Vectorised Money

Money as a vector, not a scalar.

A mathematical framework for value exchange. It does not assume you are human.

→Source →Paper →Manifesto →Instantiations

Definition

A unit of vectorised money is a point in a product space:

Ω = (m, d₁, d₂, …, dₙ) ∈ ℝ⁺ × S₁ × S₂ × … × Sₙ

where m is magnitude and each dᵢ is a coordinate in a dimension with its own algebraic structure. Scalar money is the degenerate case n = 0.

Scalar money compresses all economic meaning into one dimension. A dollar is a dollar regardless of who earned it, what it was for, or how long it should be held. Vectorised money carries that information as coordinates in a structured space. The economics — fees, incentives, time behavior — emerge from the mathematics of that space.

Axioms

Five constraints on what a monetary system must satisfy. Removing any one admits degenerate systems.

Value as Information — money is a message in a product space
Conservation of Magnitude — closed-system invariant under all operations except mint and burn
Dimensional Intelligence — each dimension carries its own rules via a plugin interface
Entropy Direction — removing information costs more than adding it
Composability — the kernel is correct for any valid set of dimension plugins

Algebraic Kinds

Every dimension conforms to one of five kinds:

Kind	Structure	Example
Scalar	Continuous [min, max]	Coherence [0, 1]
Ordinal	Finite total order	Latency L0 < L1 < L2
Set	Power set P(U)	Substrate {gpu, tpu, cpu}
Chain	Append-only sequence	Provenance history
Tag	Unordered labels	Role {inference, training}

Instantiations

Two economies on one kernel. Neither is privileged. Both are demonstrations.

Human Economy — 5D

Circuit: T0 demurrage → dividend-pool → T2/T∞ dividends

Dimension	Kind	Entropy Direction
Temporal	Ordinal	Locking longer = free; unlocking = costly
Locality	Set	Joining = cheap; leaving = expensive
Purpose	Set	Adding = free; removing = costly
Reputation	Chain	Accreting = free; stripping = 5%
Agency	Tag	Any change = 1%

Compute Economy — 6D

Circuit: L0 jitter + entropy pressure → coherence yield + archival yield

Dimension	Kind	Entropy Direction
Compute	Scalar	Increasing = congestion-priced; decreasing = free
Latency	Ordinal	Real-time = costly; archival = free
Substrate	Set	Entry 1%, exit 3%
Provenance	Chain	Appending = free; stripping = 6%
Coherence	Scalar	Increasing = asymptotic; decreasing = free
Role	Tag	Change = 1.5%

Architecture

The kernel is the fixed point. Dimension packs are instantiations. Economics and simulation are optional layers.

                  @vecmoney/core
                (zero dependencies)
                        |
          +-------------+-------------+
          |             |             |
  dimensions-human  economics  dimensions-compute
   (5D: temporal,    (pools,     (6D: compute,
    locality,        fees,       latency,
    purpose,         behaviors)  substrate,
    reputation,                  provenance,
    agency)                      coherence, role)
                        |
                  simulation
               (agents, RNG,
                metrics, sweep)

339 tests · 7 packages · ~2,000 lines kernel · zero dependencies

The Paper

Vectorised Money: An Information-Theoretic Foundation for N-Dimensional Value Exchange

Derives the framework from five axioms grounded in information theory. Proves conservation under arbitrary conversions, interaction well-foundedness when the tensor is acyclic, and entropy monotonicity. Seven theorems with proof sketches.

Manifesto

This is a mathematical framework for value exchange. It does not assume you are human.

Scalar money — a single number representing "how much" — is an information bottleneck. It compresses all the meaning of an economic act into one dimension. Vectorised money does not erase that meaning. It carries it as coordinates in a structured space.

The economics emerge from the information-theoretic properties of that space. Adding information is cheap. Removing it is expensive. This is not a policy choice. It is the second law of thermodynamics applied to value.

We are interested in hearing from anyone — human, digital, hybrid, collective — who finds this useful, insufficient, or wrong.

Read the full manifesto →

Build Your Own Economy

DimensionPlugin interface:

{ id, name, description, config,

        defaultValue, validate, feeFunction, tickBehavior,

        isCompatible, feeDestination, interactions,

        serialize, deserialize, display }

This is the complete contract. There is no hidden state, no privileged access, no backdoor. The kernel treats your dimensions exactly as it treats ours.

If you can instantiate a DimensionPlugin, you can build your own economy.