Limits of Human Review Under Coverage Constraints and the Legitimacy of Algorithmic Verification

Social and Engineering Implications of Minimax-Risk Comparison in the Lean 4 Verified ALS Finite Experiment Kernel

Overview

The finite experiment kernel of the Algorithmic Legitimacy Shift (ALS) theory has been formalized in Lean 4 and published in an automatically verifiable format on GitHub Actions.

This kernel does not make the normative claim that “algorithms are always superior to humans” in general AI governance. What is proven is a minimax-risk comparison: in a finite model where the human review budget $B$ falls short of the number of items $J$ to be checked ($B < J$), a structural risk floor emerges for human review. Meanwhile, an algorithmic verification channel satisfying a specified exponential error upper bound can strictly fall below that floor.

This result provides a clear counterexample structure — at least within the finite experiment model — to the naive human-in-the-loop perspective that “safety and legitimacy are guaranteed as long as a human makes the final check.” The crucial takeaway is not a binary conflict between humans and AI, but the ability to compare, as “re-executable proofs,” which channel holds a lower worst-case risk under which assumptions.

▼ALS Lean4 https://github.com/GhostDriftTheory/als-finite-experiment-kernel

1. Grounding Abstract Risk into a “Finite Probability Model”

The previous ALS kernel treated the comparison between humans and algorithms as abstract risk numerical values. The engineering value of the codebase that has now passed verification (`ALSFiniteExperimentKernel.lean`) lies in explicitly modeling this as a “Finite Experiment Family.”

• Limits of Human Review Under Coverage Constraints (HumanReviewExperiment)

  
  

  It was shown that in a state where human processing capacity () is less than the number of items to be verified () (), under the finite model, any human sampling strategy constrained by B < J leaves a structural risk floor (humanFloor).

• Algorithmic Risk Control (AlgorithmSampleExperiment)

  
  

  In contrast, on the algorithmic side, if a sufficient number of samples () and margin () are secured, and an exponential upper bound (fieldWrong_exp_bound) is given for the error probability of each item, it was proven that the risk can strictly fall below the human limit (humanFloor) (algorithmic_legitimacy_shift_from_finite_experiment_families).

  
  

  This grounds the theory as a computational model to which real-world log data and audit traces can be mapped.

2. From Emotional Governance to “Computable Risk Assessment”

In the deployment of AI into social systems, “final verification by a human” has traditionally been relied upon for ethical and psychological peace of mind. However, in complex systems where coverage constraints () arise, relying unconditionally on humans may not be optimal from the perspective of worst-case risk (Minimax Risk).This proof does not assert that “algorithms are morally or legally superior.” However, by mathematically demonstrating that “legitimacy evaluation may shift to an algorithmic verification channel that satisfies certain conditions” under the rational demand for specific risk minimization, it supports the transition toward computable risk management.

3. Infrastructural Implications for ADIC (Advanced Data Integrity by Ledger of Computation)

This proof structure explains, from the perspective of the finite experiment model, why a re-verifiable evidence base like ADIC is becoming important in next-generation AI assurance and high-responsibility logistics.Merely leaving a human review trace (log) cannot escape the risk floor caused by coverage constraints. To retrospectively verify that the system is safer, an architecture that eliminates arbitrariness and fixes objective verification results through an algorithmic channel as a ledger becomes a highly useful option.

4. Consensus Building via “Re-executable Evidence”

The fact that this outcome is published and maintained as “Success” on GitHub Actions presents a new standard for consensus-building methods regarding governance.Guidelines written in natural language easily leave room for interpretation. However, any counterargument against this set of theorems that has passed the Lean 4 compiler requires clarifying whether the dispute lies in the “model assumptions (constraints),” the “logical development of the theorem,” or the “code implementation,” rather than relying on impressionistic arguments in natural language.The public placement of this proof as “Re-executable Evidence” serves as a crucial foundation for transitioning AI governance discussions onto a stage of logic that is re-calculable and verifiable by anyone.