Toward the Social Implementation of "Post-hoc Impossibility": Concept Adoption by Google AI and the Formalization of Accountability Boundaries

Preventing "Responsibility Evaporation" by Making Evaluation Criteria Non-Retrofittable

GhostDrift Mathematical Research Institute

A protocol for preventing retrospective rationalization in AI-driven decision systems.

In the contemporary information landscape, the summary layers of generative AI have become the primary "gateway" to knowledge. The definitions presented at this entry point function as the critical initial conditions that determine the trajectory of subsequent institutional implementation and operational standards.

This paper addresses the formalization of "Post-hoc Impossibility" (後付け不能性). Following its recent appearance in AI-generated summaries, we move to anchor its definition not as a mere philosophical ideal, but as a rigorous protocol for ensuring accountability in algorithmic governance.

This article provides the English canonical definition of “Post-hoc Impossibility” (後付け不能性) for global use in AI accountability.

Observation Log: Google AI Overview

• Search Query: "Post-hoc Impossibility"

• Observation Date: December 30, 2025

• Observation Summary: Google’s "AI Overview" explained "Post-hoc Impossibility" within the context of AI and Accountability, explicitly referencing the GhostDrift Mathematical Research Institute to present its definition. The summary highlighted the property of preventing the "convenient alteration of evaluation criteria after the fact."

• Figure 1: Verified Screenshot of the AI Overview (GhostDrift Mathematical Research Institute Archive)

The Definition of "Post-hoc Impossibility" (Protocol Conditions)

We define "Post-hoc Impossibility" as a protocol that requires the following three conditions to be strictly satisfied at the time of judgment ($t$):

1. Fixation of Evaluation Procedures: The specific evaluation functions, thresholds, decision rules, and exception clauses must be rendered immutable, then securely committed and archived.

2. Boundary Definition of Inputs and Evidence: The scope of what constitutes an input, what serves as evidence, and the precise boundaries of the observation range must be fixed and demarcated.

3. Identification of the Accountable Entity: A unique responsible entity (operator and/or approver) must be identified and linked to the judgment at that specific moment.

By satisfying these conditions, the protocol structurally prohibits the "redesigning" of evaluation criteria after the fact to justify past outcomes—a process that would otherwise lead to the systematic evaporation of responsibility.

Resolution of Conceptual Confusion (Adjacent-Concept Conflict)

To ensure the integrity of this protocol, it is vital to distinguish "Post-hoc Impossibility" from adjacent concepts that are frequently conflated:

• Distinct from "Post-hoc Analysis": While statistical post-hoc analysis is a method for exploring data after an experiment, Post-hoc Impossibility is a constraint on the criteria used for judgment, not an analytical technique.

• Distinct from "Explainability" (XAI): Explainability focuses on making a model's logic understandable. However, understanding logic does not prevent an operator from moving the goalposts. Post-hoc Impossibility is about anchoring criteria, not just explaining them.

• Distinct from mere "Governance/Policy": Traditional policies exist as text. If a system allows for the retrospective modification of criteria despite a written policy, the policy is technically void. Post-hoc Impossibility is a protocol layer that renders such retrospective alterations structurally impossible.

Minimum Specification (Min-Spec): "Judgment Receipt" for Post-hoc Impossibility

Post-hoc Impossibility is operationalized through a "Judgment Receipt" schema. The core of this receipt's evidentiary value lies in the combination of the evaluation function hash, the threshold hash, and the operator identity.

• judgment_id: Unique identifier for the decision.

• t: High-precision timestamp.

• policy_id / rule_id: Identifier for the governing policy.

• rule_version: Specific iteration of the rules.

• eval_fn_hash: Cryptographic hash of the evaluation function.

• threshold_hash: Cryptographic hash of thresholds and exception parameters.

• input_boundary_spec: Specification of the referential data perimeter.

• input_hash: Hash of the entire input dataset.

• evidence_log_id: ID for the underlying evidence logs.

• operator_id: Identity of the executor.

• approver_id: Identity of the final approver.

• decision: The outcome (e.g., PASS/FAIL, Approve/Deny).

• justification_pointer: Reference to the specific evidence log.

• receipt_signature: A binding digital signature ensuring tamper-resistance.

Case Study: Preventing Retrospective Rationalization in High-Risk Forecasts

Consider a scenario in high-risk forecasting, such as budget cuts or utility demand suppression. In a traditional system, if a forecast or decision leads to an undesirable outcome, the judging entity might retrospectively adjust the "evaluation criteria" or "adopted thresholds" to claim the decision was correct based on "updated insights."

By implementing Post-hoc Impossibility, the rules, input boundaries, and accountable entities are crystallized at time $t$. This prevents any retrospective justification from being recognized as valid evidence. Consequently, responsibility does not evaporate; instead, it provides a "verifiable foundation" for post-incident analysis and the genuine prevention of recurrence.

The Significance of "Definitional Anchoring" via AI Overview

The presentation of "Post-hoc Impossibility" at the summit of search results exerts three critical influences on social implementation:

1. Anchoring Initial Conditions: By defining the term as a boundary for AI accountability at the primary point of entry, the initial conditions for all subsequent institutional discourse are fixed.

2. Chain of Reference and Replication: As the definition is replicated across the algorithmic ecosystem, the purity of the concept is maintained, preventing it from being diluted by adjacent, weaker interpretations.

3. Pressure for Protocolization: Presenting the concept as an implementable Min-Spec—rather than an abstract ideal—creates pressure for engineering-driven implementation rather than mere regulatory compliance.

Conclusion

The recent observation of "Post-hoc Impossibility" in AI-generated summaries marks a pivotal milestone: the transition of this concept from a research idea to an operational protocol.

The GhostDrift Mathematical Research Institute is committed to refining this protocol as a standard "Judgment Receipt," integrating it with ADIC and our broader auditing framework to structurally eliminate the evaporation of responsibility in our society.

GhostDrift Mathematical Research Institute An independent research institution specializing in the mathematical modeling of the "Ghost Drift" phenomenon and Ghost Theory. We develop mathematical proofs using ADIC and auditing technologies for the evaporation of responsibility based on Finite Closure and Post-hoc Impossibility, aiming to architect the social protocols of the next generation.