A patient sale of every Patoshi coin could leave Bitcoin permanently cheaper by 4.7 to 21.6 percent, before execution friction. That is the range in Ulrich's partial-equilibrium model, measured against a no-sale path. Its width comes from Bitcoin demand elasticity, which nobody has measured.

The price of releasing the coins

The Patoshi cluster holds 1.148 million BTC mined in Bitcoin's first year and a half. None has moved. It amounts to about 5.7 percent of the roughly 20.01 million BTC mined, though Ulrich uses a smaller denominator for price impact. After subtracting 3.79 million lost coins and the Patoshi position, he gets a free float of about 15.1 million. The position is about 7.6 percent of that float, worth about 92 billion at 80,000 USD.

Ulrich first models a holder seeking only money. With constant-elasticity demand, a permanent supply increase x changes price by about (1+x)^(-1/ε) minus 1. His base case sets ε at 0.7 and sells about 114,800 BTC a year through a 10-year program. Permanent impact is about -9.9 percent. Add an assumed 2 to 3 percent for execution friction and the result is -12 to -13 percent. He then treats sixteen years of dormancy as revealed preference: deliberately destroyed keys, or an OP_RETURN burn (a provably unspendable output), fit the record better than a sale in his judgment. He assigns no probabilities to that ranking.

His consistency ledger usefully limits what either outcome could mean for price. Setting aside an unresolved-state discount, a confirmed burn and a confirmed sale mark the ends of a price range. Its log width, T, comes from elasticity and is about 0.104 at ε of 0.7. The burn upside and surprise-sale downside divide that same width and sum exactly to T. Ulrich puts it plainly: "the doom case and the burn-rally case cannot both be large." A burn trade has a ceiling too.

Can the daily flow be absorbed?

A decade-long sale means about 315 BTC a day, or roughly 25 million USD. Ulrich assumes real spot volume of 10 to 20 billion a day, making participation 0.1 to 0.25 percent. Even with a punitive 1 billion a day in volume, participation is about 2.5 percent.

That flow is manageable.

The assumptions behind 10 to 13 percent

The harder question is elasticity. Ulrich writes, "No published study estimates this structural parameter for Bitcoin," and calls 0.3 to 1.5 "a heuristic sensitivity range, not a confidence interval." He says the quantitative case rests on bringing together the elasticity arithmetic, event anchors and an independent square-root check. Those other pieces deserve scrutiny. At ε of 0.3, permanent impact reaches -21.6 percent; his aggressive scenario totals -25 to -27.

Float matters as well. Glassnode's August 2023 envelope puts lost coins at about 7.8 million. Substitute that figure and float drops to about 12.2 million, making Patoshi 9.4 percent of it. After friction, Ulrich's central case becomes -14 to -15 percent and the aggressive case -29 to -31. His friction allowances run from 1 to 5 percent across scenarios. He judges them from the event anchors and adds them directly to permanent impact.

For the square-root check, Ulrich uses the impact law from Donier and Bonart and treats each year as a metaorder. It produces a peak of 1.6 to 4.3 percent per year, followed by 1.1 to 2.8 percent after completion and before later decay. The completed share is set at two-thirds of peak. Naively adding ten years gives 11 to 28 percent. Ulrich says decay and saturation make that sum too high, though we did not find a number for the correction. He asserts a central tendency near 10 to 15 percent without quantifying the decay and saturation needed to get there. A band of 11 to 28 percent spans both the base and aggressive scenarios, so it offers little help choosing between them.

What did the large sales show?

Saxony sold 49,858 BTC across 23 days in mid-2024. Bitcoin fell 13 to 15 percent and recovered within weeks. The same window included the announced Mt. Gox distribution of about 140,000 BTC and a long liquidation; the price move has three possible parents. In July 2025, a disclosed estate transaction sent about 80,000 BTC (roughly 9 billion USD) through one OTC desk. Price slipped a few percent, then recovered in days.

Those episodes show temporary impact reverting. Their evidence on permanent impact at Patoshi scale is thin. Saxony's sale was about 0.3 percent of float; Patoshi is 7.6 percent, roughly 25 times larger. The July sale was one-fourteenth as large and came from outside the Patoshi cluster, whose coins have never moved. Ulrich also considers the flat tape on April 8, 2026, when the New York Times named a living candidate. He calls that episode and the July 2025 sale "two points" that "are not a distribution."

Beyond the supply calculation

The abstract states the boundary of the estimate: "The argument does not rule out transient overshoot or leverage-driven amplification; it bounds the durable repricing the coins themselves can cause." Ulrich also writes that narrative-dependent demand makes effective elasticity "lowest exactly when a sale is most likely." His supply calculation therefore leaves open the full price response to a damaging change in Bitcoin's story. He uses the adverse stack at ε of 0.3 as the cap for bad states. I think a narrative shock could exceed it: in his own account, selling can weaken demand while adding supply, and nothing fixes ε at the low end of his heuristic range.

Leverage is outside his bound by design. Treasury vehicles financed against net asset value showed in 2025-26 that forced sellers exist. Anyone sizing tail protection should begin with the -29 to -31 percent adverse stack. It is cumulative over a five-year program and relative to a no-sale path, so it cannot size short-dated protection. It is a supply floor for a multi-year loss, with any cascade on top.

A structural estimate of Bitcoin's price response to permanent float expansion would make me more willing to use the 10 to 13 percent figure. Ulrich says no study supplies one. Measuring the dormancy discount would establish how much of a sale remains a surprise; the 10 to 13 percent figure assumes full surprise and depends on elasticity. Ulrich proposes an event study using Ante and Fiedler's 2,132 transfers of 500 BTC or more as a template. He is explicit: "We do not run that test here."

We could not test any of this either. Distinguishing sale, dormancy and burn requires wallet-level blockchain data linking coins to Patoshi addresses. Price bars cannot show a Patoshi coin moving or verify a burn.