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Formal Verification Registry

Isabelle/HOL Mechanized Specification.

The 30 formal mathematical proofs (16 Domain, 14 Constraint) establishing the deterministic boundary conditions for autonomous systems.

GCCAI > Formal Verification Registry
Isabelle/HOL Mechanized Specification.

Federal Mandate Notice: SR 26-2 (Effective April 17, 2026)

Federal Reserve SR 26-2 explicitly excludes generative and agentic AI from the Model Risk Management framework. The following proofs constitute the deterministic mathematical baseline required to cure that exclusion.

The Constitutive Completeness standard for autonomous systems is not a theoretical proposal or a probabilistic assertion.

Deterministic vs. Conventional: Key Distinctions

The Core TheoremConventional LimitationDeterministic Boundary
The Boundary
Constitutive Completeness
Probabilistic systems require infinite testing because the environment is infinite. You can never legally prove a system won't fail tomorrow.
  • We do not test infinity; we mathematically bound the perimeter.
  • The system cannot physically act outside the verified boundary.
  • Reduces infinite operational risk to a zero-defect constant.
The Continuity
Deterministic State Continuation
When probabilistic AI hits an unknown variable, "fail-safes" trigger a hard system halt. Halting operations triggers costly Business Interruption claims.
  • Mechanically converts unpredictable variables into verified logic.
  • Requires no system halt to maintain safety.
  • Maintains continuous operational validity.
The Engine
O(1) Verification Synthesis
Probabilistic AI slows down when complexity increases because it must constantly calculate probabilities. Relying on humans or secondary models to monitor safety introduces severe operational delay.
  • Executes at O(1) algorithmic time complexity.
  • Ensures mathematical verification is applied before execution.
  • Adds zero computational weight or delay.

Public Data Execution Record

While theoretical mathematics provides the foundation, practical validation is essential.

  • Tested against public BigQuery data to empirically validate the mathematical boundary.
  • Maintained strict separation to avoid retroactive fitting.
  • Secured the mathematical boundary first, then observed the data flow.

Assurance Level

Formal Verification & The Good-Turing Halting Limit

While the architecture was originally aligned with international security assurance design criteria, the core logic has been transitioned to absolute cryptographic certainty.


Domain Proofs

16 Mechanized Formal Specification Proofs

Each domain proof is a formal, machine-checkable theorem applying the root Constitutive Completeness standard to a specific operational sector.

The complete registry of domain proofs can be audited by any institution.

The Evidentiary Shift

Before the formal administrative lodgment of this baseline, fiduciaries relied on probabilistic safety claims and industry custom to defend against liability, as deterministic mathematical models for autonomous systems did not exist at scale.

The formal publication of this baseline provides a new mathematical reference point.

The formal verification of autonomous domain completeness is now a matter of public administrative record. Fiduciaries may now reference this structural completeness to align with the objective auditing requirements necessary for FASB ASC 450 Capital Release.


Architectural Constraints

14 Constraint Proofs — Architectural Verification

The root Constitutive Completeness proof was deemed structurally insufficient on its own.

Isabelle/HOL source code for these proofs is maintained as Confidential Commercial Information. Verification access is granted under formal request and protective order from qualifying regulators or authorized GCCAI fiduciaries.

The constraint proofs mathematically enforce the structural integrity of the root theorem.


NIST AI RMF Structural Mapping

Four-Function Formal Coverage

The 14 architectural constraint proofs directly formalize the four core functions of the NIST AI Risk Management Framework, transforming behavioral guidelines into compiled structural constraints.


NIST Cybersecurity Framework 2.0 Structural Mapping

Six-Function Lifecycle Coverage

The same architectural constraint proofs that formalize the AI RMF also provide structural coverage across all six core functions of the NIST Cybersecurity Framework 2.0.

The architectural proofs deterministically map to the six stages of the CSF 2.0 lifecycle.

This mapping is presented as a factual structural alignment, not as a compliance certification.

When the systems that serve communities — their hospitals, their power grids, their financial institutions — operate within mathematically verified boundaries, those communities are freer to grow.

ESTABLISHED: 2025.10·CURRENT REVISION: 2026.05.01·CLASSIFICATION: PUBLIC BASELINE