The Asset That Pays Rent to Exist
Gold sits in a vault. Equity sits on a register. BTC has to be bought back from the world every ten minutes, and the bill is indexed to its own price.
Gold sits in a vault. Equity sits on a register. BTC has to be bought back from the world every ten minutes, and the bill is indexed to its own price. At $1 million a coin the bill is 7% of world electricity generation. At $10 million it is 70% — spent to move seven transactions a second.
Keywords: BTC, power law, carrying cost, security budget, proof-of-work, gold, equities, store of value, block subsidy, halving, fee market, transaction throughput, electricity constraints, energy economics
1. The claim under test
There is a genre of chart in which the logarithm of the BTC price is regressed on the logarithm of time since genesis, a straight line emerges, and the line is extended to $1 million, $10 million and beyond. The fitted line is offered as a structural feature of the asset — a “power law” — rather than as what it is, which is a description of a realised path. It is presented with the confidence of a physical law: the orbit of a planet, the decay of an isotope. And the analogy is meant seriously. The people who draw these charts believe that BTC’s price obeys a scaling relationship as reliable as gravitation, and that the only rational response is to hold and wait for the curve to carry the number upward.
The statistical objection has been made, and made well. The same econophysics machinery that fits smooth power-law trends to financial time series also fits bubbles and negative bubbles to them, and it fits them to BTC. When Fry and Cheah bring that apparatus to the cryptocurrency markets they identify statistically distinguishable endogenous and exogenous shocks in the BTC series — a November 2012 endogenous bubble, a March 2013 exogenous one, a December 2013 exogenous crash — and they find a spillover from Ripple that exacerbates BTC’s subsequent falls (Fry & Cheah, 2016, Table 2, §5.2). Their models are drawn from the physics of critical phenomena, the same intellectual lineage the power-law charts invoke; and what that lineage actually delivers, applied honestly, is not a smooth escalator but a diagnosis of a speculative process that produces both manias and crashes as its own special cases. A curve that contains its own reversals is a description of sentiment. It is not a law of motion, and it carries no promise about the future that its own machinery does not immediately undercut.
But the statistical objection, however sound, concedes too much. It argues about whether the line is a good fit. The objection I want to make does not care whether the line fits. It concerns what the line, taken at face value, actually commits its believers to — and the commitment turns out to be physically and economically incoherent long before the line reaches the numbers printed on it.
Gold, equities and BTC are habitually placed in the same sentence as “stores of value,” as though the phrase named a single category with three members. It does not. The three assets have fundamentally different cost structures, and the difference is not a matter of degree. Two of them are stocks: quantities that, once produced, persist without further expenditure. Gold, once mined, is gold; a share, once registered, is registered. Neither asset has to be continuously re-manufactured to go on existing. BTC is not like that. BTC is a flow — a service that must be re-purchased from the physical world continuously, block after block, at a price the protocol pins directly to the market price of the asset itself. The moment you write that distinction down with any care, the power-law extrapolation stops looking merely optimistic and starts looking impossible, because the thing being extrapolated is a claim on a quantity of real resources that rises in lockstep with the price on the chart.
This essay makes that case in three figures and closes each of them against the physical and economic constraints the discourse never models. The first figure disposes of the standard “BTC is cleaner than aluminium” talking point by repairing a denominator. The second draws the carrying cost the power-law charts omit. The third shows where the extrapolation collides with the electricity system. Along the way the fee market — the mechanism that is supposed to keep the whole thing solvent once the block subsidy decays — is shown, from the peer-reviewed theory of exactly this system, to be structurally incapable of the job assigned to it.
2. Production is not custody
Figure 1 starts from the comparison that already exists in the literature and then repairs its denominator, because the uncorrected version is the single most-cited defence of BTC’s energy use and it rests on a category error.
Averaging daily data from 1 January 2016 to 30 June 2018, Krause and Tolaymat computed the energy consumed to generate one US dollar of value for four cryptocurrencies and five mined commodities. Their headline figures are 17 MJ per dollar for BTC, against 122, 4, 5, 7 and 9 MJ for aluminium, copper, gold, platinum-group metals and rare earth oxides respectively — so that, aluminium excepted, cryptomining consumed more energy per dollar than conventional mineral mining (Krause & Tolaymat, 2018, p. 711, p. 714). Across fifteen published rig-efficiency scenarios the BTC figure ranges from 5 to 34 MJ per dollar, and in fourteen of those fifteen it still exceeds gold (ibid., p. 714). The one bar that sits above BTC is aluminium at 122, and that single exception is the number the bulls quote: even aluminium is dirtier than BTC. It is an artefact of a broken denominator, and once the denominator is fixed the comparison inverts and then collapses.
