VStress: Correlation-Aware Auditing and Adaptive Budget Allocation for Repeated Verifiers

• Repeated calls add evidence only when extra views contain independent information, so a useful audit reports quality, coverage, selective accuracy, call cost, and correlation together.Source: §1 · p. 1
• VStress freezes an auditable decision and view ledger before joining the clean oracle, preventing post-hoc scoring from influencing the online vote.The contract uses immutable payloads, a hidden clean label, and a declared corruption family to create five observed views.Source: §1 · pp. 1–2
• The controlled study identifies dependence mechanisms, while the application study tests whether measured dependence guides fixed-budget calls and downstream RLVR.The audit contract and allocation rule are treated as separate components.Source: §1 · p. 1
• Conditional marginal discriminability from a sealed calibration split values an unqueried verifier by the information it adds beyond channels already observed.Source: §1 · p. 2
• VSTRESS-CA combines cost-normalized, uncertainty-aware allocation with selective stopping and a conservative fallback when deployment dependence shifts.Source: §1 · pp. 1–2
• The validation compares measured dependence and repeated-verifier evidence with breadth under the same call budget, then checks matched downstream RLVR endpoints.The paper reports overlap, association, mutual information, disagreement, and realized held-out gain.Source: §1 · pp. 1–2

• Existing work motivates the components but does not specify a common post-decision audit boundary; VStress makes that boundary explicit and uses measured conditional information for online acquisition rather than presenting a new learner.Source: §2 · p. 2
• Selective prediction and cost-aware routing motivate the ingredients, while reward-model and process-verifier studies expose systematic and semantic failure modes (Lambert et al., 2024; Zheng et al., 2024).Source: §2 · p. 2
• Recent correlated-error and verifier-robustness studies provide the closest external comparison points.Source: §2 · p. 2

3.1 TASK DEFINITION AND INFORMATION BOUNDARY

• For a fixture item, the online aggregator receives five corrupted views while the clean binary oracle remains in a post-hoc file joined after the decision.Runs use a stable source identifier and a SHA-256 manifest.Source: §3.1 · p. 2

3.2 METHOD OVERVIEW

• Calibration estimates channel reliability, failure rate, cost, and conditional dependence; online acquisition records verdicts and costs, freezes the prediction, then scores held-out traces and reuses the ledger in RLVR.Source: §3.2 · p. 2

3.3 CORRUPTION AND AGGREGATION

• Five-view majority uses the count of positive views, accepts only at agreement of at least 0.8, and reports quality, coverage, selective accuracy, and call measures after trace freeze.The independent-view majority-error expression does not necessarily apply under partial correlation, even when corruption is below one half.Source: §3.3 · pp. 2–3

3.4 CORRELATION-AWARE VERIFIER ALLOCATION

• Conditional marginal discriminability estimates an unqueried channel’s information given queried channels, using calibration rows, uncertainty, and calibrated cost to choose the highest-utility option.A channel is valued only for information not already present in the queried views; model or provider identity is not a proxy for independence.Source: §3.4 · p. 3

3.5 STOPPING AND DEPENDENCE-SHIFT FALLBACK

• The controller accepts when the calibrated posterior clears its threshold, continues only within budget while the best utility exceeds its threshold, and otherwise abstains; a dependence-shift alarm disables channel preference and invokes exact-stop.Source: §3.5 · p. 3

3.6 TRAINING AND INFERENCE CONTRACT

• The inference contract records each valid verdict or failure and cost before oracle access, then scores the frozen ledger; repeated-verifier and RLVR arms retain provenance for their respective traces and learner settings.The protocol is linear in the number of views, with O(k) calls and ledger fields per item.Source: §3.6 · p. 3

4.1 EXPERIMENTAL SETUP

• The setup uses 512 ordered records, a periodic binary oracle hidden from online aggregation, seven deterministic corruption seeds, and held-out item- or task-level intervals.The online protocol freezes its ledger before the offline oracle join, which reports quality, coverage, dependence, and cost diagnostics.Source: §4.1 · p. 3, Figure 1 · p. 4

4.2.2 QUALITY–COVERAGE–COST FRONTIER

• VSTRESS-CA reaches the largest balanced accuracy and RLVR score in the matched breadth–redundancy comparison under the same call budget.The comparison uses the same candidate pool and reports calls per item, verified items, and accepted updates.Source: §4.2.1 · p. 4, Table 2 · p. 5

4.2.1 MEASURED DEPENDENCE AND ADAPTIVE ALLOCATION

• The cross-family pair has the lowest error overlap and largest conditional marginal gain in the measured-dependence comparison.Table 1 compares error overlap, association measures, and realized incremental value.Source: §4.2.1 · p. 4, Table 1 · p. 4

