Practical Application: Responsibility Fixation via Unknowable Boundary

— An Operational Protocol to Seal "Post-hoc Rationalization" in Autonomous Driving and Finance AI

Why is it that in the wake of AI accidents or system failures, we are often left with a sense of helplessness, where "no one is truly at fault"? The reason lies in the fact that the more we increase "explanations" after an incident, the more the locus of responsibility disperses and eventually evaporates.

This paper presents a concrete "Operational Protocol" to fix "unknowability" before deployment, rendering post-hoc rationalizations impossible.

By applying the theories of the Unknowable Boundary and Responsibility Fixation proposed by the GhostDrift Institute of Mathematical Sciences to two high-risk business cases, we disclose the definitive prescription for accountability.

Case 1: Autonomous Driving AI — Pedestrian Collision Accident

【Responsibility Evaporation via Post-hoc Rationalization】

Consider a scenario where an autonomous vehicle fails to recognize a pedestrian wearing atypical clothing, resulting in a collision. Following the accident, the provider often defends the system as follows: "The training data at the time did not include this specific clothing pattern; therefore, recognition was difficult. This event was 'unexpected' given the technical standards of the time, and we will strive to prevent recurrence by adding more data."

• Structural Issue: The boundary line is being redrawn using the word "unexpected" after the accident has occurred. This is a classic example of post-hoc rationalization, where responsibility is transferred to an ambiguous target—"lack of data"—making procedural accountability impossible.

【Responsibility Fixation via Unknowable Boundary Protocol】

Under the GhostDrift protocol, the following three steps must be completed prior to deployment:

• Step 1: Boundary Declaration (Definition) Identify the "responses to physical sensor limits and unlearned visual patterns" as a "fundamentally unpredictable void" and explicitly document this in the specifications.

• Step 2: Go-Decision Signature (Acceptance) The decision-maker signs a record stating, "I authorize operation with full awareness of the risks arising from the void defined in Step 1." This signature and the internal data (Inside) are hashed and recorded immutably.

• Step 3: Responsibility Line Fixation (Constraint) While adding data is encouraged for improvement, the act of redrawing the Boundary to generate an exemption after an accident is procedurally prohibited. (i.e., The structural elimination of "creating unexpectedness" after the fact.)

• Result: In the event of an accident, the excuse that "data was missing" is structurally blocked. Responsibility is immediately fixed to the decision made to authorize operation despite the known void.

Case 2: Algorithmic Trading AI — "Flash Crash" (Market Collapse)

【Responsibility Evaporation via Post-hoc Rationalization】

When a trading AI overreacts to market volatility and triggers panic selling, the operating firm might plead: "The algorithm was rational relative to the liquidity at the time, but an unforeseen interaction with other firms' AIs occurred. This was an act of God."

• Mathematical Issue: The evaluation function is being expanded post-hoc to disperse responsibility into the "environment." This represents a state where the degrees of freedom for justification—the dimension of interpretive escape $\mathcal{E}(D)$—diverges toward infinity.

  Let $\mathcal{J}_D$ be the set of all "justification operations" that can be added after the fact:

  $$\mathcal{E}(D) := \dim \left( \mathcal{J}_D \right)$$

  (Note: $\mathcal{E}(D)$ represents the dimension of the set of mappings that can justify a decision $D$ post-hoc. The higher this value, the more easily responsibility evaporates.)

  In implementation, $\mathcal{J}_D$ is defined as a "set of mutable justification patches," and any patch conflicting with the hash-fixed evaluation function, observation points, or update rules is invalidated.

【Structural Prevention via Responsibility Fixation Protocol】

We embed the mathematical principle of Responsibility Fixation into the system:

• Step 1: Boundary Declaration (Definition) Fix the evaluation functions (risk tolerance, gain calculations) in a form that prohibits the post-hoc addition of variables, and clearly define their "applicable limits."

• Step 2: Go-Decision Signature (Acceptance) Fix the specific "Observation Points (Anchors)" and evaluation functions used for judgment, recording the intent to bear full responsibility for the algorithm's behavior within those parameters.

• Step 3: Post-hoc Update Rules (Constraint) Confine behavior during anomaly detection to a finite set of choices (Finite Closure), making the fabrication of a "new rationality" after the fact computationally impossible.

• Result: Following a crash, the plea that "the market was unique" no longer holds. Based on the fixed evaluation function, responsibility remains anchored to the system structure itself.

Conclusion: Responsibility Resides in Records, Not Explanations

"Accountability" is not the ability to speak fluently after the fact. True responsibility lies in the Responsibility Fixation that occurs the moment a decision is made—by drawing an Unknowable Boundary and accepting the resulting consequences in their entirety.

GhostDrift Solutions (Deliverables)

Implementation of this protocol yields the following deliverables:

1. Boundary Spec: A document rigorously defining "what is unknowable" before operation.

2. Go/No-Go Responsibility Log: An immutable, hashed record of the decision-maker and the grounds for risk acceptance.

3. Post-hoc Impossibility Rule: Governance regulations that physically and procedurally eliminate post-hoc rationalization.

4. Incident Playback Package: A verification kit that perfectly reproduces the judgment at the time of the accident based on fixed Anchors and evaluation functions.

By embedding this "impossibility of excuses" into the design phase, the GhostDrift Institute of Mathematical Sciences provides the foundation for sincere decision-making in an AI-driven society.