ADIC Core Lemma Formally Verified in Lean

We have formally verified a core lemma of ADIC (Advanced Data Integrity by Ledger of Computation) using the Lean theorem prover.

The significance of this announcement lies not merely in publishing a proof script. ADIC’s verifier core has already been defined in our paper, and with this machine-checked Lean formalization, it is now connected to the audit artifact demonstrated in our power demand forecasting demo.

With this three-layer structure — Theory → Formal Proof → Implementation — now in place, we believe ADIC has advanced from a concept to a verifiable responsibility-fixing architecture.

The core soundness lemmas of ADIC have been mechanically verified using Lean 4.

The Core of ADIC: From Explanation to Verification

The core of ADIC is not about adding plausible explanations after the fact, but about fixing verifiable boundaries beforehand. Based on a fixed certificate and ledger, an independent verifier can perform a deterministic replay. Because this structure is established first, explanation becomes supplementary, not the primary entity.

In technologies dealing with responsibility, relying on human interpretation or goodwill for the core mechanism leaves it vulnerable. The Lean proof (ADIC_RSound.lean) released this time demonstrates that a part of ADIC's verifier core holds up not merely as an informal claim, but in a form that can be mechanically re-verified by third parties.

Connecting Theory, Formal Proof, and Implementation

These released assets do not float in isolation; they are connected in a single continuous line.

• Theory: The paper presents the verifier core, certificate replay, and the verification structure on a finite primitive core.

• Formal Proof: In the Lean repository, the core lemma is proven in a machine-checkable form, anchoring a part of the safety claims as formal evidence.

• Implementation: In the power demand forecasting demo, the operational model of a fixed certificate, append-only ledger, and independent verifier is connected as a real-data system.

As an Implementation of Responsibility Engineering

What the GhostDrift Research Institute consistently addresses in Responsibility Engineering is the principle of "fixing the permissible conditions for responding beforehand, and remaining silent or rejecting outside of those boundaries."

This Lean formalization signifies that a part of the technical foundation supporting this philosophy has been anchored—not as mathematical decoration, but as solid, irrefutable evidence.

Public Asset Links

• Lean proof artifact:  https://ghostdrifttheory.github.io/adic-lean-proof/

• Power demand forecasting demo:  https://github.com/GhostDriftTheory/ghostdrift-adic-audit/tree/main

• Paper:  https://zenodo.org/records/18897322

• Responsibility Engineering examples: https://www.ghostdriftresearch.com/post/%E8%B2%AC%E4%BB%BB%E5%B7%A5%E5%AD%A6%EF%BC%88responsibility-engineering%EF%BC%89%E3%81%AE%E5%AE%9F%E6%96%BD%E4%BE%8B%EF%BC%88%E5%90%84%E6%A5%AD%E7%95%8C%E3%83%87%E3%83%A2%EF%BC%89

Conclusion

This Lean proof does not mean we have exhaustively proven the entirety of ADIC. However, we believe we have demonstrated that the core of ADIC is beginning to be supported not only by theory but from both sides: formal proof and implementation.

Theory → Formal Proof → Implementation.

By strongly binding these three layers, we will continue to advance ADIC as a responsibility-fixing architecture.