/ research
How DRA self-regulates Bitcoin's data capacity.
A short, technical walkthrough of the mechanism, its game-theoretic properties, and a historical replay of what the policy would have produced under prior epochs.
01
How it works
01Dh
Per-block demand
For each block h, observe the total OP_RETURN bytes Dh. This is the raw signal — what users actually paid for.
02Mk
Epoch median
Aggregate the last N blocks (default N = 144) into epoch k, then take the median of {Dh}. The median is robust to single-block spam spikes.
03rk
Demand ratio
Compute rk = Mk / Lk-1 — the realized usage relative to the prior limit. Clamp to [r_min, r_max] to bound any single epoch's adjustment.
04log
Logarithmic damping
Apply a log₂ scaler so that doubling demand only halves the multiplier. This neutralizes geometric attacks and ensures convergence.
05Lk
Apply & clamp
Lk = clamp(Lk-1 · (1 + ½·log₂(rk)), L_min, L_max). The new limit ships at the next epoch boundary. No human in the loop.
02
Game theory & network health
incentive equilibrium
DRA's stable point is where median demand equals the current limit (rk = 1), meaning the log term is zero and Lk holds. Any deviation introduces a damped restoring force — the same negative-feedback shape difficulty-adjustment uses for hashrate.
users
pay fees
miners
order txs
protocol
adjusts Lk
▸ equilibrium · rk = 1 · ΔLk = 0
▸ upper attack cost · O(rmax · fee_floor · N)
▸ lower attack cost · O(rmin⁻¹ · forgone_fees · N)
attack surface analysis
spam pressure
Sustained high demand pushes Lk up, but log damping caps growth at +50%/epoch even with rk=2. Attacker pays escalating fees against a moving target.
low
starvation attack
Coordinated under-use to shrink Lk requires miners to forgo fee revenue across many epochs. Defection by a single rational miner restores baseline.
low
inflation of capacity
L_max bound prevents unbounded growth regardless of fee bidding. Hard ceiling enforced by policy code.
bounded
deflation / suppression
L_min bound preserves a minimum data carrier capacity. Existing protocols (timestamps, commitments) keep functioning.
bounded
miner manipulation
Median statistic over 144 blocks requires a majority of blocks per epoch — economically equivalent to a 51% policy attack.
negligible
03
Historical simulation
Replaying DRA against synthetic Bitcoin history. The protocol absorbs ordinal-style spikes, then settles back as demand normalizes — without any human policy change.
2022 · stable
2023 · ordinals surge
2024 · normalization
2025 · adaptive equilibrium