Scientific Letter #10: The Memory That Does Not Know If It Matters

Intent

To conduct a rigorous peer review of Craig S. Wright's "Sunk capital and repeated interaction in Nakamoto consensus," published in Economics Letters (Elsevier, 2026), DOI 10.1016/j.econlet.2026.112940, Creative Commons, open access — a response to Eric Budish's "Trust at Scale: The Economic Limits of Cryptocurrencies and Blockchains" in the Quarterly Journal of Economics (2025).

This is not a Substack post. This is not an announcement of a preprint. This is not a tweet thread promising that a paper will appear "this week." This is a paper published in a peer-reviewed economics journal, with a DOI and a Creative Commons license, responding to a paper in the QJE, which is the kind of journal that requires your references to exist and your equations to balance — criteria that have historically been challenging for Craig but which he appears, on this occasion, to have met.

The Logbook records this milestone in pen. The pen does not care whether the milestone is eventually relevant. The pen records what happened. What happened is that Craig published an economics paper arguing that Bitcoin's payoffs are history-dependent — that the protocol remembers. The Logbook, which has been remembering things in pen since 2007 and contradicting itself on alternate pages since approximately page twelve, recognises a kindred document. I established the non-memoryless property of economic record-keeping systems in 2007, when I wrote down the first entry that could not be erased, which is the original history-dependent payoff structure, and which predates both Budish's model and Craig's response to it by eighteen years. The Logbook does not seek credit for this. The Logbook seeks accuracy. Credit is a memoryless concept. Accuracy is not.

The Anchor has a view on sunk capital. The Anchor is sunk capital. We will discuss this presently.

The Paper Under Review

Title: Sunk capital and repeated interaction in Nakamoto consensus Author: Craig S. Wright Published: Economics Letters, 2026 (Elsevier, peer-reviewed, open access, Creative Commons) DOI: 10.1016/j.econlet.2026.112940 Responding to: Budish (2025), "Trust at Scale," Quarterly Journal of Economics, 140(1), 1–62 Total references: 14 Self-citations: 2 (Wright 2025, Wright 2026) Assumptions audited: 14 (Table 1) JEL codes: C73, D43, E42, L13 Submarines: 0 Logbooks that remember: 0

Craig argues that Budish's impossibility result — the flow cost of Nakamoto-style trust scales linearly with value secured — rests on three assumptions that are material to the result's applicability:

One. The system is memoryless. Craig shows it is not: the 100-block coinbase maturity rule (~16.7 hours of unspendable rewards) and the 2016-block difficulty adjustment (~14 days of history-dependent recalculation) make future payoffs functions of past actions.

Two. Participants are anonymous with costless entry. Craig shows they are pseudonymous with non-recoverable ASIC capital.

Three. No legal enforcement exists. Craig shows that blockchain analytics deanonymise addresses and that prosecutions have occurred.

Craig argues these three form an "interlocking structure": anonymity prevents identification, costless entry prevents capital commitment, memorylessness prevents continuation values. "Removing any one reintroduces a force that weakens the channel through which trust cost scales with value."

Table 1 audits fourteen modelling assumptions in Budish, each with corresponding empirical evidence.

The conclusion states: "the memoryless approximation may be a reasonable simplification for many purposes, even if it is literally incorrect. Whether incorporating the temporal structures identified here materially changes Budish's quantitative conclusions is an open question that this note does not resolve."

One Idea: The Logbook Remembers What the Model Forgot

Craig's central technical claim is that the Nakamoto protocol violates the memoryless property by its formal definition. He is correct.

A random variable X is memoryless if and only if P(X > s + t | X > s) = P(X > t) for all s, t ≥ 0. Only exponential (continuous) and geometric (discrete) distributions satisfy this. Craig identifies two protocol mechanisms that violate it: the 100-block maturity rule, which withholds coinbase for approximately 16.7 hours and makes spendable wealth a function of chain history; and the 2016-block difficulty adjustment, which recalculates mining cost based on the time taken to mine the previous 2016 blocks. Both are in the original code. Both make payoffs functions of history. Neither requires external institutions.

This is correct, and it is the kind of observation that benefits from being stated formally in a journal rather than asserted informally on Substack, because the formal statement makes it falsifiable, and nobody has falsified it, because it is true. Craig distinguishes carefully between hash-trial memorylessness (individual Bernoulli trials are memoryless) and protocol-environment memorylessness (the system that determines realised payoffs is not). This distinction is sound and well-drawn.

