid elsewhere while improving the target score.
Faithfulness: The extent to which an externalized explanation tracks the causal basis of the model’s answer.
Calibration: The relationship between expressed confidence and actual correctness.
C.3 Agentic terms
Harness: The environment-backed interface that turns a model rollout into trainable and auditable data, including task inputs, tool access, state, execution, logging, and reward computation.
Deployment interface: The real interface the system will use at serving time, including tools, state, latency limits, user inputs, and logging.