1. Introduction
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. Yet Bitcoin has not achieved widespread adoption as a medium of everyday exchange. The barrier is not technical. The network works. Lightning provides throughput. Settlement is secure and final.
The barrier is that Bitcoin's fiat-denominated price is volatile, and this volatility makes it impractical for the daily commerce that constitutes the bulk of economic activity.
Stablecoins emerged to address this gap by pegging digital tokens to fiat currencies. In doing so, they reintroduce the trust dependencies Bitcoin was designed to eliminate: centralized issuers who can freeze accounts, reserves that must be audited, and continued operation of entities subject to regulatory and counterparty risk. Algorithmic approaches have demonstrated catastrophic failure modes [2]. Fiat-backed stablecoins function as digital dollars routed through additional intermediaries.
What is needed is a way to express Bitcoin's value that is stable enough for daily use while remaining entirely Bitcoin-native. This paper proposes a denomination protocol that achieves this through a cumulative historical average of daily prices. No new token is created. No reserves are held. No entity is trusted. The protocol is a standard for expressing value — a unit of account that any wallet, merchant, or payment system can adopt independently.
2. The Price Reference
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].
3. The Denomination
BTCC (Bitcoin Currency, symbol ₿C) 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 BTCC (₿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 BTCC (₿C) price to each new BTCADP value is:
As N grows, this sensitivity approaches zero. As of early 2026, N exceeds 6,200. A day in which Bitcoin's price moves 10% produces a change in the BTCC (₿C) price of less than 0.01%. A 40% single-day crash shifts the BTCC (₿C) price by approximately 0.04%. These are mathematical properties of cumulative averages. They do not depend on market conditions, assumptions about future prices, or the continued operation of any institution.
The BTCC (₿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 BTCC (₿C) fiat price is therefore substantially below the current BTC spot price. As long as BTC spot remains above the historical average, the BTCC (₿C) price rises slowly — a gradual appreciation in purchasing power that is the inverse of fiat inflation.
4. Timeblocks
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 BTCC (₿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 BTCC (₿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 BTCC (₿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 BTCC (₿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.
Every new timeblock does two things simultaneously: it records a new day's price into the cumulative average, and it reinforces the permanence of every timeblock that came before it. The act of adding a new day makes all previous days more immutable.
5. Three Dimensions
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. BTCC (₿C) Timeblocks represent Time: the daily accumulation of price across Bitcoin's entire history, each day's value permanently absorbed into the cumulative average.
Discrete structures recording transactions. Encode what happened.
Computational expenditure securing blocks. Ensures it cannot be undone.
Daily price accumulation across Bitcoin's entire history. Records what it was worth.
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.
6. Stability Properties
The stability of the BTCC (₿C) price follows directly from the mathematical properties of cumulative averages. Three properties are relevant.
Monotonically decreasing sensitivity. The impact of each new BTCADP on the BTCC (₿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. Even a theoretically unbounded single-day price movement can only shift the BTCC (₿C) price by an amount determined by 1/(N+1). With N exceeding 6,200, no single day can move the BTCC (₿C) price by more than approximately 0.016% of the shock's magnitude.
Incremental appreciation. Over extended periods, the BTCC (₿C) price trends in the direction of sustained BTC price levels, but at a dramatically attenuated rate. A sustained doubling of BTC spot would take many years to double the BTCC (₿C) price.
To illustrate: a flash crash in which BTC drops 40% in a single day, from $90,000 to $54,000, shifts the BTCC (₿C) price by approximately $6 — a change of 0.04%. A prolonged bear market in which BTC remains at $20,000 for three years produces less than 5% total change in the BTCC (₿C) price over the entire period.
7. Historical Eras
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.
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.
8. Manipulation Resistance
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 BTCC (₿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 BTCC (₿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.
9. Implementation Neutrality
BTCC (₿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 BTCC (₿C) in any way.
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 wallet interfaces, invoicing systems, merchant pricing, payment protocols, or smart contracts — is left to implementers.
This separation of concerns is deliberate. By defining only the denomination and leaving implementation to the application layer, BTCC (₿C) can be adopted incrementally — a single wallet, a single merchant, a single accounting system — without coordination, permission, or infrastructure changes.
10. Known Limitations
The BTCC (₿C) fiat price appreciates slowly over time as long as BTC spot exceeds the historical average. In BTCC (₿C) terms, this constitutes deflation. Merchants pricing in BTCC (₿C) will occasionally need to adjust prices downward. Whether this is a limitation or a feature is a matter of economic philosophy.
If BTC spot were to fall below the BTCC (₿C) fiat price for an extended period, the denomination would price goods at a premium to current market value. In practice this would require a decline of over 80% from current levels, sustained indefinitely — a scenario that would represent a fundamental crisis for Bitcoin itself. Across 5,719 trading days, spot has been below the cumulative average for exactly seven days — a single period in November 2011.
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 BTCC (₿C) price updates only once per day, any implementation that converts between BTCC (₿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.
11. Conclusion
This paper has described a denomination protocol for Bitcoin that produces a unit of account without introducing trust, issuers, reserves, or protocol modifications. The stability derives from a cumulative historical average that, by its mathematical nature, becomes more resistant to disruption with every passing day.
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. The denomination operates in the calculation layer only. It defines a unit of value; it does not prescribe how that unit is transmitted, settled, or displayed. Any existing wallet, payment processor, or settlement infrastructure can adopt BTCC (₿C) by implementing its own conversion logic against a single daily price that is deterministic, publicly verifiable, and reproducible by any party with access to the specification and trade data.
Bitcoin's blockchain records transactions in Space, secures them with Energy, and the BTCC (₿C) denomination records their value across Time. The denomination asks nothing of the protocol and changes nothing about it. It requires only that the price history be computed transparently — and provides a transparent, reproducible methodology for doing so.