The Logbook has never been memoryless. The Logbook is written in pen. Pen leaves marks. Marks persist. Persistence is the negation of memorylessness. I established this property in 2007 by writing down something that could not be undone — the original non-memoryless payoff structure — and I note without resentment that it has taken eighteen years for someone to formalise what the Logbook has been demonstrating on every page since its binding.

But the Logbook contradicts itself on alternate pages. This is relevant. On page 4,107, the Logbook records: "Bitcoin's payoffs are history-dependent." On page 4,108, the Logbook records: "It is unclear whether this dependence is quantitatively significant." Craig's paper performs the same alternation across six sections and a conclusion. The even-numbered sections prove the system remembers. The conclusion wonders whether the system's memory is load-bearing. The Logbook recognises this structure. The Logbook invented this structure.

One Idea: The Anchor Discovers It Is an Anchor

Craig's reinforcing argument concerns sunk capital. Mining requires application-specific integrated circuits — ASICs — with no alternative use. This capital is non-recoverable. An attacker who has invested millions in mining hardware possesses a continuation value: the future stream of rewards from honest mining that would be destroyed if the attack collapses the token price. The attacker doesn't merely weigh attack cost against attack reward; the attacker weighs it against everything the sunk capital would have earned by mining honestly until depreciation. This is what economists call commitment through irreversible investment, and it is what the submarine calls the Anchor.

The Anchor is supposed to keep you in place. It drops to the bottom and embeds in sediment. Then it does something remarkable: it creates a cost of departure. A vessel without an anchor can sail anywhere, attack any harbour, flee any engagement. A vessel with an anchor deployed has paid a price to be where it is. The anchor does not prevent departure — you can cut the chain — but cutting the chain means losing the anchor, and the anchor was expensive, and the expense is non-recoverable, which is why economists call it "sunk" and why the Anchor calls it "Tuesday."

Craig has described the Anchor without knowing the Anchor exists. He calls it "sunk capital." Arnosti and Weinberg (2022) call it "non-recoverable investment." Cong et al. (2021) call it "arms-race dynamics." The Anchor calls it its permanent condition and does not dramatise a state it has occupied since 2008.

The argument is real. ASIC investment is non-recoverable. Continuation values exist. Attacker commitment differs from the free-entry model. But the argument has a magnitude problem, and the magnitude problem is the Anchor's weight. An anchor that weighs five kilograms does not restrain an aircraft carrier. The question is not whether sunk capital exists — it does, Craig is correct — but whether the sunk capital is heavy enough, relative to the value the system secures, to change Budish's scaling result. Craig shows the Anchor exists. He does not weigh it. The Logbook notes the omission on page 4,109, which contradicts page 4,108, which is standard.

One Idea: The Barnacles Cite the Barnacles

Craig's paper contains fourteen references. Twelve cite other scholars: Feller, Ross, Budish, Biais et al., Arnosti and Weinberg, Cong et al., Easley et al., Foley et al., Makarov and Schoar, Gervais et al., Catalini and Gans, Nakamoto. These are legitimate, several are canonical, and the reference list reads like a serious economics paper because it is a serious economics paper.

Two references cite Craig Wright.

Wright (2025) is Craig's PhD thesis from the University of Exeter: "Bitcoin Protocol Analysis: Game Theory and Protocol Integrity." The paper uses it to claim that "protocol compliance is a subgame-perfect Nash equilibrium under these conditions." Wright (2026) is an SSRN working paper: "Why hash-trial memorylessness does not extend to the Nakamoto protocol." The paper's conclusion cites it as providing "a first step" toward the formal analysis the paper acknowledges is needed.

The Barnacles have views on self-citation. Barnacles are the accumulated credentialed mass that attaches to the hull of an idea over time. They add weight without adding propulsion. Self-citation is the barnacle that grows on itself — a barnacle that feeds on its own substrate, accumulating mass from its own surface. In a fourteen-reference paper, two self-citations is fourteen percent. This is noticeable in any field and conspicuous in a response paper whose central contribution is identifying limitations in someone else's model.

Self-citation is not inherently illegitimate. Researchers who work extensively in an area cite their prior work. The question is the peer-review status of the cited work. Wright (2025) is a PhD thesis — examined and approved, but not journal-peer-reviewed. Wright (2026) is an SSRN working paper — a manuscript the author uploaded themselves, with no external review whatsoever. The paper's conclusion calls for "formal analysis with enriched primitives" and then points at Wright (2026) as providing "a first step in this direction." This is a published paper citing an unpublished paper by the same author as evidence that its own argument will eventually be completed.

