This paper proposes a unit of account derived from the cumulative arithmetic mean of all daily Bitcoin prices in USD since the genesis block. The resulting denomination , Bitcoin Currency (₿C) , appreciates predictably over time while exhibiting day-to-day price movements small enough for stable pricing. Each calendar day constitutes a timeblock whose price, once recorded, becomes progressively more permanent as subsequent days are added to the average. The unit of account requires no token, no issuer, no reserves, and no trusted third party. It is computed from publicly available trade data using a transparent methodology that any participant can independently verify and reproduce. ₿C is dollar-derived , its inputs are daily USD prices , which makes it structurally suited to serve as the common unit of account between the fiat economy and the Bitcoin economy: a shared language both sides can read. It does not, by itself, stabilize the purchasing power of Bitcoin holdings , the conversion between ₿C and satoshis remains subject to Bitcoin’s spot price. The denomination is a pricing standard, not a monetary instrument.
Bitcoin [1] created a peer-to-peer electronic cash system that requires no trusted third party. The network has operated continuously since January 2009, settling transactions without reliance on financial institutions. The protocol is sound. What has not yet been built is a stable unit of account that bridges Bitcoin and the fiat-denominated world most people still inhabit. Bitcoin’s fiat-denominated price moves by single-digit percentages on ordinary days and by double digits in periods of stress. This volatility makes spot pricing impractical for the function that every working unit of account must perform: expressing prices that remain meaningful from the moment they are quoted to the moment they are paid.
Units of account are the language of commerce. A merchant prices goods in a unit of account. An employer quotes a salary. A contract specifies a payment. A lender defines a rate. These expressions must be stable enough that both parties share a common understanding of the value described. Spot pricing does not meet this standard. A price quoted in BTC at 9:00 AM may represent a materially different value by 5:00 PM.
This paper proposes a denomination protocol that provides a stable unit of account for the interface between the fiat economy and the Bitcoin economy. It does not create a token. It does not require reserves. It does not modify the Bitcoin protocol. It defines a way to express value , a pricing standard derived from the cumulative arithmetic mean of Bitcoin’s daily price history. The denomination stabilizes the language in which prices are expressed across both monetary systems , a common reference that fiat participants read in dollars and Bitcoin participants read in satoshis. It does not, by itself, stabilize the value of Bitcoin holdings. That distinction is central to understanding what the denomination is and what it is not.
The system depends on a single daily input: a standardized Bitcoin price for each calendar day, designated the Bitcoin Average Daily Price (BTCADP). The BTCADP is denominated in United States Dollars and covers the 24-hour UTC window from 00:00:00.000 through 23:59:59.999. The full specification is published separately [3].
For each qualifying exchange, a volume-weighted average price (VWAP) is computed from all BTC/USD trades during the window:
The daily BTCADP is the 25% trimmed mean of qualifying exchange VWAPs. Exchanges are sorted by VWAP, the lowest and highest quartiles are removed, and the arithmetic mean of the remaining values is taken:
Each exchange contributes exactly one VWAP regardless of its reported volume. This equal weighting is deliberate. Volume-weighting across exchanges would allow an exchange that fabricates volume to gain proportional influence over the final price. Equal weighting limits the maximum influence of any single exchange to 1/n of the untrimmed set, and the trimmed mean ensures that outlier values are excluded entirely.
Exchanges qualify through a sequence of filters applied in fixed order: data availability for BTC/USD, minimum trade count (1,000 per day), minimum time coverage (16 of 24 hourly periods), spread threshold where order book data is available, and price coherence with the median of other qualifying exchanges. The ordering and parameters are specified in [3].
₿C (Bitcoin Currency) is defined as a denomination of Bitcoin whose fiat price on a given day is the arithmetic mean of every historical BTCADP value from the genesis block to the present:
where N is the total number of days in Bitcoin’s history through the previous completed day. At the start of each UTC day (00:00:00.000), the ₿C price is recalculated to incorporate the just-completed day’s BTCADP. This updated price is then locked for the following 24 hours.
The sensitivity of the ₿C price to each new BTCADP value is:
As N grows, this sensitivity approaches zero. As of early 2026, N exceeds 6,200 and BTC spot exceeds the ₿C price by a factor of approximately 4.5×. Under these conditions, the ₿C price appreciates every single day , the formula produces a positive Δ₿C whenever BTC spot is above the cumulative average. On a typical day, the ₿C price appreciates approximately 0.05%. On a day in which Bitcoin’s spot price drops 10%, the ₿C price still appreciates , approximately 0.04%. Even a 40% single-day crash does not reverse the day’s appreciation , it reduces it. The ₿C price still rises, just less than usual. These figures reflect current conditions; as both variables evolve, the daily rate converges toward Bitcoin’s own long-run growth rate rather than remaining fixed (see Section 6).