The metric is “energy per dollar of value created.” For the metals it means exactly what it says. At the end of the process a kilogram of copper exists that did not exist before. It conducts electricity, it can be drawn into wire, it has industrial uses that persist for as long as the metal does. When someone pays for that kilogram, the dollars are payment for a physical thing brought into existence by the expenditure of energy. The denominator is real output.
For proof-of-work there is no such thing. Nothing is produced. The hashes computed in the mining tournament are not a good, a service, or an input to anything; they exist only to be expensive. Gill, Stinner and Tyrell put the point precisely in their formal analysis of exactly this question: in proof-of-work “the computational output — hashes — has no intrinsic productive value. It functions solely as a cost signal that sustains decentralized consensus” (Gill et al., 2026, p. 1). The dollars in Krause and Tolaymat’s BTC denominator are therefore not payment for output. They are the market value of newly issued coins — dollars paid by buyers to acquire coins from the pool of existing and newly minted supply. That is a transfer between parties, a change in who holds a claim, not a quantity of value brought into existence by the energy spent. Put the correct denominator in and the “energy per dollar created” ratio for BTC does not fall somewhere between copper and aluminium. It has no denominator at all, because the quantity it purports to divide by — value created — is zero. Coin issuance creates no value; it relabels ownership.
There is exactly one thing the BTC network sells, and it is not coins. It sells settlement: the inclusion of a transaction in the ledger. That service is real, and it has a price — the transaction fee. So the honest version of Krause and Tolaymat’s question is: how much energy does the network burn per dollar of the one service it actually sells? The arithmetic is unforgiving. In 2026 the network consumed roughly 148.1 TWh, which is 5.33 × 10¹¹ MJ. Over the same period fees ran at about 0.6 per cent of miner revenue — $85.8 million against $14.3 billion of total miner revenue. Divide the energy by the dollars users actually paid for the service and BTC costs 6,214 MJ per dollar of output sold: roughly fifty-one times aluminium and twelve hundred times gold. The bar that the bulls point to as evidence of BTC’s efficiency, properly denominated, towers a factor of fifty over the dirtiest thing on the original chart. Count the coin issuance as though it were output and you recover 37 MJ per dollar on 2026 data — a number of the same family as the 17 that flatters BTC, and the number that is simply wrong, because it divides energy by a transfer.
Figure 1 shows both bars side by side so the gap between them is visible: the issuance-as-output denominator that flatters the network, and the settlement denominator that describes what it does. The metals produce a commodity that exists afterwards; BTC produces a cost signal and settles a payment. On the only comparison that is not a category error, it is fifty times aluminium.
And even that comparison — properly denominated — answers a question nobody should be asking of a store of value. Every figure in Figure 1, corrected or not, prices production: the energy to make the commodity or render the service, once. Smelting a tonne of aluminium costs what it costs, and then the tonne exists, and nothing further is spent to keep it aluminium. The question that matters for an asset held across decades is not what it cost to produce but what it costs to keep. That is the carrying cost, and on the carrying cost the three assets are not merely different in degree — they are different in kind.
Gold. An ounce mined in 1850 is still an ounce today, and its integrity is a property of the metal itself. Nobody has to expend energy in 2026 to keep the 1850 ounce from ceasing to be gold. The accounting reflects this exactly. The life-cycle literature on metals is cradle-to-gate, denominated in mass, and it stops at the gate. Nuss and Eckelman assemble cumulative energy demand and global warming potential per kilogram for sixty-three metals, and they are explicit about where their accounting ends: among their study’s limitations they list “the cradle-to-gate focus, thereby not considering use and end-of-life stages, which are particularly important for metals, being durable and readily recyclable” (Nuss & Eckelman, 2014, Discussion). Krause and Tolaymat use the same convention, putting gold production at an average of 215 GJ per kilogram of gold — per kilogram, incurred once, not per dollar of whatever the metal is later worth (Krause & Tolaymat, 2018, p. 714). The unit of account is a kilogram at the gate. After the gate the energy accounting simply stops, because a bar of gold does not consume anything in order to remain a bar of gold.
