V4-Native · Deflationary · ImmutableMS. 01 / 2026

EntropyTheory

Scarcity is engineered.
Asymmetry is the point.

Abstract

Bitcoin made value emerge from the impossibility of creating more. entr0py asks what happens when the impossibility runs in the other direction.

Read the mechanism The question

Ticker $ENTROPYBuy 1.00%Sell 5.00%Standard ERC-20Continue

§ 01 — PREMISE

The Question

every scarcity model answers a different question. this one inverts it.

Bitcoin proved that an asset’s value could emerge from the impossibility of making more of it.

Entropy Theory asks the inverse question:

What happens when the supply itself becomes the scarce resource?

§ 02 — PROTOCOL

The Entropy Mechanism

four steps. one direction.

Trade enters the V4 pool

A user calls swap() on a Uniswap V4 PoolManager. The pool is registered with the Entropy hook.

entry point

The hook intercepts

The hook reads the swap direction through beforeSwap / afterSwap.

Buying ENTROPY 1% feeSelling ENTROPY 5% fee

direction decides the cost

Fee → buyback → burn

Buy fees are burned directly. Sell fees are converted back into ENTROPY through the internal pool mechanism and then burned. The final destination is address(0).

one-way street

Supply only decreases

No mint function.No rebase.No emission schedule.No admin-controlled supply expansion.

The supply only moves in one direction.

Down.

monotonic

Fig. 01 — Swap path

Userswap()

Uniswap V4 PoolManager

Entropy HookbeforeSwap / afterSwap

Buyfee 1.00%

Sellfee 5.00%

Burn

address(0)

Fig. 01 — Execution path of a single swap through the Entropy hook. Both fee branches terminate at the same sink. Directional asymmetry is enforced at the hook layer, not at the token layer.

§ 03 — DIRECTIONAL COST

Asymmetry is the point

the two directions are not priced the same. that is the whole design.

Holding is cheap.
Exiting is expensive.

Buy1.00%

0%5%

entry is nearly frictionless

Sell5.00%

0%5%

exit pays five times over

Buy tax1.00%Sell tax5.00%

5×Burn%sell ÷ Burn%buy

Every exit makes everyone else’s share larger.

ii.

Selling pressure is not neutral — it is converted into permanent supply removal.

iii.

The fee schedule is fixed at the hook layer. It applies identically to every address.

§ 04 — DECAY MODEL

Supply Decay

a conceptual curve, not a promise. the shape is what matters.

S(t) = S₀ · e⁻ᵏᵗ

Conceptual model — continuous supply decay under sustained activity

Fig. 02 — Decay curve

Fig. 02 — Total supply plotted against time. The smooth curve is the continuous idealisation; the stepped line is what the chain actually records — one discrete burn per taxed swap.

Reading the model

The conceptual model represents supply continuously decreasing over time as market activity destroys tokens. Every taxed swap subtracts from the total; nothing in the protocol adds back.

Terms

S(t)Total supply remaining at time t

S₀Supply at deployment

kDecay constant — a function of volume and swap direction

tElapsed protocol time

k is not fixed. It is whatever the market decides to do.

§ 05 — FORMALISM

Information Theory

borrowed language, used precisely.

H(X) = −Σ pᵢ log pᵢShannon entropy of a discrete distribution

Entropy Theory borrows the language of information theory to frame uncertainty, distribution and scarcity. In Shannon’s formulation, H(X) measures how much is unknown about a random variable: a distribution concentrated on a single outcome carries no information, while a distribution spread evenly across outcomes carries the most.

Applied to a token, the same expression describes how ownership is distributed across addresses. A supply held by one address has an entropy near zero. A supply dispersed across many independent holders approaches the maximum, log n.

The protocol does not attempt to optimise H(X). It only guarantees that the sample space itself is shrinking: every taxed swap reduces the total quantity over which any distribution can be defined. Scarcity, in this framing, is not a constraint on issuance — it is a constraint on persistence.

^† Notation follows Shannon (1948), A Mathematical Theory of Communication. The analogy is descriptive, not a claim that token distributions satisfy the assumptions of a memoryless source.

Fig. 03 — Distributions

Fig. 03 — Two ownership distributions over the same number of addresses. Left: concentrated, low H(X). Right: dispersed, high H(X). The protocol is indifferent to which obtains; it acts on the total, not the shape.