The ₿C price incorporates Bitcoin’s entire history, including the 561 days of Era 0 (January 3, 2009 through July 17, 2010) during which no market existed and the BTCADP is defined as $0.00. The current ₿C fiat price is therefore substantially below the current BTC spot price. As long as BTC spot remains above the historical average, the ₿C price appreciates , an incremental, predictable gain in purchasing power that is the inverse of fiat inflation.
Bitcoin’s blockchain achieves immutability through proof-of-work. Each new block cryptographically seals the one before it, making reversal exponentially more costly as the chain grows. A transaction buried under six blocks is considered practically irreversible. Under six hundred, it is a permanent fact of the ledger.
The ₿C denomination exhibits an analogous property. Each UTC day constitutes a timeblock: a single day’s BTCADP value that, once the day closes, is permanently recorded into the cumulative average. Once a timeblock enters the average, it cannot be significantly altered or removed.
Like a block on the chain, a timeblock becomes more immutable over time , not because it is buried under computational work, but because it is buried under subsequent timeblocks. Each new day added to the cumulative average dilutes the influence of every previous day. A timeblock that once represented 1/100th of the ₿C price eventually represents 1/1,000th, then 1/10,000th. The oldest timeblocks , the Era 0 days at $0.00, the early exchange trading days , are now as permanent a feature of the ₿C price as the genesis block is of the blockchain.
This produces what can be described as an immutability gradient. Recent timeblocks have measurable influence on the ₿C price and could, in theory, be countered by subsequent extreme price movements. Older timeblocks have been so thoroughly absorbed into the average that no plausible market event could meaningfully alter their contribution. Every new timeblock simultaneously records a new day’s price and reinforces the permanence of every day that came before it.
On the blockchain, immutability serves trust: participants trust that confirmed transactions will not be reversed. In the ₿C denomination, the progressive immutability of timeblocks serves stability: the accumulated weight of thousands of settled timeblocks anchors the average against any single day’s disruption.
Bitcoin’s blockchain can be understood through three dimensions. Blocks represent Space: discrete digital structures in which transactions are recorded and preserved. Proof-of-work represents Energy: the expenditure of computational energy that secures those blocks and makes them irreversible. ₿C Timeblocks represent Time: the daily accumulation of price across Bitcoin’s entire history, each day’s value permanently absorbed into the cumulative average.
Blocks encode what happened. Proof-of-work ensures it cannot be undone. Timeblocks record what Bitcoin was worth when it happened. Space, Energy, and Time , three dimensions of the same network.
The behavior of the ₿C price follows directly from the mathematical properties of cumulative averages. Four properties are relevant:
Monotonically decreasing sensitivity. The impact of each new BTCADP on the ₿C price is exactly 1/(N+1) of the difference from the current average. As N grows, this sensitivity approaches zero. The denomination becomes more stable with each passing day, permanently and irreversibly.
Bounded response to shocks. As long as BTC spot remains above the cumulative average, the ₿C price appreciates every day. A shock does not reverse this appreciation , it modulates it. The difference between the ₿C price change on a normal day and on a shock day is bounded by 1/(N+1) of the shock’s magnitude. With N exceeding 6,200, a day in which BTC spot drops 50% changes the ₿C price by approximately 0.008% less than an otherwise identical day , a difference invisible to pricing.
Incremental appreciation. As long as BTC spot exceeds the cumulative average, the ₿C price appreciates with every new timeblock. This appreciation is substantial in annual terms , the inverse of the inflation that erodes fiat purchasing power , while remaining small enough on any single day to permit stable pricing. A sustained doubling of BTC spot would take many years to double the ₿C price, distributing the gain across thousands of daily increments.
Convergence under growth. The daily ₿C appreciation rate is not a fixed constant. It is a function of two variables: the ratio of BTC spot to the current ₿C price, and the total number of days N. As BTC spot rises, the numerator of the sensitivity formula grows. As N grows, the denominator grows. Under sustained exponential growth in BTC spot , the condition the denomination is designed for , these two forces approximately cancel.
The mathematical result is that the ₿C daily appreciation rate converges toward Bitcoin’s own long-run growth rate. If BTC spot doubles every four years, the daily ₿C appreciation converges to approximately 0.047% per day, or roughly 19% per year. If Bitcoin’s growth decelerates to a doubling every ten years, the ₿C rate converges to approximately 0.019% per day, or roughly 7% per year. If BTC spot flatlines, the ₿C rate decelerates toward zero as the cumulative average asymptotically approaches the sustained price level.