The financial literature reaches the same asymmetry from the opposite direction. In the models that price gold, the cost of holding it is an opportunity cost — the coupon forgone on the bond you did not buy — not a resource burn. O’Connor, Lucey, Batten and Baur, in their survey of the empirical work, note that the canonical models rest on “assuming low storage costs and an assumed, but not empirically assessed, negligible convenience yield from holding gold” (O’Connor et al., 2015, §7.1). The physical cost of custody is treated as small enough to ignore, and the survey is candid that nobody has measured it precisely. But the same survey supplies something far more telling than a custody estimate: gold’s stock can be lent, and lending it pays. The leasing market is supplied by central banks and large trading banks who put their bullion out “to provide income from their physical gold holdings,” and the survey concludes that the gold lease rate “should perhaps be more correctly described as the benefit of holding gold” (ibid., §2.4). Read that against BTC. A tonne of gold, sitting in a vault, can be lent to a jeweller or a miner and earn a return; its holder is paid for holding it. Ten thousand BTC cannot be lent to the network to be hashed on the owner’s behalf in exchange for a fee. The security burn that keeps the BTC ledger intact is protocol-mandated, network-wide, and entirely non-assignable: no holder can capture it, redirect it, or earn from it. Gold’s cost of custody can be negative — you can be paid to hold it. BTC’s is a continuous, unavoidable, price-indexed drain.
Equities. For equities the cleanest source is, of all places, the BTC literature itself. Huberman, Leshno and Moallemi build a formal model of the BTC payment system and, in the course of it, compare it directly with the same settlement service run by a conventional profit-maximising firm. They write down both cost functions explicitly: “the cost of operating the BPS is c_m · N, while the cost of operating a firm-run payment system is c_f · λ_H” (Huberman et al., 2021, p. 3030). Look at the two expressions. The firm’s cost, c_f · λ_H, is a constant marginal cost per transaction, c_f, multiplied by the volume of transactions it processes, λ_H. It contains no term in the market value of the assets recorded on the register, and no term in any exchange rate. A registry that records ownership of a trillion dollars of equity costs no more to operate than one recording a billion, holding transaction volume fixed, because the cost is driven by activity, not by value. That is why a share is cheap to keep: its cost of existence is the marginal administrative cost of the entries against it, and that cost does not rise when the share price rises. BTC’s cost, by contrast, is c_m · N — the cost per unit of mining capacity times the equilibrium quantity of mining, N, and that quantity is pinned by the revenue flowing to miners, which is pinned by the price. The authors draw the comparison’s conclusion in their own words: “It appears that it is more expensive to run the BPS because the decentralized protocol requires additional computational overhead” (ibid.). A firm-run register does not get more expensive because the shares on it appreciated. The BTC ledger does exactly that, mechanically, block by block.
BTC. The mechanism is a one-line identity. Annualised miner revenue is
R = s(t) · B · P(t) · (1 + f)
where s(t) is the per-block subsidy in coins, B = 52,560 is the number of blocks per year at the ten-minute target, P(t) is the price, and f is the ratio of fee revenue to subsidy revenue. In a competitive mining industry with free entry, this revenue is spent — driven toward the resource cost of producing the hashes, because any margin above cost attracts entrants until it is competed away. Hence the annual real resource commitment required to secure the ledger is linear in the price within any subsidy epoch. Double the price and you double the burn. There is no analogous term for gold and none for equities, because neither has a protocol that converts its own quotation into a mandatory annual purchase of real resources.
Figure 2 draws all three, indexed to today, as the price rises. Gold is a flat line at ×1: at every price, holding tonnage fixed, the resource cost of custody is unchanged, because the cost function has no price term. Equities are a flat line at ×1 for the same reason: c_f · λ_H has no price term either. BTC is a straight line rising with the price. From the realised July 2026 price of $64,390 in the 3.125 BTC epoch, the carrying cost reaches ×16 at $1 million and ×155 at $10 million on the pure price effect. Honour the halving schedule — which cuts the subsidy and therefore the burn — and the post-2028 epoch reads ×8 and ×78 instead. Either way, the world is being asked to hand over between eight and a hundred and fifty-five times as much real resource every year, for the same twenty-one million coins, doing precisely what they do now. The coins do not become more useful. The ledger does not settle more transactions. Only the bill goes up.
That is the distinction the power-law chart erases by omission. It plots the price and stops there, as though the price were free-standing. It is not. The price is a claim on the second chart — the carrying-cost chart — and the second chart is the one nobody in the BTC discourse draws, because it is the one that ends the argument.
3. The ratio that halves regardless
There is a second effect layered on top of the first, and it points in a direction that surprises people on both sides of the argument, so it is worth stating carefully.