Information flow per swap

Swapevent

Direction1 bit

Fee selector1% | 5%

Burn quantityΔ supply

Supply stateS(t)

one bit of direction decides how much disappears.

§ 06 — LINEAGE

The Origin

one idea, read backwards.

Bitcoin: A Peer-to-Peer
Electronic Cash System

Satoshi Nakamoto
2008

Abstract

REF. 2008PAGE 1

the reference, not the reproduction.

Bitcoin introduced digital scarcity through a system where additional supply is fundamentally constrained. Nothing about the network prevents you from holding — it only prevents anyone from printing more.

Entropy Theory takes inspiration from that principle and experiments with the opposite direction: instead of preventing creation, preventing survival.

BitcoinScarcity through limited creation

EntropyScarcity through continuous destruction

Same premise — value follows from what cannot be done. Only the impossible operation has changed.

§ 07 — ARCHITECTURE

Why Uniswap V4?

because the rule belongs at the swap, not at the transfer.

The protocol’s mechanism is implemented at the swap layer through a Uniswap V4 Hook. A hook is contract code thePoolManager calls at defined points in a swap’s lifecycle — which means the fee logic runs where the trade actually happens, with full knowledge of its direction.

Earlier deflationary tokens enforced taxes inside transfer(). That approach cannot distinguish a buy from a sell without heuristics, breaks composability, and taxes transfers that were never trades. A V4 hook does not need to guess.

Direction is known

beforeSwap receives the swap parameters. Buy and sell are distinguishable facts, not inferences.

The token stays clean

ENTROPY remains a standard ERC-20. Wallets, bridges and contracts see ordinary transfers.

Fixed at registration

The hook address is bound to the pool at creation. The mechanism cannot be swapped out afterwards.

Fig. 04 — Call stack

Userexternally owned account

initiates

Uniswap V4 PoolManagersingleton

routes every pool

Entropy Hookregistered at pool creation

the rule lives here

beforeSwap / afterSwapdirection resolved

reads which way the trade goes

Fee1.00% buy · 5.00% sell

asymmetric by design

Burnbuy: direct · sell: buyback

irreversible

address(0)terminal sink

no key exists

Supply after execution: S(t) < S(t−1)

Fig. 04 — The call stack from user intent to terminal sink. Each descent is a contract boundary; the last one has no return path.

§ 08 — SPECIFICATION

Properties

what is present, and — more importantly — what is not.

RefPropertyDefinitionState

P.01V4-NativeFee logic executes inside a Uniswap V4 hook, not inside transfer().Asserted

P.02DeflationaryEvery taxed swap terminates in a burn to address(0).Asserted

P.03ImmutableHook is bound to the pool at creation and cannot be replaced.Asserted

P.04No mintNo function exists that increases total supply.Absent

P.05No rebaseBalances are never rewritten by protocol action.Absent

P.06No emissionsThere is no schedule, no inflation curve, no reward issuance.Absent

P.07No admin supply controlNo privileged address can expand the supply.Absent

Specification sheet · Rev. AVerify against the deployed bytecode

§ 09 — DEPLOYMENT

Contract

verify before you trust. always.

NetworkEthereum

StandardERC-20

IntegrationUniswap V4 Hook

AddressPending

0x0000000000000000000000000000000000000000

HookPending

0x0000000000000000000000000000000000000000

†Addresses are placeholders until deployment. Confirm the canonical values against the official channels listed below before interacting with any contract claiming to be ENTROPY.

§ 10 — REFERENCES

Documentation

read the source. the source is the argument.

Read the whitepaperThe full specification: mechanism, fee derivation, hook lifecycle and the decay model in long form.Open View contractSource for the ERC-20 and the V4 hook. Read it before you form an opinion about it.Open View on EtherscanDeployed bytecode, verified source, burn history and the balance held at address(0).Open

Links resolve once the corresponding artefacts are published.

§ 11 — CHANNELS

Where the work happens

no announcements. only the record.

Every claim on this page can be checked somewhere below.

if a link is quiet, it hasn’t shipped yet.

Bitcoin made scarcity permanent.Entropy makes destruction permanent.