Apoth3osis
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OmegaProof

VERIFIED0 SORRY5 MENTAT CERTSLean 4 + Mathlib
>_VERIFICATION.SEAL
FORMALLY VERIFIED • LEAN 4 • MACHINE-CHECKED • APOTH3OSIS∀∃⊢→∧∨¬≡QED0 SORRY

Formal Verification Certificate

All theorems formally verified in Lean 4 with zero sorry gaps.

0 SORRY

OmegaProof • Lean 4 + Mathlib • Apoth3osis Labs

❓

The Central Question

Can neural network properties be formally verified with machine-checkable proofs? OmegaProof expresses neural network properties — robustness, fairness, monotonicity — as algebraic constraints over weight matrices and activation functions. These constraints are verified in Lean 4, and the results are packaged as CAB v2 certificates with IPFS-pinned evidence for auditability. The goal: move neural network verification from empirical testing to mathematical certainty.

Key Verified Results

weight_norm_bound

Weight matrix norms bounded for stability

WeightNorm.lean

activation_lipschitz

Activation functions are Lipschitz continuous

Activation.lean

composition_bound

Layer composition preserves norm bounds

Composition.lean

property_propagation

Input property propagates to output

EndToEnd.lean

Resources

GHGitHub RepositoryIDXAll Research Projects
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>_MENTAT.JOIN

“Once men turned their thinking over to machines in the hope that this would set them free. But that only permitted other men with machines to enslave them.”

Frank Herbert, Dune

A janitor who proves a theorem outranks a tenured professor who publishes noise.

Not as a slogan. As a structural fact of how the network operates. The only currency that matters is the quality of your contribution, measured not by committee but by mathematics.

ONTOLOGICAL ENGINEER8 designations
IDEA

A valid, original framing or conjecture

THEORY

Formal argument with paper-level rigor

APPLICATION

Connecting theory to observable outcomes

CODE

Working software the project depends on

EXPERIMENT

Reproducible research with methodology and data

PROOF

Machine-verified claim checked by a proof assistant

KERNEL

Foundational, load-bearing implementation

BRIDGE

Connecting subsystems or knowledge domains end-to-end

NOETIC ENGINEER8 designations
VISIONARY

Strategic direction & roadmaps

NARRATOR

Writing, documentation & papers

DESIGNER

Visual, UX & information design

EDUCATOR

Teaching, tutorials & workshops

CULTIVATOR

Community, outreach & events

DIPLOMAT

Partnerships, governance & policy

INTERPRETER

Translation, media & accessibility

SENTINEL

Ethics, review & quality assurance

Every accepted contribution receives a MENTAT Contribution Record — cryptographically signed, IPFS-pinned, permanently yours. No committee decides your worth. The type checker does.

APPLY TO MENTATEXPLORE PROJECTSMESH-ENCRYPTED NETWORK FOR TRUSTED AUTONOMOUS TRANSACTIONS
>_MENTAT.CERTIFICATES

Contribution Certificates

Immutable contribution records per MENTAT-CA-001. Each certificate is cryptographically anchored with IPFS CIDs.

MENTAT-CA-001|MCR-OP-001
2026-02-01

MENTAT Contribution Record

IDEA

Conceptual Contribution

CONTRIBUTION LEVEL: IDEA

Ontological Engineer

Machine-Checkable Algebraic Proofs for Neural Networks

Contributor

Apoth3osis Labs

R&D Division

Core insight: neural network properties (robustness, fairness, monotonicity) can be expressed as algebraic constraints over weight matrices and activation functions. These constraints are then machine-checkable in Lean 4, and the verification results are packaged as CAB v2 certificates for auditability.

MENTAT · Mesh-Encrypted Network for Trusted Autonomous TransactionsImmutable · Content-Addressed · Tamper-Proof
MENTAT-CA-001|MCR-OP-002
2026-02-01

MENTAT Contribution Record

THEORY

Mathematical Foundation

CONTRIBUTION LEVEL: THEORY

Ontological Engineer

CAB v2 Certificate Architecture for ML Verification

Contributor

Apoth3osis Labs

R&D Division

Complete framework: (1) property specification — algebraic constraints expressed as Lean types, (2) verification pipeline — weight extraction, constraint checking, proof generation, (3) CAB v2 certificates — cryptographically signed verification results with IPFS-pinned evidence, (4) evaluation harness — reproducible benchmark suite for verification claims.

Builds Upon

MCR-OP-001
MENTAT · Mesh-Encrypted Network for Trusted Autonomous TransactionsImmutable · Content-Addressed · Tamper-Proof
MENTAT-CA-001|MCR-OP-003
2026-02-01

MENTAT Contribution Record

PROOF

Formally Verified

CONTRIBUTION LEVEL: PROOF

Ontological Engineer

Lean 4 Formalization — Neural Network Property Verification

Contributor

Apoth3osis Labs

R&D Division

Machine-checked Lean 4 formalization of neural network algebraic property verification. Weight matrix norms, activation function bounds, layer composition, and end-to-end property propagation. All proved without sorry/admit.

Builds Upon

MCR-OP-001MCR-OP-002
MENTAT · Mesh-Encrypted Network for Trusted Autonomous TransactionsImmutable · Content-Addressed · Tamper-Proof
MENTAT-CA-001|MCR-OP-004
2026-02-05

MENTAT Contribution Record

KERNEL

Computationally Verified

CONTRIBUTION LEVEL: KERNEL

Ontological Engineer

OmegaProof Verified Kernel

Contributor

Apoth3osis Labs

R&D Division

All theorems kernel-checked by Lean 4. Guard-no-sorry passes. Standard axioms only.

Builds Upon

MCR-OP-003
MENTAT · Mesh-Encrypted Network for Trusted Autonomous TransactionsImmutable · Content-Addressed · Tamper-Proof
MENTAT-CA-001|MCR-OP-005
2026-02-05

MENTAT Contribution Record

BRIDGE

Cross-Level Connection

CONTRIBUTION LEVEL: BRIDGE

Ontological Engineer

Documentation Repository + Evaluation Examples

Contributor

Apoth3osis Labs

R&D Division

Published as documentation repository with evaluation examples demonstrating the CAB v2 certificate workflow for neural network verification.

Builds Upon

MCR-OP-003MCR-OP-004
MENTAT · Mesh-Encrypted Network for Trusted Autonomous TransactionsImmutable · Content-Addressed · Tamper-Proof

Governed by MENTAT-CA-001 v1.0 · March 2026

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