Define the security expenditure per unit of market capitalisation as ρ = S / (P · N), where S is the annual security spend, P the price, and N the coin supply. Because S is proportional to P — that is the whole content of Section 2 — the price appears in both the numerator and the denominator and cancels. What is left is determined entirely by the block subsidy schedule and the supply trajectory, neither of which has anything to do with the price. On the $1M-by-2030 path the ratio runs at 0.84% per year through 2027, steps down to 0.41% after the April 2028 halving, to 0.20% from 2032, to 0.10% from 2036, and to 0.012% per year by 2048.
Hold those two facts side by side. The absolute security bill rises with the price — that is Figure 2, the carrying cost climbing ×16, ×155. But the security purchased per dollar of stored value halves every four years no matter what the price does, because it is governed by the halving schedule, and the price cancels out of it. Both are true at once, and together they are worse than either alone. Holders pay vastly more in aggregate as the price climbs, and simultaneously receive proportionally less protection for each dollar they are storing, epoch after epoch. A power law in the price is completely powerless against the second effect, because you cannot outrun a ratio the price has already cancelled out of. You can put the price on the moon and the protocol will still be spending an eighth of a basis point per year defending each dollar of value by mid-century.
It is worth pausing on a number that circulates in this debate and is quietly wrong. The figure quoted everywhere is “$167 billion a year of security spend at $1 million a coin,” and it is used to reassure holders that the budget will be enormous. But $167 billion belongs to the 3.125 BTC subsidy epoch, which ends at the April 2028 halving. A peak dated 2031 — the date the popular scenarios use — falls after that halving, in the 1.5625 BTC epoch, where the subsidy is halved and the correct figure is $83.8 billion. Anyone quoting $167 billion at a 2031 peak has overstated the security spend by exactly a factor of two, and every physical quantity scaled off that revenue — the energy, the hashrate, the incidence on power markets — inherits the same doubling. The model-consistent number at a 2031Q4 peak is $83.8 billion, and the essay uses that throughout.
4. Efficiency does not rescue it
The standard reply at this point is that hardware keeps getting better, so the energy per unit of security will fall and the whole problem evaporates. Hardware does get better. It does not help, and the reason is structural rather than a matter of how fast the improvement runs.
Gill, Stinner and Tyrell give the argument its formal statement in Energy Economics, and they give it a name: the productivity trap. In an ordinary digital technology, efficiency gains decouple output from resource use — you get the same computation for less power, and total power can fall even as output rises. In proof-of-work this cannot happen, because “the computational output — hashes — has no intrinsic productive value. It functions solely as a cost signal that sustains decentralized consensus” (Gill et al., 2026, p. 1). The hashes are not the output; the cost of the hashes is the output. Their first main result follows directly and is counterintuitive on its face: an increase in the supply of cheap surplus energy raises both total energy demand and the number of active mining rigs, because miners respond to the cheaper input by substituting into it, lowering their average unit cost, and deploying more machines in equilibrium until margins are competed away again — “such resource expansion does not enhance network security, which depends solely on cost levels” (ibid., p. 2). Efficiency does not reduce the burn; it enlarges the fleet. Their second result is that abundant surplus energy reduces emissions but increases e-waste, and identifies equilibria in which the net externality actually worsens as the “green” energy arrives.
This is the exact inverse of the precedent the bulls invoke. The reassuring historical analogy is information technology: alarmists once forecast that IT would consume half of US electricity by 2010, and instead efficiency gains plateaued the load near two per cent (Huber and Mill’s forecast, cited in Gill et al., 2026, p. 1). But that decoupling happened precisely because the output of a data centre is the computation it performs, so making each computation cheaper let the same output run on less power. In proof-of-work the output is the cost, and the difficulty adjustment exists specifically to keep the cost high: if efficiency improves and the network’s aggregate hashing becomes cheaper, difficulty rises to restore the ten-minute block interval, and the savings are immediately reinvested in more hashing. You cannot make a cost signal cheaper. You can only make it larger for the same money. The IT analogy runs backwards.
There is a further consequence the productivity-trap framing makes explicit and the bulls rarely confront. Because security “depends solely on cost levels,” the only way to buy more security is to spend more — there is no efficiency dividend to bank, no technological path by which the network becomes both cheaper to attack against and cheaper to run. The two move together by construction. Efficiency, subsidy, surplus energy: every lever that in an ordinary industry would reduce resource intensity, in this one either leaves security untouched or enlarges the resource footprint. The trap is not an unfortunate side effect that better engineering will escape. It is the mechanism.