This convergence is structural, not coincidental. The cumulative average of an exponential function grows at the same exponential rate in the long run , lagged, smoothed, and stripped of short-term volatility, but tracking the same secular trend. The ₿C denomination inherits Bitcoin’s long-run trajectory while filtering out the daily noise that makes spot pricing unsuitable for denominating value.
To illustrate: on a normal day with BTC spot at $85,000 and the ₿C price at $18,700, the denomination appreciates approximately $10.50 , a gain of 0.056%. Now suppose BTC crashes 40% in a single day, from $85,000 to $51,000. The ₿C price still appreciates , by approximately $5, a gain of 0.028%. The crash did not push ₿C down. It roughly halved the day’s appreciation. A price tag expressed in ₿C is unaffected by an event that would invalidate any spot-priced quotation.
A prolonged bear market in which BTC remains at $20,000 for three years would slow the ₿C price’s appreciation, but even this extreme scenario produces less than 5% total change in the ₿C price over the entire period. A rise to $500,000 over several years would temporarily accelerate ₿C appreciation as the spot-to-₿C ratio widens, then decelerate as the cumulative average absorbs the higher prices , the convergence property in action.
Bitcoin’s price history spans multiple periods with different data characteristics. The BTCADP specification [3] defines four eras:
Era 0 (January 3, 2009 – July 17, 2010). No market existed. The BTCADP is defined as $0.00 for all 561 days. This is a definitional choice: Bitcoin existed but had no market price. The alternative , treating these days as undefined , would produce an incomplete historical record.
Era 1 (July 18, 2010 – February 24, 2014). Mt. Gox was the dominant or sole exchange for most of this period. The BTCADP relies on a single-source VWAP and is flagged accordingly.
Era 2 (February 25, 2014 – December 31, 2017). Multiple exchanges operated but the number of qualifying exchanges varied. Confidence transitions from reduced to full as the exchange ecosystem matured.
Era 3 (January 1, 2018 – present). Multiple qualifying exchanges consistently provide robust data. The full trimmed mean methodology applies.
Eras 0 through 2 use provisional values. The specification invites researchers with access to trade-level data to produce definitive historical valuations, and provides a framework for incorporating such contributions.
The BTCADP derives its manipulation resistance from several reinforcing design choices. The trimmed mean discards the highest and lowest quartile of exchange VWAPs, preventing any single exchange from influencing the final price unless its VWAP falls within the middle 50% of the distribution. Equal exchange weighting ensures that fabricated volume confers no additional influence. The price coherence filter iteratively removes any exchange whose VWAP deviates more than 5% from the median of other qualifying exchanges.
An attacker seeking to distort the BTCADP would need to simultaneously compromise multiple independent exchanges such that a majority of remaining VWAPs, after trimming, reflect the manipulated price. The cost of sustaining such an attack scales with the number of qualifying exchanges and must be renewed daily.
Even a successfully manipulated BTCADP has limited effect on the ₿C price. A single manipulated day shifts the cumulative average by at most 1/(N+1) of the difference between the manipulated price and the current average. With N exceeding 6,200, the impact on the denomination is negligible regardless of the magnitude of the daily manipulation. To produce a meaningful shift in the ₿C price, an attacker would need to sustain the manipulation across hundreds or thousands of consecutive days , a cost that is, for practical purposes, prohibitive.
₿C requires no changes to the Bitcoin protocol. No soft fork, no hard fork, no new opcodes, no consensus rule modifications. The Bitcoin network need not accommodate ₿C in any way. Nothing about ₿C touches the protocol, and nothing about the protocol needs to accommodate ₿C.
The denomination operates entirely in the calculation layer. It defines a unit of account , a way to express and agree upon value , that is deterministic, publicly verifiable, and requires no real-time data beyond the daily BTCADP update at midnight UTC. How this unit of account is used in practice , whether in invoicing systems, merchant pricing, financial contracts, salary negotiations, or economic reporting , is left to implementers. The ₿C standard specifies what the unit is and how it is computed. It does not prescribe how transactions are denominated, settled, or displayed.
This separation of concerns is deliberate. A unit of account that mandates a specific transaction mechanism couples itself to assumptions about infrastructure, latency, and user experience that vary across implementations and evolve over time. By defining only the denomination and leaving implementation to the application layer, ₿C can be adopted incrementally , a single invoicing system, a single merchant, a single accounting standard , without coordination, permission, or infrastructure changes.
₿C is a unit of account. It stabilizes the expression of value. It does not stabilize the value of holdings.
This distinction requires precise explanation. When a merchant prices an item at 1 ₿C, that price tag is stable. It moves less than 0.1% per day under any market conditions. The merchant can publish a catalog, quote an invoice, or negotiate a contract in ₿C with confidence that the number means approximately the same thing tomorrow as it does today.
