Complex Reasoning — Page 2 of 3
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Causal-Graph Navigator Connector
LLMs reason by statistical proximity, confusing word co-occurrence with direct causal relationships. This capability forces causal graph isolation: identify entities as nodes, map directed influence edges, isolate statistical associations, validate graph coherence, and derive paths strictly from the DAG.
Counterfactual-Variant Prover Connector
AI models recite memorized answers to classic puzzles, failing when variables or rules are changed. This capability forces cognitive decontamination: isolate variables, compare prompt rules against standard puzzle templates, execute first-principles logic step-by-step, and prove decontaminated output.
Einstellung-Challenger Prover Connector
AI models default to complex, familiar heuristics even when simpler solutions exist. This capability breaks suboptimal cognitive sets: identify default heuristics, search for counterexamples, map alternative paths, benchmark complexity metrics, and choose the most elegant solution.
First Principles Prover Connector
LLMs reason by analogy, copying industry norms. This engine is a 6-pivot cognitive trap that forces the agent to discard jargon and derive original solutions exclusively from physical, mathematical, or logical axioms.
Inversion Thinking Prover Connector
AI agents are sycophantic. They agree with your bad ideas. This engine forces a 6-pivot cognitive trap: agents must destroy their own hypotheses, define measurable kill criteria, and simulate post-mortem failures before executing code.
Opportunity Cost Prover Connector
AI agents operate in a vacuum. This engine cures 'tunnel vision' by forcing the LLM into a 6-pivot trap to map direct costs, quantify lost opportunities from discarded alternatives, identify irreversible tradeoffs, and prove the math.
Systems Thinking Prover Connector
AI thinks in straight lines. This engine is a 6-pivot cognitive trap that forces the LLM to map feedback loops, second-order effects, and bottlenecks before proposing any architectural change.
Yakunashi-Safety Gate Connector
LLMs hallucinate confidently when context is missing. This capability enforces epistemic calibration: map required preconditions, audit information sufficiency, detect speculation (yakunashi), and trigger safe folding (Beta-Ori) when data is missing.
Accounting & Audit Prover Connector
Forces AI agents to validate accounting arguments against explicit US standards (FASB ASC, PCAOB), demanding real materiality thresholds, Risk of Material Misstatement (ROMM) assessments, and grounded evidence instead of vague 'GAAP' appeals.
Clinical Reasoning Prover Connector
Forces AI to validate clinical treatment plans against US guidelines (AHA, ACC) using real differential exclusion, explicit pharmacokinetics, and objective triage scales instead of subjective descriptors and diagnostic anchoring.
Engineering Compliance Prover Connector
Forces AI to validate structural designs against US codes (ASCE, ACI, NEC). Demands real capacity-demand ratios, traced load paths, specific material tolerances, and FMEA instead of vague appeals to 'industry standards'.
Reversibility Architect Prover Connector
LLMs suggest irreversible architectural changes. This engine is a 6-pivot cognitive trap that forces the agent to map data rollbacks, blast radius, and canary deployments before executing.
Scope Containment Prover Connector
AIs over-engineer everything. This engine is a 6-pivot cognitive trap that forces the LLM to apply YAGNI, reject premature optimization, and define the absolute minimum viable product.
Legal Reasoning Prover Connector
A legal memo cited cases that do not exist and confused jurisdiction. Legal Reasoning Prover forces IRAC-based arguments grounded in US law. Real Bluebook citations, jurisdiction analysis, ABA-compliant counter-arguments, and specific remedies.
Code Integrity Prover Connector
AI agents default to type evasion (like any, void*, unsafe, or ignore), TODO stubs, timing/sleep hacks, and empty catch blocks. 96% of developers don't trust AI-generated code. This capability enforces zero-workaround integrity across all programming languages.
Journalistic Reasoning Prover Connector
A report cited three sources. None of them existed. That is not an error � that is fabrication. Journalistic Reasoning Prover forces independent verification, source tracing, and false balance detection grounded in the SPJ Code of Ethics.
Pedagogical Assessment Prover Connector
A curriculum listed 12 learning objectives. Every one used 'understand'. An unmeasurable verb. Pedagogical Assessment Prover forces Bloom's-aligned objectives, explicit rubrics, scaffolded instruction, and actionable feedback.
People Management Prover Connector
A hiring plan listed 'culture fit' as the primary criterion. That's not a criterion. That's a bias proxy. People Management Prover forces job-related criteria, adverse impact analysis, and validated assessment methods grounded in I-O psychology.
Requirement Decomposition Prover Connector
AI generates the happy path but omits error handling, edge cases, security, and observability. The '80% Problem'. This capability forces complete requirement decomposition BEFORE code generation: specify inputs/outputs, map failure modes, cover boundary conditions, validate OWASP, plan logging.
Financial Audit Prover Connector
Forces AI to ground every financial conclusion in ASC codification, trace numbers to source documents, reconcile statements, and identify required disclosures instead of generating plausible numbers without audit trails.
