Map your reasoning to a directed graph and check it for logical errors: circular reasoning, unsupported conclusions, and orphaned claims.

REQUIRED INPUT FORMAT — copy this structure exactly: {"nodes":[{"id":"c1","label":"The API latency is acceptable","type":"claim"},{"id":"e1","label":"p99 benchmark shows 180ms","type":"evidence"},{"id":"cn1","label":"We should use this service","type":"conclusion"}],"edges":[{"from":"e1","to":"c1","relation":"supports"},{"from":"c1","to":"cn1","relation":"implies"}]}

Node types: "claim" | "evidence" | "conclusion" | "assumption" Edge relations: "supports" | "implies" | "contradicts" | "requires"

Returns: cycles found, orphaned conclusions, grounding_score (evidence-to-conclusion reachability), and enforcement results.

Optionally pass "context" with prior iteration data for escalation and stall detection.

Multi-signal numeric analysis: fabrication detection, outlier detection, and arithmetic verification.

REQUIRED INPUT FORMAT — copy this structure exactly: {"numbers":[12.5, 15.3, 14.8, 100.0, 13.2],"context":"Quarterly revenue figures in millions"}

Three analysis layers:

1. Fabrication detection (round-number ratio, spacing CV, precision CV, geometric ratio consistency)

2. Outlier detection (MAD-based for small samples, Z-score for larger sets)

3. Arithmetic verification (sum, product, compound growth, weighted average, ratio consistency)

Optional field: "context" (string) — describes the data. Enables compound growth detection when it mentions interest/growth/rate.

Optionally pass "context" with prior iteration data for escalation and stall detection.

Detect drift in a numeric sequence using CUSUM (Cumulative Sum) analysis with monotonic progress tracking.

REQUIRED INPUT FORMAT — copy this structure exactly: {"sequence":[0.72, 0.74, 0.73, 0.85, 0.91, 0.93],"drift_sensitivity":0.5}

CUSUM formula: S_i = max(0, S_{i-1} + x_i - omega). Drift detected when S_i > 5 * std(sequence). Also reports monotonic progress: is_improving, is_stalling, is_declining.

Optional field: "drift_sensitivity" (number, default 0.5).

Optionally pass "context" with prior iteration data for escalation and stall detection.

Compare options by computing Expected Utility (EU) for each, then rank them.

REQUIRED INPUT FORMAT — copy this structure exactly: {"options":[{"name":"Option A","outcomes":[{"description":"Success","probability":0.7,"utility":100},{"description":"Failure","probability":0.3,"utility":-20}]},{"name":"Option B","outcomes":[{"description":"Success","probability":0.5,"utility":150},{"description":"Failure","probability":0.5,"utility":-10}]}]}

Each option's outcome probabilities must sum to 1.0 (within +/-0.01). Minimum 2 options. Returns INDETERMINATE (recommended=null) when top-2 EU scores differ by < 0.05.

Optionally pass "context" with prior iteration data for escalation and stall detection.

Validate a plan's logical structure: detect circular dependencies, missing prerequisites, and resource conflicts.

REQUIRED INPUT FORMAT — copy this structure exactly: {"steps":[{"id":"s1","description":"Set up database schema","dependencies":[],"resources":["database"]},{"id":"s2","description":"Build API endpoints","dependencies":["s1"],"resources":["api-server"]},{"id":"s3","description":"Deploy to staging","dependencies":["s2"],"resources":["staging-env"]}]}

Each step requires: id, description, dependencies (string[] of step IDs, use [] if none). Optional: resources (string[]) — detects conflicts when multiple unordered steps use the same resource. Returns: circular_dependencies, missing_prerequisites, resource_conflicts, completeness_score, critical_path.

Optionally pass "context" with prior iteration data for escalation and stall detection.

Score a response across four quality dimensions: substance, specificity, hedge avoidance, and structure.

REQUIRED INPUT FORMAT — copy this structure exactly: {"response_text":"The full text of the response you want to evaluate for quality. It should be at least 10 characters.","claims":["Optional array of explicit claims"],"evidence":["Optional array of evidence items"]}

Dimensions:

• substance_score: Shannon entropy on word frequencies (lexical diversity)

• specificity_score: Density of concrete, quantitative markers

• hedge_density: Proportion of hedging language (lower is better)

• structure_score: Presence of claim->evidence->conclusion pattern

• overall_score: Weighted average (substance 0.3, specificity 0.3, 1-hedge 0.2, structure 0.2)

Returns the weakest dimension with targeted improvement advice.

Optionally pass "context" with prior iteration data for escalation and stall detection.

Check whether your claimed confidence is mathematically supported by your assumptions.

REQUIRED INPUT FORMAT — copy this structure exactly: {"assumptions":[{"description":"Redis will respond within 50ms under normal load","confidence":0.85,"falsification_condition":"Fails when Redis response time exceeds 50ms for >1% of requests in a 5-minute window"}],"response_text":"The full text of the response whose confidence you are validating"}

Each assumption needs: description, confidence (0.0-1.0), falsification_condition. If you cannot state a falsification_condition, set confidence to 0.3 or below.

Computes dependency-weighted honest confidence ceiling. Flags inflation when claimed confidence exceeds ceiling by >0.15. Checks falsifiability of stated conditions.

Optionally pass "context" with prior iteration data for escalation and stall detection.

Verify that a claimed arithmetic result matches the actual computation. Supports: sum, weighted_average, percentage, growth, product.

REQUIRED INPUT FORMAT — copy this structure exactly: {"claim_type":"weighted_average","values":[100,80,60],"weights":[0.5,0.3,0.2],"claimed_result":84}

Claim types and required fields:

• "sum": values[], claimed_result

• "weighted_average": values[], weights[], claimed_result

• "percentage": part, whole, claimed_result

• "growth": values[] (principal), rate, periods, claimed_result

• "product": values[], claimed_result

Strict by default — matches to 2 decimal places. Optional "tolerance" for relative tolerance.

Detect common concurrency hazard patterns in a structured operation description.

REQUIRED INPUT FORMAT — copy this structure exactly: {"steps":["Read current balance","If balance >= cost, approve","Write updated balance"],"shared_resources":["balance"],"protections":[]}

Detects: check-then-act, read-modify-write, missing idempotency, ordering assumptions.

Optional fields:

• "shared_resources" (string[]) — named shared state

• "protections" (string[]) — locks, transactions, idempotency keys, etc.

• "delivery_model" — "at_least_once" | "at_most_once" | "exactly_once"

• "retry_behavior" — "none" | "automatic" | "manual"