Hiroshima Responsibility Functor-Formalizing Hiroshima’s Place-Based Meaning as a Responsibility Structure for AI Assurance
- kanna qed
- 5 日前
- 読了時間: 5分
The Core Problem
When AI is deployed in society, performance is not the only question.
What conditions did the decision pass through? What evidence did it leave behind? Who can verify it afterward? The essence of AI assurance is whether we can say not “please trust us,” but “this can be checked.”
Yet there is a deeper question.
AI is a technology that can turn human beings into “data, scores, thresholds, and optimization targets.” Once an objective function such as “because it is convenient” or “because it is accurate enough” is allowed to govern the decision, human dignity, exceptional cases, unexplained suffering, and future generations may fall outside the decision structure.
Nuclear weapons and AI are not the same technology. But they belong to the same layer: the layer in which humanity became aware that it could damage the conditions of its own survival through its own technology. The structural connection is this: a powerful technology can convert human beings into objects inside an objective function, while dignity, exceptions, and future generations outside that function are dropped from the decision structure.
Nuclear weapons converted cities and human beings into “blast power, radius, and strategic effect.” When AI converts human beings into computational objects, the same structure can appear in a different context.
▼Lean verification
Why Hiroshima?
The important point is that AI assurance should not be discussed in Hiroshima merely because “Hiroshima is a symbol of peace.”
Hiroshima is an exceptionally strong reference point for AI assurance because it satisfies the following three conditions with unusual density.
### First, Hiroshima is a historical witness to a decision that broke responsibility conditions and produced consequences at a civilizational scale.
The side that dropped the atomic bomb broke what should have been a non-negotiable condition: not incorporating noncombatants into a strategic objective function. This is not written to condemn any specific people or any present-day state. It is written to describe how the decision at that time broke responsibility conditions.
The results were Hiroshima and Nagasaki. And the damage did not move in only one direction. The moral foundation of the side that broke the condition also remained burdened by an unresolved question. For the world, a precedent was inscribed: the most powerful actor could exceed its own constraints. The damage caused by breaking responsibility conditions extends in three directions: toward the target, toward the actor, and toward the world order.
### Second, that memory has been preserved as an institution.
Not merely as a record, but as an institution. Memory does not merely preserve the past; it continues to function as a ground for responsibility toward the future.
### Third, Hiroshima is already an institutional anchor for AI governance.
The Hiroshima AI Process, launched from the 2023 G7 Hiroshima Summit, chose Hiroshima as the place for forming international principles on the safety, trustworthiness, and responsibility of generative AI. “From Hiroshima” is already connected to the international language of AI governance as an institutional fact.
The Responsibility of Raising AI Assurance in Hiroshima
If Hiroshima becomes a hub for AI assurance, then the responsibility of companies and researchers operating in Hiroshima becomes heavier, not lighter.
To use Hiroshima’s place-based meaning is not simply to borrow a “trustworthy regional brand.” It means taking a stronger position against AI decisions that turn human beings into computational objects, skip responsibility conditions, and flow into society without evidence or re-verifiability.
Therefore, anyone who raises AI assurance in Hiroshima must assume at least the following responsibilities for their own AI, systems, and business decisions:
- Show what conditions each decision passed through
- Preserve evidence of that decision
- Make it possible for third parties to re-verify the decision afterward
- Do not leave human dignity, exceptional cases, and future generations outside the decision structure merely because they fall outside the objective function
If Hiroshima is called a hub for AI assurance, AI businesses conducted in Hiroshima must assume stronger accountability than ordinary AI businesses. This is not a burden imposed from outside. It is the very legitimacy of raising AI assurance in Hiroshima.
Mathematical Formulation
This repository describes Hiroshima-based responsibility in the language of category theory.
An ordinary corporate decision is represented by the following category $\mathcal{C}$:
$$
\mathcal{C}: D \to P \to O
$$
Decision $\to$ profit / efficiency evaluation $\to$ outcome.
The Hiroshima Responsibility Category $\mathcal{R}$ maps this into a responsibility path:
$$
\mathcal{R}: D_H \to P_H \to B \to E \to V \to A \to O’
$$
Decision in Hiroshima context $\to$ context evaluation $\to$ Beacon review $\to$ evidence $\to$ verification $\to$ accountability $\to$ outcome.
This mapping is defined as the Hiroshima Responsibility Functor:
$$
F_H : \mathcal{C} \to \mathcal{R}
$$
$B$ denotes Beacon admissibility. It is the boundary that determines whether a decision satisfies the conditions required to pass.
$V$ denotes Verification. It indicates whether the decision remains as evidence that can be re-verified afterward.
$\text{Adm}_{BV}$ is defined as the condition that a morphism passes through both $B$ and $V$. A path that skips either Beacon or Verification is not a responsible admissible morphism in the sense of $\text{Adm}_{BV}$.
What Has Been Verified in Lean
The Lean 4 file mechanically verifies the following points:
- The functor $F_H$ preserves identity morphisms and composition
- $F_H(q \circ p)$ becomes responsible composition
- Any path that skips either $B$ or $V$ does not belong to $\text{Adm}_{BV}$ (universal exclusion)
- `AdmBV_iff_factorizes`: the equivalence between the implementation and the factorization definition is proved as a theorem, not assumed as an axiom
GitHub Actions runs automatic verification, and every push to `main` confirms that all theorems pass.
To be explicit: category theory does not prove the historical facts themselves: that Hiroshima is a civilizational-scale witness to a decision that broke responsibility conditions; that its memory is preserved as an institution; and that the Hiroshima AI Process exists. These are explicitly declared as external axioms in the Lean file. What category theory proves is the structure of the responsibility path.
## What This Claims, and What It Does Not Claim
What This Claims
Hiroshima’s place-based meaning can be described as a structure that maps AI decisions into responsibility, evidence, and re-verification. A decision that does not pass through Beacon and Verification is not admissible in the sense of $\text{Adm}_{BV}$. Hiroshima is a strong reference point because it satisfies the three historical premises supporting this structure with unusual density.
What This Does Not Claim
It does not claim that a company automatically becomes ethical simply by being based in Hiroshima. It does not claim that category theory proves historical facts. This is not a political or nationalistic claim.
Closing
Before AI turns human beings into computational objects, return what falls outside the objective function as responsibility. Leave each decision as evidence that anyone can trace afterward.
This is not merely a technical proposal. It is a mathematical proposal carrying historical weight.
The code and verification environment that make this structure verifiable in Lean and category theory are publicly maintained in the following repository:
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