5. Where the extrapolation stops: $10 million a coin
Now take the power law at its word and push the price up the fitted line, and ask what the physical world is being ordered to deliver at each point on it.
The tool for this is the revenue identity from Section 2, read as an upper bound. The top-down energy literature has used exactly this ceiling since 2018: in a competitive mining industry, electricity spending is driven toward miner revenue, so the electricity the network can command is bounded above by what its revenue can buy. World gross electricity generation is about 31,734 TWh a year. Electricity is taken at 60 per cent of miner spend — the calibrated share, the rest going to hardware, operations and margin — and power is priced at the $45/MWh ERCOT tariff anchor, one of the cheapest large-scale industrial rates available anywhere.
At $1 million a coin, in the current 3.125 BTC epoch, miner revenue is $167.5 billion a year, of which $100.5 billion buys electricity. At $45/MWh that is 2,234 TWh — 7.0 per cent of all the electricity generated on Earth. This is not a rounding error and not a rhetorical flourish. It is seven per cent of everything the planet generates, consumed by one asset, at a price the fitted line clears within roughly a decade on its own extrapolation. To hold that in perspective: seven per cent of world generation exceeds the entire annual electricity consumption of most industrialised nations. It is a claim on the output of thousands of power stations, dedicated to producing a cost signal that settles seven payments a second.
At $10 million a coin the same arithmetic gives 22,338 TWh — 70.4 per cent of world generation. Half of all the electricity humanity produces is crossed at $7.10 million a coin. These are the numbers on the current subsidy epoch; honour the April 2028 halving and they fall by half, to 3.5 per cent at $1 million and 35.2 per cent at $10 million, with the halfway line pushed out to $14.2 million. Push the other way — assume the whole of miner revenue, not merely sixty per cent, goes on power — and they rise to 11.7 per cent, 117.3 per cent and a crossing at $4.26 million, at which point the identity demands more electricity than the planet generates. Every one of those cells is plotted on the same chart, and every one of them is a floor, not a central estimate, because at loads approaching a tenth or a half of world generation the marginal power price would be nowhere near $45/MWh. Bidding for that much electricity would drive its price up, which raises the revenue required to buy it, which pushes every crossing point lower still. The identity, read honestly, understates the collision.
That is the arithmetic the power-law extrapolation is committed to. It is not a caricature of the bull case; it is the bull case, its own headline price carried to its own accounting conclusion. A line that keeps compounding reaches prices at which the network’s own revenue identity demands the majority of the electricity on Earth to secure it.
It does not get there, and the reason it does not get there is the whole point. Even the seven per cent at $1 million is an order of magnitude above what the electricity supply side will actually clear. A solved regional equilibrium — one that models upward-sloping residual supply curves across six regions, endogenous miner entry at roughly 0.32 of the gap closed per quarter, interconnection queues and policy caps on new load, and the exact halving schedule — puts the $1M-by-2030 peak at 257.3 TWh, which is 0.81 per cent of world generation. The Monte Carlo band around that peak runs from 225 to 291 TWh at the tenth and ninetieth percentiles, and the full range across correlated, heavy-tailed and doubled-spread ensembles is 172 to 353 TWh. Across 1,500 adverse draws the worst world share reached in any single draw is 0.92 per cent. The black diamond in Figure 3 marks that solved peak, sitting on the floor of a chart whose ceiling is the extrapolation’s own 7-per-cent demand. The demand exceeds what the grid delivers by more than a factor of eight, at $1 million, before the price has even begun the climb to the numbers the power law actually promises.
The gap between the 7 per cent the identity demands and the 0.8 per cent the grid supplies is not a modelling quibble to be split down the middle. It is the economics of the collision. Revenue that the identity says should be spent on electricity, but that the electricity system will not sell at $45/MWh, does not vanish. It is redirected. It becomes appreciation in regional power prices, scarcity rent captured by the owners of generation, and rent to the holders of sunk, non-repurposable ASIC capital who can charge for a hashrate the market cannot quickly replace. In the solved run, realised hashpower peaks at 5,139 EH/s against an unconstrained zero-profit equilibrium of 6,418 EH/s: the physical security the network actually fields falls short of what its revenue would buy in a frictionless world, and the difference is soaked up as rent rather than delivered as security. Expenditure and physical security diverge — the dollars go up, the protection does not follow them up in proportion.
