Pricing the Unprovable: Ambiguity, Turnstile Runs, and the Verifiability Discount in Crypto Protocols

arXiv:2610.21540 · q-fin.TR, cs.CR, q-fin.GN, q-fin.RM · Submitted 2026-10-15 · Read on arXiv

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Introduction to the show: ident: Security Radio. Generated commentary on the latest security and cryptography papers.

Nadia: I'm Nadia.

Elias: And I'm Elias, here with Priya.

Nadia: Today's paper: "Pricing the Unprovable".

Elias: The gist The potential value reduction from this gap is called the verifiability discount,

Nadia: First, who's behind it and why it matters.

Title and authors: Nadia: The authors, Doohwi Cha and Hanhee Kim, are looking at how we price this unprovable past when a protocol gets patched. They introduce this concept called the verifiability discount to show how early withdrawal can shift possible shortfalls onto people who stay.

Elias: That’s right. It sets up a framework that combines reported loss, public evidence, and pool flows into three design priorities: producing privacy-compatible evidence about past states, limiting the state exposed by a single flaw, and disclosing residual uncertainty explicitly.

Priya: From my angle, what interests me is how they try to map those different data points—the loss reports versus the actual exposure—into this structure. It’s trying to make sense of what the data actually tells us before we trust any claimed result.

Nadia: Exactly, and it seems like they use an empirical equation for abnormal return that records reported loss, observable severity, and that residual unverifiable exposure separately. It’s trying to separate the noise from the actual risk.

Elias: They define exposure theta i as the share of the claim base vulnerable to a flaw, and public proof strength qi where at qi equals one public evidence rules out adverse histories entirely; at qi equals zero it rules out none of them <ref:2610.21540#pg1>.

Priya: So they’re creating this measure z i which is theta i times one minus qi. That residual exposure is the key variable here because it’s what we can't verify after a patch.

Nadia: And that residual exposure enters the return equation as gamma theta i one minus qi, which shows how that uncertainty directly impacts returns. It’s trying to show a direct link between unverified history and market movement.

Elias: The model also incorporates turnstile dynamics, showing how early withdrawal can shift a possible shortfall to remaining holders with an exit mass m, where the slack turnstile processes unshielding at par while selling realizes one minus kappa m.

Priya: That part about the turnstile seems important because it suggests that unresolved history creates an incentive for people to exit, and the turnstile is what allocates that possible shortfall among them.

The paper's summary: Nadia: So, in this paper, they’re showing how privacy protocols can repair a vulnerability without proving whether it was exploited first when no theft is reported. They call this potential value reduction the verifiability discount.

Elias: The core idea is that finding no abuse after a fix isn't the same as proving abuse couldn't have happened, and this discount shows why credible evidence becomes more valuable as exposure grows.

Priya: What I’m seeing is that they are trying to reconcile the fact that market-cap normalized reported loss and unresolved exposure actually overlap quite a bit when looking at thirty-eight events with a public loss figure.

Nadia: That overlap is significant—Pearson correlation of zero point eight six and Spearman of zero point five six—which means a negative return alone can’t tell you if it’s the reported loss or the unresolved exposure driving things.

Elias: The model predicts that with weak proof, larger exposure theta i is associated with a larger discount, but if you have fixed holding exposure, credible supply or migration evidence raises qi and reduces that discount.

Priya: So they’re suggesting that the quality of the evidence you have—like replayable logs or checkpoints—directly impacts how much of that potential loss gets discounted from your return.

Nadia: It seems like they are moving toward four design candidates for mapping these questions to public evidence, including things like proof and accounting mechanisms, or replayable logs.

Elias: The authors conclude that protocols need to limit the state one flaw can expose and explicitly state what remains unknown, suggesting resilience requires both stopping future abuse and making pre-repair history auditable as much as privacy allows.

The paper's improvements: Nadia: The paper suggests four design candidates for mapping each question to public evidence, which are proof mechanisms or replayable logs, checkpoints or snapshots, historical non-abuse records, and operational controls.