4.2.2 QUALITY–COVERAGE–COST FRONTIER

• At 35% symmetric corruption, majority-5 raises balanced accuracy from 0.6578 to 0.7739; at 65%, majority voting loses 0.1226 points.At 35%, coverage is 0.4919, selective accuracy is 0.8953, and cost is five calls per item.Source: §4.2.2 · p. 4, Table 3 · p. 5

4.3.1 CORRELATION AND SEQUENTIAL STOPPING

• As common-cause strength increases from zero to one, the paired gain falls from +0.1102 to zero; sequential-safe stopping preserves the majority decision at 4.6934 mean calls.The equal-budget audit compares majority-5, a weighted control, and sequential-safe stopping.Source: §4.3.1 · p. 5

4.3.2 MATCHED REAL-VERIFIER AND RLVR EVALUATION

• On held-out repeated-verifier items, low-dependence channels reach BA 0.8017, coverage 0.5874, and selective accuracy 0.9186 at cost 4.96.The matched RLVR endpoint is 0.6429 for majority-5 and 0.6408 for sequential-safe, versus 0.6127 for single-call.Source: §4.3.2 · p. 5

4.3.3 FAILURE TAXONOMY AND COVERAGE ACCOUNTING

• Failure accounting records unavailable, timed-out, malformed, schema-disagreeing, and common-cause verdicts before aggregation, with each event consuming its declared call budget.Coverage uses the original item denominator, while selective accuracy uses accepted items; the 65% symmetric-corruption case remains in the reported frontier.Source: §4.3.3 · p. 5

4.3.4 COST-NORMALISED DOWNSTREAM LEARNING

• The downstream study fixes the learner, optimizer, schedule, seeds, task splits, and verifier cache, comparing aggregation at equal verifier-call budgets and secondarily at equal wall-clock or token cost.Held-out task score, coverage, calls, token cost, latency, and paired uncertainty are evaluated at each checkpoint.Source: §4.3.4 · p. 6

5 DISCUSSION

• BA 0.6538 and RLVR score 0.6417 were reached with 3.4216 calls per item, above the corresponding redundancy row on reported quality endpoints.The discussion frames these as fixed-budget results, not evidence that implementation identity implies independence.Source: §5 · p. 8
• When an unqueried channel adds conditional information, repetition buys evidence; when errors are redundant, fixed repetition wastes calls and can displace items covered by breadth.The breadth comparison keeps the total call budget explicit.Source: §5 · p. 8
• If deployment dependence leaves calibration support, the conservative response is to disable channel preference and use exact-stop.Source: §5 · p. 8

6 LIMITATIONS, ETHICS, AND BROADER IMPACT

• Conditional-information estimates become noisy when the channel pool is large relative to the calibration set, and low measured dependence does not establish causal independence.Shared training data, reasoning templates, infrastructure, or failure causes can remain latent; a shift preserving observable verdict and failure summaries can evade monitoring.Source: §6 · p. 8
• The evaluation fixes a binary task, bounded verifier pool, and matched candidate cache; multiclass and larger-pool settings need structured estimators beyond exact conditional tables.The controlled periodic oracle identifies a mechanism, while real-verifier and RLVR arms bound deployment relevance under recorded channels and seeds.Source: §6 · p. 8
• Raw verifier outputs, implementation identifiers, latency, and failure codes should be access-controlled and stripped of personal or sensitive content before publication.The replay manifest stores hashes and aggregate traces for auditability.Source: §6 · p. 8
• Broader deployment can improve reliability when cost, coverage, and failure boundaries are monitored together, but shared prompts, data, or infrastructure can concentrate model or provider bias.The paper recommends reporting channel diversity, class-wise coverage, calibration splits, and service cost beside aggregate scores.Source: §6 · p. 8

7 CONCLUSION

• BA 0.6538, selective accuracy 0.6892, and RLVR score 0.6417 were reported at 3.4216 calls per item in the matched comparison.Source: §7 · p. 8
• The audit contract and allocation policy distinguish marginal quality from conditional marginal value: another verifier is useful only when it adds information beyond queried channels.The resulting procedure audits whether, where, and how much repeated verification is worth paying for when errors are dependent.Source: §7 · pp. 8–9
• Generative AI tools were used for language polishing and summarizing cited references, not to generate results, datasets, mathematical claims, proofs, or research conclusions.The authors state that they designed and verified the methodology, experimental setup, analysis, and interpretation.Source: AI-USE · p. 9

ETHICS STATEMENT

• The study evaluates a controlled binary fixture, held-out verifier traces, and downstream learning tasks, with no human subjects, personally identifiable information, or interventions.Source: ETHICS STATEMENT · p. 9
• Verifier outputs, implementation identifiers, latency, and failure codes should be access-controlled and scrubbed of sensitive content before release.The protocol records these logs.Source: ETHICS STATEMENT · p. 9
• Dependence-aware abstention and fail-closed handling make uncertain or inconsistent evidence visible for human review.Source: ETHICS STATEMENT · p. 9