This is the economic frontier, and it is important to be exact about what kind of wall it is. It is not a wall the price hits. The price is set in asset markets by what buyers will pay, and nothing in the electricity system stops a coin from trading at $10 million if enough people want it there. It is a wall the security hits. Past the frontier, each additional dollar of market capitalisation buys proportionally less defence, because the marginal dollar of revenue meets a supply curve that will not deliver proportional electricity at a constant price. The ratio that was already halving every four years on the subsidy schedule now begins losing on a second, independent front — the physical one — and the two erosions compound.
And the electricity BTC is bidding for is not lying idle waiting to be claimed. The frontier is a contested queue. Alex de Vries, writing in Joule, projected that by 2027 NVIDIA’s AI-server shipments alone could carry 9.75 to 15.3 GW of new demand and consume 85.4 to 134.0 TWh a year (de Vries, 2023, p. 2193). Mining does not draw on some reservoir of spare generation; it competes, for the same interconnections and the same cheap power, against the highest-value computing load in industrial history — a load whose output is genuine computation that people pay for, set against a load whose output is a cost signal. In any contest for scarce grid capacity decided by willingness to pay, the load that produces something will tend to win the marginal megawatt, and the load that produces a cost signal will pay the congestion premium. The frontier is not a distant abstraction; it is an auction BTC is already in, against a bidder with a real product.
6. Seven transactions a second
Everything to this point concerns the cost side. Turn now to what the cost buys — the product — because the product is where the argument becomes not merely expensive but absurd.
The BTC network’s throughput ceiling is approximately seven transactions per second. Run saturated every second of every day, that is 220,903,200 transactions a year, and the ceiling is fixed by the protocol. It does not rise with the price, it does not rise with the market capitalisation, and it does not rise with the value being settled. Huberman, Leshno and Moallemi state the same constraint in the units of the protocol: the one-megabyte block limit, at roughly half a kilobyte per transaction, caps each block near 2,000 transactions, and — crucially for everything that follows — capacity is a protocol constant while it is congestion, not capacity, that varies as demand changes (Huberman et al., 2021, n. 29). The pipe does not widen when more people want through it. Only the queue lengthens.
Panel (b) of Figure 3 takes the energy figures and divides each by that fixed ceiling, to express the whole thing as energy per transaction. Today’s roughly 148 TWh, spread across a fully saturated year, is about 670 kWh per transaction — already, for a single payment, several weeks of a household’s electricity. At the solved $1-million equilibrium of 257 TWh it is 1,165 kWh. At the identity’s 7-per-cent demand for $1 million it is 10,112 kWh per transaction. At $10 million: 101,121 kWh — a hundred thousand kilowatt-hours of electricity, on the order of a decade of a typical home’s entire consumption, to move money once.
Gold’s utility does not scale with the gold price either — a bar’s usefulness as a store of value is roughly constant regardless of the quote. But gold does not have to buy its own defence out of transaction fees, and a bar sitting in a vault consumes nothing while it sits. In BTC the throughput is a hard constant while the resource bill compounds with the price, so the energy cost of each unit of the one service the network renders rises without bound. Seven transactions a second is, in throughput terms, roughly the capacity of a single mid-range payment terminal in a supermarket. That is the product. The frontier arithmetic of Section 5 says the majority of world electricity generation is what the extrapolation would have the world spend to keep that terminal running.
7. The fee market will not survive
There is a standard answer to all of this from within the BTC community, and it deserves to be met on its own ground. The block subsidy — the s(t) in the revenue identity — is scheduled to halve toward zero. Everyone agrees on that. The claim is that as the subsidy decays, transaction fees will rise to replace it, so the security budget will be sustained by users paying for settlement rather than by issuance. The fee market, on this view, is the mechanism that keeps the whole system solvent forever. It will not do the job, and the reason is not a forecast about user behaviour but a set of theorems about exactly this system.
Take the arithmetic first, because it settles the question before the theory is even needed. Suppose you wanted merely to hold the dollar security flow at its 2031Q4 modelled level of $83.8 billion a year, at a $1-million plateau price, funding the shortfall from fees as the subsidy halves out. Fees would have to fund 51 per cent of the budget in 2032, 75 per cent in 2036, 88 per cent in 2040, and 97 per cent by 2048. Spread across the full seven-transactions-a-second ceiling running saturated all year, that works out to about $193 per transaction in 2032, rising to $368 per transaction by 2048. Against what baseline? Fees today run well under one per cent of miner revenue — on the saturated-throughput basis, about thirty-nine cents per transaction. The required move is a factor of roughly 950, an increase of nearly three orders of magnitude in the fee per transaction, sustained indefinitely.
