Documentation — Vellum Cash

§Abstract & High Concept#

[ NOTE ]

Vellum Cash is a non-custodial, zero-knowledge cross-chain privacy viaduct engineered specifically for the Arc Blockchain—Circle's open, stablecoin-native Layer-1—and EVM ecosystems. It provides mathematically verifiable, irreversible severance between the origin of funds on an ingress chain and their final egress destination.

Public blockchain ledgers are forever. Every transaction, calldata payload, gas parameter, and timestamp is permanently indexed by surveillance software, chain analysis firms, and automated clustering algorithms. Even when users attempt to sever links manually, statistical heuristics and graph correlation algorithms reconstruct user identity with frightening precision.

Vellum Cash re-architects cross-chain settlement from the ground up:

No address reuse: Ingress conduits are single-use and ephemeral.

Zero ABI trace: Shielded deposits are ingested into cryptographic pools with zero public calldata linking recipient addresses.

ZK mathematical proofs: State inclusion is verified via Groth16 zero-knowledge SNARKs over the BN254 pairing curve.

Counter-heuristic design: Inherent Poisson-distributed delay buffers and tranche sharding dissolve graph clustering algorithms.

§The Problem with Public Ledgers#

Every EVM transfer creates a directional edge in a public directed acyclic graph (DAG):

CODE

[ Source Wallet: 0xAlice ] ───( Transfer 5.0 ETH )───► [ Exchange / DApp: 0xBob ]
                                     │
                        Analyzed by Heuristic Clustering:
                        • Gas Price Footprint
                        • Temporal Proximity (Δt < 2m)
                        • Round Amount Correlation
                        • Interaction History

When a user tries to move funds to a clean address using traditional bridges, the bridge contract itself logs both the sender address on Chain A and the recipient address on Chain B. Chain analytics software effortlessly follows this link, entirely negating the intended privacy of the new address.

§The Vellum Paradigm#

Vellum Cash replaces deterministic state bridges with an ephemeral cryptographic aqueduct. Just as ancient Roman viaducts carried freshwater across uneven ravines without preserving the memory of the mountaintop springs from which the water flowed, Vellum Cash channels liquidity through zero-knowledge shielded pools where all origins are mathematically destroyed.

CODE

=========================================================================================
  INGRESS CHAIN (EVM)         ARC BLOCKCHAIN (ZK CORE)            EGRESS CHAIN (EVM/ARC)
=========================================================================================
[ Wallet / App Order ]                                            [ Pristine Recipient ]
          │                                                                 ▲
          ▼                                                                 │
[ Ephemeral Conduit ] ──► [ Groth16 Shielded Pool ] ──► [ Poisson Delay ] ──┤
(Single-use, zero trace)    Poseidon Merkle Tree (2^20)   Tranche Sharding   (Clean Relayer Node)
                            Nullifier Secret Computed     Heuristic Severance
=========================================================================================

Fundamental Sovereign Axioms

Deterministic Ephemeral Formulation: No address is ever reused for more than one deposit.

Mathematical Absence: The link between deposit commitment C and spend nullifier η cannot be computed in polynomial time.

Non-Custodial Sovereignty: Funds are secured exclusively by Circom-verified zero-knowledge circuits; no admin keys, no multisig custody, and no centralized operator can seize or divert liquidity.

§Key System Capabilities#

Capability	Specification	Cryptographic Mechanism
ZK Proof System	Groth16 SNARK	BN254 Elliptic Curve (SnarkJS / Circom)
Cryptographic Hash	Poseidon t=3	Optimized for arithmetic circuits over F_q
Merkle Tree Capacity	Depth 20	$2^{20} = 1,048,576$ shielded deposit commitments
Deposit Ingress	Dual-Mode	Direct Web3 Wallet Connect OR App Order Ingress Address
Egress Settlement	Permuted Relayers	Independent, stake-incentivized relayer nodes
Timing Defense	Poisson Buffer	Stochastic delay distributions Δ t ∼ Poisson(λ)
Liquidity Sharding	Tranche Shred	Non-uniform tranche disbursement across multiple blocks

§High-Level Architecture#

The protocol is partitioned into four decoupled layers:

Ingress Layer: Deployed across Ethereum Mainnet, Arbitrum One, Base, and Optimism. Generates single-use conduit contracts or tracks unique app order deposits.

Arc Shielded Pool: The immutable settlement core running on the Arc Blockchain (Circle's stablecoin-native L1), maintaining Poseidon Merkle trees and nullifier registries.

Heuristic Severance Engine: The off-chain and on-chain coordination layer managing Poisson timing queues and tranche sharding logic.

Clean Egress Relayer Network: A decentralized pool of permuted relayer nodes that dispatch native assets to destination addresses without any cryptographic link to the ingress caller.