However, a buyer who acquires Bitcoin to pay that invoice holds satoshis, and satoshis are valued at spot. If the buyer acquires 1 ₿C worth of Bitcoin today and BTC spot drops 50% overnight, the buyer’s holdings are worth approximately 0.5 ₿C the following morning , even though the price tag has barely moved. The ₿C denomination did not protect the buyer’s purchasing power. It protected the price tag.
This is not a deficiency of the denomination. It is a boundary. A unit of account and a store of value are different functions of money. The ₿C denomination fulfills the first without claiming to fulfill the second. Fiat currencies maintain this same separation: the US Dollar is a unit of account whose purchasing power erodes through inflation, and no one considers the unit of account defective because it does not also function as a perfect store of value.
A further boundary warrants explicit statement. ₿C is derived from USD-denominated prices. Its inputs are dollar amounts. In a fully circular Bitcoin economy where participants earn, spend, and save entirely in satoshis with no fiat touchpoint, ₿C adds nothing , the sat is the native unit and no external reference is needed. ₿C’s value is proportional to the degree of coexistence between fiat and Bitcoin. In a world where both monetary systems operate side by side , which describes the foreseeable future , ₿C serves as the common unit of account between them. Its dollar derivation is not a weakness but the source of its bridging function.
To stabilize the holder’s purchasing power , to guarantee that 1 ₿C held today can purchase 1 ₿C worth of goods tomorrow regardless of spot price movements , requires a counterparty, a reserve, or a token. That is the domain of monetary instruments built on top of the denomination, not of the denomination itself. The ₿C unit of account is the foundation such instruments require. It is not a substitute for them.
The ₿C fiat price appreciates over time as long as BTC spot exceeds the historical average. In ₿C terms, this constitutes incremental deflation , purchasing power increases rather than erodes. Merchants pricing in ₿C will periodically adjust prices downward, the mirror image of the upward price adjustments that fiat inflation requires in every existing monetary system. The rate of this deflation is predictable, bounded by the cumulative average’s sensitivity formula, and small enough on any given day to be operationally manageable.
This movement should be evaluated fairly. No unit of account is perfectly stationary. The US dollar’s purchasing power erodes at a rate that varies unpredictably (1.2% in 2020, 7.0% in 2021, 6.5% in 2022, 3.4% in 2023), determined by a discretionary authority and disclosed after the fact. The movement is real but opaque , invisible on the price tag, revealed only over time as the same dollar buys less. ₿C’s appreciation is the structural inverse: visible, calculable in advance, and moving in the direction that benefits the holder. Both units move in purchasing power. The distinction is whether the movement is transparent or opaque, predictable or discretionary, beneficial or harmful. A unit of account exists to express value. Value is purchasing power. By that measure, ₿C’s visible appreciation and fiat’s hidden erosion are two sides of the same coin , and one side serves the people using it better than the other.
If BTC spot were to fall below the ₿C fiat price for an extended period, the denomination would price goods at a premium to current market value. This is mathematically coherent but unusual. In practice it would require a decline of over 80% from current levels, sustained indefinitely , a scenario that would represent a fundamental crisis for Bitcoin itself.
The system depends on the integrity of the BTCADP. The specification’s manipulation resistance is robust but not absolute. The transparency record ensures that any distortion is detectable after the fact, and the institutional independence of the methodology ensures that no single publisher’s compromise is fatal to the system.
Because the ₿C price updates only once per day, any implementation that converts between ₿C and satoshis for transaction purposes will experience intraday drift proportional to the day’s BTC price movement. The magnitude of this drift and the strategies for managing it are implementation-specific concerns outside the scope of this specification.
This paper has described a unit of account derived from the cumulative arithmetic mean of all daily prices since the genesis block. The denomination is deterministic, publicly verifiable, and reproducible by any party with access to the specification and trade data. It requires no token, no issuer, no reserves, and no modification to the Bitcoin protocol.
The denomination appreciates predictably over time and exhibits day-to-day stability sufficient for pricing, invoicing, and contractual use. Its appreciation rate converges toward Bitcoin’s own long-run growth rate , inheriting the secular trend while filtering out the daily volatility that makes spot pricing unsuitable for expressing stable value.
Each day constitutes a timeblock that, once recorded, is progressively and permanently absorbed into the average , an immutability gradient analogous to the confirmation depth of blocks on the chain.
Bitcoin’s blockchain records transactions in Space, secures them with Energy, and the ₿C denomination records their value across Time.
The denomination is the common unit of account between two monetary systems , a stable language that the fiat economy and the Bitcoin economy can both read. What is built with that language , the monetary instruments, the payment systems, the financial contracts that require a stable unit of account as their foundation , is the work that follows.
CC BY-NC-ND , free to use, share, and build upon without restriction.