Nobody pays two hundred dollars to move money, still less three hundred and sixty-eight. Long before the fee reaches those levels the users leave, and when the users leave the fee base leaves with them — you cannot collect $368 from a transaction that no longer occurs. That is not rhetoric; it is the model’s own boundary condition, stated in the theory. Huberman, Leshno and Moallemi show that once participation is made endogenous — once users can choose not to transact when it becomes too expensive or too slow — “revenue will be bounded, as agents may not participate as the system gets congested” (Huberman et al., 2021, p. 3030). The fee budget of a fixed-capacity chain has a ceiling, and the ceiling is set by how much delay and cost users will tolerate before they walk, not by how much value the chain happens to be securing.
That last distinction is the one that kills the replacement plan outright, and it is the deepest result in the paper for present purposes. In their equilibrium, “the fee level does not increase if user WTP increases” (ibid., p. 3013). Fees are the price of delay reduction — you pay to jump the congestion queue — and not the price of value secured. A user moving $100 million and a user moving $100 face the identical congestion market and pay the identical fee, because the fee reflects the externality the transaction imposes on the queue, which has nothing to do with the sum being moved. Total fee revenue, they show, “depends only on K, ρ, and the distribution of delay costs F” — block size, congestion, and how impatient users are — “and therefore does not depend on the exchange rate” (ibid., p. 3029). The fee base is fundamentally disconnected from the thing it is supposed to secure. The security budget must scale with the value at stake on the ledger, because that is what an attacker stands to gain; the fee base scales with the impatience of the marginal transactor, which is an entirely different and much smaller quantity, and which does not grow when the value on the ledger grows.
From that disconnection the authors draw two conclusions in language that leaves nothing to interpretation. First: “there is no guarantee that the equilibrium number of miners is adequate for the system’s reliability and security.” Second, and decisively: “a shortage of mining resources does not lead to higher fees or a more favourable exchange rate; if anything, it is likely to result in the opposite” (ibid., p. 3029). There is no negative-feedback loop. In a well-designed system, a shortfall in security would raise the price of security and call forth more of it. In this one, if security falls short, the fee market does not notice and does not respond; nothing in the mechanism bids the missing security back into existence. The thermostat is not merely weak. It is not wired to anything.
There is one result in the same paper that appears to cut the other way, and honesty requires meeting it rather than omitting it. Their Theorem 7 shows that the delay cost required to raise a target revenue grows as Θ(K / log K), so that “a lower value of K allows raising any level of revenue at a lower delay cost to users” (ibid., p. 3034) — smaller blocks are actually better at extracting a given dollar of revenue from congestion, which sounds like a design lever that could be pulled to rescue the fee market. But note what the theorem actually establishes. It says congestion rent is an inefficient tax base at every block size, and grows more inefficient as capacity expands. That is an argument against funding security from congestion at all, not a recipe for doing it well. And the authors’ own prescription is not a fixed cap that could be tuned; it is elastic capacity — a protocol that adjusts the block rate, μ = λ / (Kρ*), to hold congestion and revenue stable as demand varies. They describe BTC’s fixed K and μ, the very parameters that produce the seven-transaction ceiling, as explicitly “undesirable” (ibid., p. 3031). The design the peer-reviewed theory recommends against, on efficiency grounds, is precisely the fixed-capacity design that BTC’s proponents defend as sacrosanct. The fee-market rescue is not merely unlikely to work. The canonical model of the fee market says the mechanism is built the wrong way for the job.
There is a further wrinkle that deepens the problem rather than relieving it. One line of defence in the literature holds that the network is protected after a crash by the sunkenness of mining capital: because ASIC hardware is specialised and non-repurposable, hashpower responds only weakly to falling revenue, so security does not collapse the instant the price does (this is the Garratt–van Oordt line of argument). Grant it in full. It describes a shock-absorber on the downside — a reason the ledger does not fall apart the moment revenue drops. It says nothing about the upside problem this essay is about, which is that on the way up the security budget has to be continuously purchased at a scale the electricity system will not supply, and that once the subsidy is gone the fee market cannot fund it at all. Sunk capital cushions the fall; it does not pay the rising bill. The two arguments are about opposite ends of the cycle, and the downside cushion buys nothing against the upside frontier.
