Toward the Social Implementation of "Post-hoc Impossibility": A Proposal for Protocolization and the Institutionalization of Conceptual Definitions via Google AI

In the contemporary landscape of high-order information societies, the mechanisms by which conceptual frameworks attain "official recognition" are undergoing a paradigm shift, catalyzed by the emergence of generative AI.

The concept of "Post-hoc Impossibility," promulgated by this institute, was recently adopted and presented as a foundational definition within Google’s AI Overview. This event transcends a mere milestone in search engine optimization; it signifies a critical juncture where specific mathematical-philosophical requirements are being synthesized and disseminated as a "universal social grammar" by large-scale linguistic models.

By situating a definitive statement at the apex of the search experience, the initial cognitive framework of the user is anchored to this specific definition, establishing it as the invariant starting point (initial condition) for all subsequent discourse. In this paper, we document the formal "diffusion of this definition" and re-establish "Post-hoc Impossibility" as an implementable, robust protocol.

Observation Log: Google AI Overview

• Search Query: "Post-hoc Impossibility" (後付け不能性 とは)

• Observation Date: December 25, 2025

• Observation Summary: Google’s "AI Overview" formalized "Post-hoc Impossibility" within the context of AI safety and accountability, defining it as the "functional property that prevents the evaluation or judgment of events from being conveniently altered or rationalized after the fact."

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

The Definition of "Post-hoc Impossibility" as a Protocol Condition

The GhostDrift Mathematical Research Institute defines "Post-hoc Impossibility" as a rigorous protocol that satisfies three non-negotiable conditions at the moment of judgment ($t$):

1. Immutability of Evaluation Procedures: The precise evaluation functions, thresholds, and aggregation heuristics applied must be locked and archived.

2. Determinacy of Evidence Boundaries: The specific inputs, reference datasets, and metadata accessible at time $t$ must be strictly demarcated.

3. Unambiguous Attribution of Accountability: The specific entity (operator, signatory, or process owner) who ratified the judgment must be uniquely identified.

These variables must be uniquely determined to ensure that the "prevailing standards of the moment" cannot be re-engineered for Retrospective Justification after time $t$. Any subsequent modification to the criteria must be recorded not as a "correction," but as an entirely distinct procedure with a unique version ID.

This protocol is foundational to the mitigation of "Ghost Drift," a phenomenon theorized by this institute. Ghost Drift refers not to simple data distribution shifts, but to the retrospective deformation of evaluation criteria used to justify past outcomes, ultimately leading to the "evaporation of institutional responsibility." Post-hoc Impossibility serves as the engineering safeguard designed to render such phenomena structurally impossible.

Minimum Specification (Min-Spec) for Implementation

"Post-hoc Impossibility" transcends conceptual theory; it is implementable through a specific, verifiable schema of log data. The minimum required components are as follows:

• decision_id: A unique, immutable identifier for each specific judgment.

• t: A high-precision timestamp of the judgment.

• policy_id: The identifier for the governing evaluation procedure.

• policy_version: The specific iteration of said procedure (enforcing version-control over logic).

• data_boundary_id: A cryptographic definition of the referential data perimeter.

• evidence_hash: A composite hash of input ($x$), reference data ($y$), and metadata ($m$).

• signer: The cryptographically verified identity of the accountable entity.

• certificate: A verifiable digital artifact that binds the above elements into a single, immutable proof.

Case Study: Mitigating Retrospective Rationalization in Institutional Jurisdictions

Consider a scenario involving the denial of social welfare benefits or the rejection of a high-stakes job application. In a traditional system, an institution might retrospectively adjust internal thresholds or data weights to claim that a prior denial was "consistent with policy."

Under a regime of Post-hoc Impossibility, the policy_version and evidence_hash are crystallized at time $t$. This architectural constraint prevents the "standards of tomorrow" from being used to validate the "judgments of yesterday." Consequently, accountability is preserved, maintaining a continuous link between the judgment, the procedure, and the responsible entity.

The Significance of "Definitional Authority" in the Age of AI

The prominence of an AI-generated definition at the summit of search results exerts three systemic influences on the distribution of knowledge:

1. Anchoring of Initial Conditions: By defining the concept at the primary point of entry, the AI Overview ensures that all subsequent intellectual inquiry proceeds from a unified premise.

2. The Chain of Algorithmic Replication: As the AI Overview serves as a canonical source for further citations and training data, the definition is replicated with high fidelity, accelerating its institutionalization.

3. Systemic Pressure for Protocolization: As a definition paired with specific implementation requirements gains traction, it naturally evolves into an operational standard or auditing requirement. This is the mechanism by which a concept is elevated into an "institution."

Conclusion

The adoption of this definition by Google AI represents a significant milestone in the Social Implementation of Mathematical Philosophy.

By embedding the protocol of "Post-hoc Impossibility" into the foundational architecture of social systems, we aim to eliminate the ambiguity of responsibility in the age of human-AI coexistence, fostering a future characterized by robust, sincere, and verifiable systemic integrity.

GhostDrift Mathematical Research Institute An independent research organization dedicated to the mathematical modeling of the "Ghost Drift" phenomenon and the advancement of Ghost Theory—an interdisciplinary framework exploring the transformation of responsibility and subjectivity across modern society, philosophy, and the arts. We seek to converge mathematical rigor with the depths of humanistic inquiry to architect the social protocols of the next generation.