TLDR: price peaks around 81866/210000 ~ 38.98 % of halving cycle, due to maximum of scarcity impulse metric. Price trend is derived from supply dynamics alone (with single scaling parameter).
Caveats: don't use calendar time, use block height for time coordinate. Use log scale. Externalities can play their role, but scarcity impulse trend acts as a "center of gravity".
Price of Bitcoin (Orange) in log-scale, in block-height time.
1. The Mechanistic Foundation
We treat halvings not as discrete events, but as a continuous supply shock measured in block height. The model derives three protocol-based components:
Smooth Supply: A theoretical exponential emission curve representing the natural form of Bitcoin's discrete halvings.
Bitcoin supply at block b. Smooth (blue) vs Actual (orange)
Halving-Induced Deficit (HID):
HID(block) = SmoothSupply(block) – ActualSupply(block)
The cumulative number of Bitcoin "withheld" from circulation due to halvings.
Halving Induced Difference (HID) at a block b.
Reward Rate Ratio (RRR):
RRR(block) = SmoothRewardRate(block) / ActualRewardRate(block)
The instantaneous supply pressure at any given block.
Reward Rate Ratio (RRR) at block b.
The Scarcity Impulse:
ScarcityImpulse(block) = HID(block) × RRR(block)
This is the core metric—it quantifies the total economic force of the halving mechanism by multiplying cumulative deficit by instantaneous pressure.
Scarcity Impulse (SI) at block b.
2. The Structural Invariant: Block 81866/210000
Mathematical analysis reveals that the Scarcity Impulse reaches its maximum at block 81,866 of each 210,000-block epoch ~38.98% through the cycle. This is not a fitted parameter, but an emergent property of the supply curve mathematics
This peak defines (at least) two distinct regimes:
Regime A (Blocks 0-81,866): Scarcity pressure is building. Supply dynamics create structural conditions for price appreciation. Historical data shows cycle tops cluster near this transition point.
Regime B (Blocks 81,866-210,000): Peak scarcity pressure has passed.
3. What This Means
The framework's descriptive power is striking. With a single scaling parameter, it captures Bitcoin's price trend across all cycles. Deviations are clearly stochastic:
- Major negative externalities (Mt. Gox collapse, March 2020) appear as sharp deviations below the guide
- Price oscillates around the structural trend with inherent volatility
- The trend itself requires no external justification—it emerges purely from supply mechanics
This suggests something profound: the supply schedule itself generates the structural pattern of price regimes. Market dynamics and capital flows are necessary conditions for price discovery, but their timing and magnitude follow the predictable evolution of Bitcoin's scarcity.
4. Current State and Implications
As of block 921,188, we are approximately 1 weeks from block 81,866 of the current epoch (921866)—the structural transition point.
What this implies:
- We are approaching the peak of Regime A (scarcity accumulation)
- The transition to Regime B marks the beginning of a characteristic drawdown period
- This drawdown, is structurally embedded in the supply dynamics
- This is not a prediction of absolute price levels, but of regime characteristics
The framework suggests that the structural drawdown is far more significant than pinpointing any specific price peak.
5. The Price Framework
Model suggests that price is strongly defined by scarcity, so the core of the model is a
PriceAttractor[b] = terminalPrice^BitcoinSupplySmoothNormalized[b];
For terminalPrice of $240,000 per Bitcoin we may see a decent scaling fit.
Bitcoin price (Orange) vs Terminal price (Green dashed).Log scale.
Scarcity Impulse (after normalisation) may be incorporated into Supply-driven price model via multiplicative and phase shift components:
Bitcoin price (Orange) and Scarcity Impulse – driven value.
Conclusion
Bitcoin's price dynamics exhibit a structural pattern that emerges directly from its supply schedule. The 38.98% transition point represents a regime boundary embedded in the protocol itself. While external factors create volatility around the trend, the trend itself has remained remarkably consistent across all historical cycles.
Bitcoin's (and Crypto) Price Regimes: The Formula Was in Front of Us All This Time [SERIOUS]
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Posted by AndriyTyurnikov