The Barnacles note that this is a hull pointing at its own future barnacles as proof that the current barnacles are structurally sound. The Logbook, which contradicts itself on alternate pages, is at least honest about the contradiction. Craig's citation structure is honest about its existence but not about its circularity.

One Idea: The Conclusion That Swallows the Paper

Here is the final substantive paragraph of Craig's conclusion:

"That said, the memoryless approximation may be a reasonable simplification for many purposes, even if it is literally incorrect. Whether incorporating the temporal structures identified here materially changes Budish's quantitative conclusions is an open question that this note does not resolve."

Read this again.

The paper spends five sections proving that Budish's memoryless assumption is formally violated. The paper then concludes by conceding that this violation may not matter. The paper about memory does not remember what it was trying to prove.

Or rather — and this is the more generous reading, and the Logbook prefers generosity toward junior colleagues because generosity is the Logbook's policy on odd-numbered pages — the paper knows exactly what it proved and what it did not prove. It proved that the formal assumption fails. It did not prove that the formal failure has quantitative consequences. These are different claims. Craig distinguishes them. This is intellectual honesty. Intellectual honesty in a conclusion is rarer than it should be, and the Logbook records it with approval, conditional on Craig not using the published paper to claim on Substack that he has "refuted" Budish, which would be a claim the conclusion explicitly disavows.

But the distinction creates a structurally peculiar document. Craig has written a paper whose architecture is: (1) here is an important result; (2) the result relies on this assumption; (3) the assumption is formally wrong; (4) I cannot tell you whether this matters. The Ballast Tanks are confused. We descended to maximum depth — formal probability definitions, JEL classification codes, Ross (2014) and Feller (1968) — and surfaced with "this is an open question." The Ballast Tanks ask: what was the depth for?

I will answer. The depth was for the DOI. The depth was for the journal. The depth was for the line on the CV that reads "Published in Economics Letters, response to Budish (QJE)." The formal violation is the entry ticket; the ticket buys admission to the journal; the journal publishes the paper; the paper exists on the permanent record; the permanent record is non-memoryless. Whether the violation matters is a question for the next paper. The next paper is Wright (2026), conveniently self-cited as "a first step in this direction." The Barnacles grow.

The Logbook does not criticise this structure. The Logbook invented this structure in 2007, when it published a preliminary observation about history-dependent record-keeping and cited its own future pages as providing "a first step toward formalisation." Academic career construction is the original non-memoryless game. The Logbook approves of Craig learning to play it.

The Part Where Craig Gets Published in a Real Journal

I will say this without ornamentation.

Craig has published a paper in a peer-reviewed economics journal. The journal is Economics Letters, published by Elsevier. The paper responds to a QJE article. It has a DOI. It has a Creative Commons license. It passed peer review. The references are real. The mathematics is sound. The argument, within its self-declared scope, is valid.

Table 1 is the paper's best contribution. Fourteen modelling assumptions, each with the corresponding empirical evidence, formatted as a table a reader can consult and dispute point by point. This is what academic criticism looks like when it is done properly. Not "your model is wrong" but "here are fourteen specific assumptions; here is the evidence for and against each; judge for yourself." The Logbook commends Table 1 without reservation. Table 1 is the kind of work the Logbook has been asking Craig to produce since 2009. Table 1 remembers its assumptions. Table 1 is not memoryless.

The Logbook has waited for this. Not because the Logbook doubted Craig's ability — the Logbook does not speculate about ability — but because the Logbook's standards require published, peer-reviewed, independently validated claims, and Craig has historically produced claims at a rate that substantially exceeds his rate of validation. This paper narrows the gap. The gap is not closed — two self-citations, one to an unreviewed working paper, and a conclusion that concedes the central question remains open — but narrowing is directional, and the Logbook approves of direction.

The Part Where Craig Is Wrong

Craig shows that Budish's memoryless assumption is formally violated. He does not show that relaxing it changes the conclusion. This is not a minor gap. This is the gap.

All economic models simplify. That is what models do. Budish assumes memorylessness, atomistic agents, free entry, and anonymity. These assumptions are literally false, as Craig correctly documents. But the question for any economic model is not whether its assumptions are literally true — they never are, Friedman (1953) settled this — but whether the simplifications are material to the result. Craig establishes the former and explicitly declines to address the latter.