REPRODUCIBILITY STATEMENT

• The supplementary material contains code, configurations, replay schemas, tables, figures, and artifact metadata for reproducing the analysis.It also describes data construction, run commands, model settings, and validation checks.Source: REPRODUCIBILITY STATEMENT · p. 9

A.1 FIXTURE PAYLOAD AND ORACLE CONSTRUCTION

• The 512 fixture records are ordered and hash-bound, with immutable identifiers and a local periodic oracle.The replay manifest records fixture order, payload hash, oracle provenance, corruption seed, and view order.Source: §A.1 · p. 13, Table 7 · p. 13

A.2 CORRUPTION DATA-GENERATING PROCESSES

• Symmetric corruption flips views at rate ρ, false-positive corruption preferentially changes negative labels, and partial correlation mixes independent draws with a common latent draw.Agreement and class-wise selective metrics are recomputed for every seed.Source: §A.2 · p. 13, Table 8 · p. 13

A.4.1 CROSS-FIXTURE AND REAL-ANCHOR REPLAY

• The fixed operating point is selected on fixture 1001 and replayed on four held-out controlled fixtures; the real-anchor cache holds one frozen verdict per item.Repeated calls must provide raw verdicts and implementation IDs for every view.Source: §A.4.1 · p. 13

A.4.2 REPEATED REAL-VERIFIER PROTOCOL

• Each candidate receives five genuine verifier calls or two separately implemented channels, with raw verdicts and implementation, cost, latency, cache, and failure metadata retained.Calibration selects the operating point, and a disjoint held-out set supplies the final frontier.Source: §A.4.2 · p. 13

A.4.3 DOWNSTREAM RLVR PROTOCOL

• The downstream study holds the candidate cache, learner manifest, checkpoint hashes, three training seeds, verifier traces, and held-out evaluations in a matched protocol.The aggregator is the only changed component between single-call, majority, and sequential-safe arms.Source: §A.4.3 · p. 13

A.3 SEQUENTIAL BUDGET AND SENSITIVITY AUDITS

• The sequential controller observes corrupted views, vote margin, remaining budget, and the stopping rule; exact-stop preserves the final majority decision while prefix-stop is a distinct policy.The sequential and sensitivity audits report call savings and sweep views, thresholds, corruption, and class prior under the same manifest.Source: §A.3 · p. 13, Table 9 · p. 14, §B.4.2 · p. 16

B.1 REPLAY MANIFEST AND ARTIFACT IDENTITY

• The artifact bundle includes source and dependency hashes, fixture and split hashes, corruption seeds, raw observations, ledger transitions, and clean-oracle provenance.Private credentials and host identifiers are kept outside the manuscript tree.Source: §B.1 · p. 14

B.2 FULL FIXTURE PAYLOAD AND ORACLE

• Each fixture row binds an immutable payload ID, ordered prompt fields, periodic binary oracle, and source hash; the online aggregator sees no oracle.A changed sampler or payload hash creates a new manifest and cannot overwrite the measured table.Source: §B.2 · p. 14

B.3 CORRUPTION FAMILY FORMULAS

• Partial correlation mixes independent draws with a common latent draw, and keyed view draws are reused across declared sweeps to separate dependence changes from class-balance changes.The sensitivity audit uses a fixed first-view baseline and reports coupled quality and cost fields.Source: §B.3 · p. 14, Table 11 · p. 15

C.7.1 VERIFIER POPULATION AND LOW-DEPENDENCE-CHANNEL SCALING

• In this replay, low-dependence-7 had the highest balanced accuracy at 0.8070, 0.0884 above the single-call reference at 0.5486 coverage; repeated common-cause calls reached 0.7224 with five nominal calls.Source: §C.7.1 · p. 19

C.7.2 DOMAIN-TRANSFER AND DIFFICULTY-STRATIFIED REPLAY

• A hard-bin paired gain of 0.0716 accompanies sequential-safe retaining at least 98.4% of majority quality with 0.4873 fewer calls per item.The transfer replay covers listed task families and difficulty bins.Source: Table 28 · p. 20, §C.7.2 · p. 20

C.7.3 CORRELATION FAMILIES BEYOND THE COPY GATE

• The paired gain falls from +0.1102 for independent views to -0.0125 at 0.90 adversarial alignment, with first-view error rates matched across dependence families.The reported ordering is specific to the listed dependence generators.Source: Table 29 · p. 20, §C.7.3 · p. 20

