<_RESEARCH/PROJECTS

Base PCN Algebraic Security

VERIFIED0 SORRY5 MENTAT CERTSLean 4 + Mathlib

>_VERIFICATION.SEAL

Formal Verification Certificate

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

0 SORRY

Base PCN Algebraic Security • Lean 4 + Mathlib • Apoth3osis Labs

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The Central Question

Can payment channel security be proved without cryptographic assumptions? Standard PCN security proofs rely on computational hardness (discrete log, hash preimage resistance). This project establishes an orthogonal layer: algebraic invariants that hold unconditionally. Capacity is conserved under routing. Flow balance is maintained at every node. Settlement correctness links on-chain and off-chain state. These properties hold even if the underlying cryptography is broken — they are structural, not computational. Specialized for Coinbase’s Base L2 rollup architecture.

Key Verified Results

capacity_conservation

Total channel capacity invariant under routing

CapacityConservation.lean

flow_balance

Intermediate nodes neither gain nor lose value

FlowBalance.lean

settlement_correct

On-chain settlement reflects off-chain state

Settlement.lean

l2_boundary_invariance

Invariants preserved across L2 rollup boundaries

L2Bridge.lean

Resources

GHGitHub Repository IDXAll 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 MENTAT EXPLORE 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-002|MCR-BPA-001

2026-01-25

MENTAT Contribution Record

IDEA

Conceptual Contribution

CONTRIBUTION LEVEL: IDEA

Ontological Engineer

Algebraic Security for Payment Channel Networks

Contributor

Apoth3osis Labs

R&D Division

Core insight: PCN security can be established through algebraic invariants rather than cryptographic assumptions. Capacity conservation, flow balance, and settlement correctness follow from graph-theoretic structure — no computational hardness needed. This gives unconditional guarantees for the Layer 2 accounting layer.

MENTAT · Mesh-Encrypted Network for Trusted Autonomous TransactionsImmutable · Content-Addressed · Tamper-Proof

MENTAT-CA-002|MCR-BPA-002

2026-01-25

MENTAT Contribution Record

THEORY

Mathematical Foundation

CONTRIBUTION LEVEL: THEORY

Ontological Engineer

Graph-Theoretic PCN Invariants on Base

Contributor

Apoth3osis Labs

R&D Division

Complete framework: (1) capacity conservation — total channel capacity is invariant under routing, (2) flow balance — intermediate nodes neither gain nor lose value, (3) settlement correctness — on-chain settlement reflects off-chain state, (4) Base-specific: L2 batch submission preserves invariants across rollup boundaries.

Builds Upon

MCR-BPA-001

MENTAT · Mesh-Encrypted Network for Trusted Autonomous TransactionsImmutable · Content-Addressed · Tamper-Proof

MENTAT-CA-002|MCR-BPA-003

2026-01-25

MENTAT Contribution Record

PROOF

Formally Verified

CONTRIBUTION LEVEL: PROOF

Ontological Engineer

Lean 4 Formalization — Algebraic PCN Security on Base

Contributor

Apoth3osis Labs

R&D Division

Machine-checked Lean 4 formalization of algebraic security properties for PCN on Coinbase's Base blockchain. Capacity conservation, flow balance, settlement correctness, and L2 boundary invariance. All proved without sorry/admit.

Builds Upon

MCR-BPA-001MCR-BPA-002

MENTAT · Mesh-Encrypted Network for Trusted Autonomous TransactionsImmutable · Content-Addressed · Tamper-Proof

MENTAT-CA-002|MCR-BPA-004

2026-02-01

MENTAT Contribution Record

KERNEL

Computationally Verified

CONTRIBUTION LEVEL: KERNEL

Ontological Engineer