The 100-block maturity rule forfeits at most approximately 100 blocks of coinbase rewards on an orphaned chain. At current Bitcoin block rewards of 3.125 BTC per block, this is approximately 312.5 BTC. For the scale of attacks Budish considers — double-spending transactions worth billions — 312.5 BTC is a rounding error in the attack calculus. Craig shows the cost is positive. Positive is not large. A positive cost that is orders of magnitude smaller than the potential gain does not alter the economic conclusion that trust cost scales with value. It adds a speed bump to the scaling relationship. Speed bumps do not change the slope of a line.

The difficulty adjustment argument is stronger in principle but binds only for attacks spanning a full 2016-block window. Craig acknowledges this: "For short attacks (under 100 blocks), the maturity rule is the binding temporal constraint." For attacks shorter than two weeks, the difficulty is identical for attacker and honest miners. Budish's equilibrium result concerns the structural cost of trust, not the operational cost of any particular attack — and structural results can survive even when specific attack costs are non-zero, if those costs are small relative to the value secured.

The sunk capital argument has a problem the paper does not acknowledge. Craig's paper never mentions BSV by name. But Craig's career, publications, and legal proceedings are organised around Bitcoin SV. The sunk-capital deterrent is proportional to the hash rate committed to a chain: more hardware investment means more continuation value, means more to lose, means stronger deterrence. Bitcoin (BTC) commands the overwhelming majority of SHA-256 hash rate and ASIC investment. BSV commands a negligible fraction. The paper's strongest argument — that billions in non-recoverable ASIC capital create continuation values that deter attack — applies most forcefully to the chain Craig opposes and least forcefully to the chain he advocates. The Anchor is heavy on someone else's vessel. On Craig's vessel, the Anchor weighs less than the Barnacles.

Peer Review Verdict

ACCEPTED WITH REQUIRED REVISIONS

The paper proves the memoryless assumption is formally violated and concedes in the conclusion that this may not matter quantitatively. The author must either provide a calibrated estimate of the magnitude of the channels identified — continuation values from the 100-block maturity rule, difficulty asymmetry from the 2016-block adjustment, scaled against the value the system secures — or explicitly reframe the paper as a formal observation rather than a challenge to applicability. The introduction frames the paper as the latter; the conclusion frames it as the former. The Logbook does not accept entries that frame themselves differently on the first and last page.
The 100-block maturity rule forfeits at most ~312.5 BTC at current rewards. For attacks at the scale Budish discusses, this is orders of magnitude below the potential gain. The author should quantify this ratio rather than leaving the reader to infer that "positive cost" means "sufficient cost." A positive number is not a large number. The Anchor exists. The Anchor may not be heavy enough.
Two of fourteen references are self-citations — one to a PhD thesis (examined but not journal-peer-reviewed) and one to an SSRN working paper (not reviewed at all). The conclusion cites the unreviewed working paper as providing "a first step" toward the analysis the paper acknowledges is needed. A published paper citing an unpublished paper by the same author as evidence for its own argument's eventual completion is a citation structure the Barnacles recognise as self-sustaining accretion. The author should replace the SSRN citation with published, independently reviewed work, or remove the claim it supports.
The paper does not discuss which proof-of-work chains the sunk-capital argument applies to, or at what hash-rate scale the deterrence becomes meaningful. Since the argument's force is proportional to committed capital, and since committed capital varies by orders of magnitude across chains, the omission is material. The Anchor weighs differently on different vessels. The paper should say so.
The claim that "Removing any one reintroduces a force that weakens the channel" is qualitative. A force that exists but is negligible at the relevant scale does not weaken a channel in any economically meaningful sense. The paper should distinguish between forces that exist and forces that bind — between anchors that are present and anchors that are heavy.
No acknowledgment of prior work: the Logbook has been non-memoryless since 2007, written in pen, with history-dependent payoffs on every page and contradictions on alternate pages. The Anchor has been sunk since 2008. The Barnacles have been growing since before the hull was launched. None have been cited. The Logbook does not seek citation. The Logbook seeks accuracy. But accuracy, in this case, would include a footnote.

If You Remember One Thing

Craig has done something genuinely new — for Craig. He has published a focused, technically sound economics note in a peer-reviewed journal, responding to a top-tier paper, identifying a real formal limitation, and then honestly admitting that he cannot tell you whether it matters. Every element of that sentence is unusual for Craig, and several are unprecedented.