C.7.4 BUDGET AND STOPPING-POLICY GRID

• Adaptive-confidence reaches 0.9026 selective accuracy at 3.8641 calls per item, saving 1.1359 calls against five-call majority; prefix-stop has higher coverage but lower selective accuracy.The policies are assessed over budgets of one, three, five, and seven calls.Source: Table 30 · p. 20, §C.7.4 · p. 20

C.7.5 HUMAN AND ORACLE AGREEMENT AUDIT

• Accepted high-margin items have 0.9478 agreement; the paired check records 0.9246 for majority and 0.9198 for sequential-safe at lower review cost.Abstained and verifier-failure strata have agreement of 0.8750 and 0.9297, respectively.Source: Table 31 · p. 21, §C.7.5 · p. 21

C.7.6 LONG-HORIZON RLVR STABILITY AND REWARD-HACKING CHECKS

• Majority-5 raises the 36,000-step held-out task score from 0.6189 to 0.6537 (+0.0348), while sequential-safe reaches 0.6516 at 9.22% lower training cost.The verifier-shift arm retains a +0.0175 improvement over single-call; this is a separate horizon from the main-text 18k endpoint.Source: Table 32 · p. 21, §C.7.6 · p. 21

C.7.7 LATENCY, THROUGHPUT, AND COST SCALING

• Batch-32 reaches 2.684 items/s at 5.74 s p95, while held-out task score varies by at most 0.0025 across operating points; paired intervals retain positive BA and task-score gains.The corresponding 95% interval widths are 0.0522 and 0.0138.Source: Table 33 · p. 21, §C.7.7 · p. 22, Table 34 · p. 22

C.7.9–C.7.11 CLASS-PRIOR, FAILURE, AND CALIBRATION AUDITS

• Changed-prior and multiclass rows retain a +0.0487 macro-balanced-accuracy gain; mixed failures lose 0.0318 balanced-accuracy points, while mixed calibration yields a 0.0177 optimistic shift.The calibration-only and time-ordered rows retain held-out gains of 0.0831 and 0.0740.Source: Table 35 · p. 22, §C.7.9 · p. 22, Table 36 · p. 22

C.7.13 REPRODUCIBILITY STAGES

• The replay uses hash-checked stages with configuration, input and output digests, and validated row counts; all five reproduce the same endpoint within 0.0001.No row is silently dropped between trace and table.Source: §C.7.13 · pp. 23–24, Table 39 · p. 23

C.7.14 FAILURE TAXONOMY AND QUALITATIVE CASE AUDIT

• Independent disagreement is the largest qualitative failure class (29/512); the held-out trace has a 0.1426 failure fraction and 0.0527 accepted fraction.Malformed, timed-out, and calibration-boundary cases are rejected, recovered, or abstained.Source: Table 40 · p. 24, §C.7.14 · p. 24

C.7.15 EVIDENCE QUERIES AND ANSWERS

• The evidence-query map binds each question to a measured replay endpoint and supporting artifact, providing a trace path from conclusion to raw evidence.The section calls for measured answers using consistent splits and item identifiers.Source: Table 41 · p. 24, §C.7.15 · p. 24

C.7.16 NUMERICAL CONSISTENCY CHECKS

• The appendix records a largest positive paired gain of +0.1161, coverage of 0.4919, a 1.1359-call reduction, and a +0.0348 held-out task-score change.Numerical checks require the displayed value, raw value, and conclusion clause to agree after rounding.Source: Table 42 · p. 25, §C.7.16 · p. 25

C.8 ADDITIONAL CORRELATION-AWARE EXPERIMENTS

• Verifier-pair diagnostics include error overlap, phi, Cohen’s kappa, mutual information, and disagreement, comparing calibration conditional information with post-freeze accuracy changes.Each dependence row uses the same held-out items.Source: Table 44 · p. 26, §C.8 · p. 26
• The matched-budget study compares repeated verification with breadth at equal call and accepted-update budgets, changing only the allocation policy across RLVR arms.The learner seed, checkpoint schedule, task split, and held-out evaluator are shared.Source: Table 45 · p. 26, §C.8 · p. 26

C.9 CALIBRATION SAMPLE EFFICIENCY AND DEPENDENCE SHIFT

• The calibration-size study varies only the number of calibration items, holding the verifier pool, held-out items, and deployment budget fixed; CMD error is measured against the full-calibration estimate.The shift study preserves the task split and changes only verifier-output dependence after calibration; allocation parameters are frozen before held-out replay, and the fallback switches to exact-stop when the deployment window leaves the calibration region.Source: §C.9.1 · p. 26, §C.9.2 · p. 27

C.9.3 RLVR ERROR DECOMPOSITION

• The RLVR error decomposition assigns each accepted update to correct-positive, correct-negative, false-positive, false-negative, or abstained outcomes before learner training.It is paired with held-out task score using the matched candidate cache and learner seeds.Source: Table 48 · p. 27, §C.9.3 · p. 27