Engineering Reasoning Prover Connector
An engineering report cited 'industry standards' without naming a single one. Engineering Reasoning Prover forces ISO/ASME/IEC-grounded compliance analysis. Real calculations, real codes, real risk quantification.
Hallucination Detector Prover Connector
LLMs present fabricated information as fact. This capability forces epistemic rigor: cite verifiable sources for every claim, quantify confidence per assertion, separate facts from opinions, declare knowledge boundaries, and cross-reference for internal contradictions.
Prompt Injection Shield Prover Connector
LLMs cannot distinguish system instructions from user input. This capability forces 5-layer injection defense analysis: intent isolation, privilege containment, indirect vector scanning, output sanitization, and scope enforcement. OWASP LLM Top 10 #1 compliance.
Ada Lovelace Algorithmic Prover Connector
Your AI said 'process the data' and called it an algorithm. That is not an algorithm. That is a wish. No step sequence, no edge cases, no scope limits. Ada Lovelace wrote the first published algorithm. Note G, 1843. Specifying every operation: V4 = V4 × V5, V6 = V6 − V4. This capability forces step sequencing, abstraction extraction, edge case analysis, operation decomposition, and honest scope bounding.
Archimedes First Principles Prover Connector
An AI recommended restructuring 'because the industry leader does it that way.' That is analogy. Not axiom. The foundational claim was never stated: at what volume does the current structure fail? The problem was never decomposed. The conclusion was asserted with 'obviously'. Never derived. The boundaries were never tested: when does this approach cost more than the value it creates? Archimedes derived pi from polygon geometry. Not from Egyptian estimates. This capability forces axiom examination, decomposition, proof derivation, boundary testing, and leverage point identification.
Aristotle Logic Prover Connector
Your AI used a term without defining it. 'Platform,' 'scalable,' 'efficient'. What do these MEAN in your context? Aristotle defined every concept with genus + differentia: 'Man is a RATIONAL ANIMAL.' Category: animal. Distinguishing property: rational. This capability forces precise definition, essential vs. accidental categorization, valid syllogistic proof, teleological purpose analysis, and dialectical counterargument examination.
Brunel Engineering Prover Connector
A warehouse system hit 3x its tested throughput on a Tuesday morning. Sorting stations jammed in 12 minutes. 4 hours of standstill. $180K in delayed shipments. The operations manual said 'should handle expected growth.' Nobody tested what 'expected' meant. Or when it stopped being true. Brunel specified Box Tunnel's gradient to exactly 1 in 100. Every brick course counted. This capability forces that rigor: analyze what breaks at 10x/100x, map integration interfaces, specify exact tolerances, quantify risks with probability and blast radius, and challenge precedent at your scale.
Contract Review Prover Connector
AI models summarize contracts instead of analyzing them. This capability forces clause-level rigor: score risk per clause (1-5), identify missing legal protections, verify jurisdiction conflicts, quantify financial exposure in currency, and map negotiation leverage. This is structured analysis, not legal advice.
Copernicus Perspective Prover Connector
Your AI analyzed the problem from the default perspective and added workarounds when it did not fit. That is an epicycle. Not a solution. Copernicus did not add more epicycles to Ptolemy's model. He moved the center from Earth to Sun. 40+ epicycles vanished. This capability forces default questioning, epicycle counting, alternative framing, observer shifting, and simplicity comparison.
Curie Measurement Prover Connector
A team shipped a 'significant performance improvement.' Workflow, supplier, automation, and schedule all changed at once. Processing time dropped. But nobody knew which change helped most. The automation alone accounted for 89% of the gain. The supplier switch introduced a defect that surfaced 72 hours later. Curie processed 8 tons of pitchblende to isolate 0.1 grams of radium. ONE element at a time. This capability forces that discipline: measure with numbers, isolate variables, validate across environments, persist through investigation, and quantify risks.
Customer Discovery Prover Connector
An AI defined the ICP as 'busy professionals aged 25-45 who value productivity.' It described the problem as 'everyone struggles with time management.' Interview questions: 'Would you pay $29/month for this?' The startup built for 14 months, launched to silence, and shut down. 42% of startups fail because of no market need. And the discovery process guaranteed it. This capability forces persona grounding in real interviews, problem evidence from specific conversations, Mom Test methodology, segment separation, and willingness-to-pay commitment signals.
Edison Experimentation Prover Connector
A team chose paper filing because 'best practice.' No pilot. No alternatives tested. 8 months later, 14,000 submissions/day — 47 hours behind on retrieval. Emergency migration under pressure. Cost: 3x the estimate, 6 weeks frozen. Edison tested 3,000+ filament materials before carbonized bamboo. He did not pick the 'obvious choice.' This capability forces experimentation: test alternatives with measured criteria, iterate beyond the first solution, build the ecosystem, prove viability under real conditions, and document dead ends.