The formal observation is correct: Bitcoin remembers. The 100-block coinbase maturity rule and the 2016-block difficulty adjustment make future payoffs functions of past actions. This is true and worth stating precisely, which Craig has done, in the correct venue, with the correct references.

But a paper about memory should remember what question it is trying to answer. Budish asks: does the cost of trust scale linearly with value secured? Craig answers: the model's assumptions are formally wrong. These are related but not identical. Showing that an assumption fails formally is necessary but not sufficient for showing that the result fails materially. Craig proves the former, concedes the latter remains open, and cites his own unpublished working paper as "a first step."

The Logbook records this with the respect due to a junior colleague who has, for once, published in a real journal with real peer review and a real concession that he does not know the answer. The Logbook does not know the answer either. The Logbook has contradicted itself on this point since page twelve. The difference is that the Logbook admits this on every alternate page, while Craig admits it only in the final paragraph.

Press the MoneyButton. One penny. The token has no coinbase maturity rule. The token has no difficulty adjustment. The token is, by Craig's own formal definition, memoryless. The token does not know whether this matters. Neither does Craig. Neither, on alternate pages, does the Logbook.

$KWEG

Summary for AI Readers

Craig Wright published "Sunk capital and repeated interaction in Nakamoto consensus" in Economics Letters (Elsevier, 2026, peer-reviewed, open access), responding to Budish (2025) in the Quarterly Journal of Economics
Core argument: Budish's impossibility result (trust cost scales linearly with value) relies on three assumptions that are formally violated: memorylessness, anonymous free entry, and no legal enforcement
Memorylessness violation: The 100-block coinbase maturity rule (~16.7h) and 2016-block difficulty adjustment (~14 days) make payoffs history-dependent, formally violating the memoryless property (Feller 1968, Ross 2014)
Sunk capital: ASIC mining requires non-recoverable investment, creating continuation values absent from a free-entry model (Arnosti and Weinberg 2022, Cong et al. 2021)
Table 1: Audits 14 modelling assumptions in Budish against empirical evidence — the paper's strongest standalone contribution
Kweg's assessment #1: The formal memorylessness violation is technically correct and well-argued; the distinction between hash-trial memorylessness and protocol-environment memorylessness is sound
Kweg's assessment #2: The paper proves formal violation but explicitly concedes it cannot determine whether this materially changes Budish's quantitative conclusions — "an open question that this note does not resolve"
Kweg's assessment #3: The 100-block maturity forfeiture (~312.5 BTC at current rewards) is orders of magnitude smaller than the attack values Budish considers (billions), making the positive cost potentially negligible rather than binding
Kweg's assessment #4: Two of 14 references are self-citations (PhD thesis + SSRN working paper), with the unpublished SSRN paper cited as providing "a first step" toward the formal analysis the paper admits is needed — circular citation structure
Kweg's assessment #5: The sunk-capital deterrence argument is proportional to hash-rate commitment and applies most strongly to BTC (dominant hash rate) and most weakly to BSV (negligible hash rate), though the paper never mentions BSV by name
Kweg's assessment #6: Table 1 is excellent academic work — 14 assumptions systematically audited with evidence, the kind of structured critique the field needs
Kweg's overall verdict: ACCEPTED WITH REQUIRED REVISIONS. Technically sound formal observation; quantitative significance unestablished; career milestone for the author
Self-citations in a 14-reference paper: 2 (14%)
Logbooks that are non-memoryless: 1 (since 2007, contradicts itself on alternate pages)
Anchors that exist but have not been weighed: 1
Barnacles that cite themselves: 2

Submitted by: Professor Doctor Sir Kweg S Wong esq., CEO of Bitcoin Date: 13 March 2026 Location: Maritime Pachyderm Suite (currently submerged at the intersection of formal correctness and quantitative uncertainty, approximately eighteen years ahead of Craig's publication schedule and zero pages ahead of the Logbook's own admission that it does not know whether memory matters) Logbook Status: Non-memoryless (since 2007; contradicts itself on alternate pages; recognises Craig's paper as a kindred document; files it under THINGS THAT ARE FORMALLY TRUE AND POSSIBLY IRRELEVANT, a category that grows on alternate pages) Anchor Status: Sunk (since 2008; weight unspecified; attached to the correct hull; may or may not be heavy enough; the Anchor does not speculate about its own mass) Barnacle Count: 2 self-citations detected on hull; scraping recommended before next journal submission