top of page
検索

Turning AI Governance into "Re-executable Evidence": Release of the ADIC Lean 4 Artifact

The true challenge in AI governance is not providing "explanations," but establishing "immutable evidence that can be verified after the fact."

GhostDrift Mathematical Institute has formally verified the core theory of ADIC replay verification in Lean 4, releasing it on GitHub as an artifact that third parties can reproducibly execute.

This goes far beyond merely "writing a proof in Lean."

By cloning the repository and executing lake build, anyone can mechanically verify the core architectural guarantee: that semantic validity strictly follows from the replay verifier's acceptance of an ADIC certificate.



What Has Been Released?

This artifact provides a Lean 4 formalization of replay verification for ADIC certificates. The core logic is consolidated in the following file:

ADIC_RSound_Replay.lean

It rigorously formalizes the relationships between certificate rows, spec rows, replay verification, semantic validity, and acceptance soundness within the ADIC architecture.

At a high level, the proof establishes the following theorem:

An ADIC certificate is accepted by the replay verifier (Acceptance) $\Longrightarrow$ The corresponding semantic validity condition follows (Semantic Validity)

What Has Been Expanded from the Previous Version?

While the previous iteration of the Lean artifact focused primarily on proving the R-SOUNDness of individual primitives, this major update incorporates the replay ledger and DAG certificate. It formalizes the core theory of ADIC replay verification in a near end-to-end manner.

  • Core Focus

    • Previous Version: R-SOUND of individual primitives

    • Current Version: The complete replay verification pipeline

  • Primary Scope

    • Previous Version: interval arithmetic / local soundness

    • Current Version: program replay / spec replay / replay ledger

  • Proof Granularity

    • Previous Version: Local soundness per operation

    • Current Version: Structural soundness from verifier acceptance to semantic validity

  • Milestone

    • Previous Version: primitive-level soundness

    • Current Version: Verifier closure establishing near end-to-end soundness

This represents a fundamental shift: from validating isolated operation rules to proving the closure of the overall structure (Verifier Closure) in Lean 4. It guarantees that "when an ADIC certificate is accepted by the replay verifier, the corresponding semantic conditions follow at the level of the replay-verification structure."


The Significance Beyond "Proven in Lean": Reproducibility

The most critical takeaway from this release is not the mere existence of a Lean proof.

Rather, it is the establishment of an infrastructure where any third party can pull the repository from GitHub and mechanically re-execute the verification (machine-checked) using an identical procedure.

git clone [https://github.com/GhostDriftTheory/adic-lean-proof-replay.git](https://github.com/GhostDriftTheory/adic-lean-proof-replay.git)
cd adic-lean-proof-replay
lake exe cache get
lake build

In other words, this is not just "a proof that passed on our local machines"; it is the external fixation of the theory into a "reproducible and verifiable proof asset (evidence)" available to everyone.


Verifying the "Chain of Evidence" Targeted by ADIC

The ultimate objective of ADIC goes far beyond simply storing execution logs.

  • Which conditions were satisfied to allow passage?

  • Upon what evidence was the judgment based?

  • Can that judgment be verified by a third party?

It aims to weave these answers into a verifiable "chain of evidence." This artifact distills that philosophy and its underlying mathematical structure into a reproducible Lean 4 framework.

Instead of leaving the grounds for AI judgments as black boxes or relying on post hoc explanations, ADIC transitions them into mathematically verified legitimacy. It serves as the foundational architecture to achieve exactly this.


Conclusion: Transition to Accountability Engineering

This release acts as a concrete, formal proof artifact demonstrating that ADIC is moving AI accountability away from natural language explanations and toward an evidence structure that is fully reproducible by third parties.

We are designing an AI governance paradigm that is not confined to abstract philosophies or procedural checklists, but is built as a strictly verifiable structure of accountability.

At GhostDrift Mathematical Institute, we continue to advance this trajectory under the discipline of "Accountability Engineering."

 
 
 

コメント

bottom of page