8. What actually breaks
Put the three findings together, and the power-law extrapolation is revealed not as optimistic but as internally contradictory — a promise whose own premises destroy it.
The first: the bill rises with the price. Figure 2. From today’s price the annual real resource cost of holding BTC reaches ×16 at $1 million and ×155 at $10 million, for the same twenty-one million coins rendering the same service. Gold and equities stay flat at ×1 across every price, because their cost functions contain no price term at all — gold’s cost is per kilogram at the gate, equities’ is c_f per transaction, and neither moves when the quote moves. This is the distinction the power law erases, and it is not a difference of degree that better technology narrows. It is a difference of kind. Gold and equities are stocks; BTC is a flow that must be re-bought from the physical world in perpetuity, at a price the protocol ties to its own market value.
The second: the bill cannot be paid. Figure 3. The revenue identity demands 7 per cent of world electricity generation at $1 million a coin and 70 per cent at $10 million, on the calibrated sixty-per-cent power share in the current epoch. The solved regional equilibrium, accounting for what the electricity system will actually sell, delivers 0.8 per cent. The burn therefore does not in fact scale all the way up with the price, because the grid refuses roughly nine-tenths of the order — and the revenue that cannot buy electricity does not vanish but converts into scarcity rent for power owners and for holders of sunk hardware, so that expenditure and physical security pull apart. The security you can actually field stops tracking the money you are spending.
The third: nothing replaces the subsidy. The block subsidy decays toward zero on a fixed schedule, and the fee market that is supposed to take over is priced by delay, bounded above by users’ patience, invariant to the exchange rate, disconnected from the value it secures, and empirically falling year on year. The chain is capped at seven transactions a second throughout, so the fee base cannot be widened by volume. There is no mechanism, anywhere in the protocol, that converts the value stored on the ledger into the security defending it.
Assemble those three and the destination the power law points to comes into focus. It is an asset that would cost roughly a hundred and fifty times more each year to hold than it does today; that is defended, per dollar of value stored, by a steadily vanishing expenditure as the subsidy halves away; that possesses no mechanism to convert its own soaring market value into security for itself; and that settles, throughout, seven transactions a second — the throughput of a single supermarket till. Gill and co-authors’ productivity-trap result supplies the epitaph: the enormous resource the network consumes on the way to that destination is spent producing a cost signal with no productive output, and every efficiency gain along the way is immediately reinvested in more of the same signal rather than banked as a saving.
It is worth naming the one genuinely favourable use case, because it is real and because it does not rescue the thesis. Mining can absorb electricity that would otherwise be wasted: Sarnecki and Burke model a 100 MW Irish wind farm and find that a 20 MW co-located mining installation of current-generation hardware absorbs 83 per cent of the site’s annual dispatch-down energy, lifts total system revenue by 32 per cent, and raises the effective capacity factor from 29 to 32 per cent, with a 30 MW build absorbing 93 per cent (Sarnecki & Burke, 2026, abstract, §4). That is a genuine benefit, and it is a benefit about siting — putting a flexible load where power would otherwise be curtailed. It is not a benefit about scale. Ireland’s entire 2024 dispatch-down was 1.3 TWh, roughly half of one per cent of the 257 TWh the network already consumes at a solved $1-million peak, and a rounding error against the 22,338 TWh the raw identity demands at $10 million. And the productivity-trap result bites here too: cheaper surplus energy, in equilibrium, induces more rigs rather than less total energy. The flexibility case is true, small, and orthogonal to the carrying-cost problem. It tells you where to put a load, not how to pay a bill that scales with the price.
Every extrapolation of a price series carries, whether or not its author notices, an implicit forecast about the system that has to hold the price up. Gold’s implicit forecast is trivial and self-evidently satisfiable: the vault stays shut, and the metal inside can even be lent out to earn its keeper a return. Equity’s implicit forecast is a claim on the future production of real firms — demanding, but the kind of claim an economy routinely makes good on. BTC’s implicit forecast is a claim on the world’s electricity system: seven per cent of it at $1 million a coin, seventy per cent at $10 million — and it is a claim that the electricity system’s own economics flatly reject, before the price has climbed even a fraction of the way up the fitted line.
The line on the chart does not break because the statistics behind it are shoddy, though they are. It breaks because the thing being charted has a bill attached to it, the bill is denominated in the same units as the chart itself — dollars, and behind the dollars, terawatt-hours — and no one who draws the line has ever shown who pays it. The power law is not a law. It is an invoice that assumes it will never come due, drawn on a physical world that has already declined to honour it.
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