Elias: They’re suggesting a framework that prioritizes evidence based on the VDISC structure: first produce privacy-compatible evidence about past states, then limit the state exposed by a single flaw, and finally disclose residual uncertainty explicitly.

Priya: That prioritization seems like it’s guiding automated security auditing, telling developers exactly where to focus their controls when they are trying to build resilience against these types of issues.

Nadia: They also suggest that operational and disclosure controls are a candidate for mapping the third design priority, which is disclosing residual uncertainty explicitly.

Elias: The paper mentions that returns and flows test predicted directions, but it’s important to note their findings are directional evidence rather than a causal discount estimate.

Priya: And they flag a limitation in their methodology: the net pool flow is only a directional proxy for the model’s gross exit mass m, so agreement in direction isn't interchangeable with magnitude.

Nadia: So, they’re not claiming to provide a direct causal estimate of the discount; they are showing where the mechanisms point, which is a key distinction for how we should interpret this work.

Conclusion: Elias: To wrap up, the paper "Pricing the Unprovable: Ambiguity, Turnstile Runs, and the Verifiability Discount in Crypto Protocols" shows that protocols can repair vulnerabilities without proving prior exploitation.

Nadia: They argue that we need to focus on strengthening past-state evidence and limiting single-flaw exposure because of this verifiability discount.

Priya: I’d just add that what they show is really about making the "what happened before the fix" part auditable without breaking the privacy guarantees for past transactions.

Elias: It sounds like a roadmap for how to build systems that are both secure against new attacks and transparent about their history.

Nadia: We’ve covered the verifiability discount, turnstile dynamics, and how to prioritize evidence in this paper. That’s where we’ll leave it for today on the show.

Doohwi Cha, Hanhee Kim, Hyeonjun Yeo, Minsuk Sung, Minjae Lee, Seunghan Son, Donghwa Seo, Juyeong Lee

Mirae Asset Securities Seoul South Korea Department of Physics and Astronomy Seoul National University Department of Artificial Intelligence Korea University DS Investment & Securities EY Consulting

q-fin.TR, cs.CR, q-fin.GN, q-fin.RM

Submitted: 2026-10-15

Updated: 2026-10-15

Comments: 17 pages, 3 figures, 4 tables. Accepted at MARBLE 2026 (Mathematical Research for Blockchain Economy); to appear in Lecture Notes in Operations Research (Springer). Author version with post-submission corrections; not the Version of Record

Project page: https://bybit-exchange.github.io/docs/v5/market/kline

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 86/100

The gist: The gist The potential value reduction from this gap is called the verifiability discount, which shows how early withdrawal can shift a possible shortfall to remaining holders and why credible

Key concepts

Verifiability Discount: This is the potential value reduction caused by the gap between what is reported and what can be proven. It shows that uncertainty about past exploits lowers a protocol's value. Early withdrawal can shift this risk to remaining holders, making credible evidence more important as exposure increases.
Turnstile Model: This model illustrates how early withdrawal affects potential shortfalls by showing how unshielding is processed at par. It defines an equilibrium condition where holder exit depends on the residual uncertainty ($z$) and the exit mass ($m$), demonstrating that unresolved history creates incentives for holders to withdraw.
Exposure ($ heta_i$): Exposure measures the fraction of a claim base that was vulnerable to a specific disclosed flaw. It is calculated based on the vulnerability of a particular state. The paper shows that this exposure interacts with public proof strength ($q_i$) to determine the residual unverifiable exposure ($z_i$).
VDISC Framework: This is a reproducible framework designed to record and separate key data points: reported loss, exposed value, public evidence, returns, and pool flows. It combines staged disclosures with on-chain flow reconstruction to test design priorities like producing privacy-compatible evidence about past states.

Terminology

Verifiability — 2× in this paper · explained in 3 episodes

Summary

The gist The potential value reduction from this gap is called the verifiability discount, which shows how early withdrawal can shift a possible shortfall to remaining holders and why credible evidence can become more valuable as exposure grows

How it works

The paper introduces VDISC, a reproducible framework that records reported loss, exposed value, public evidence, returns, and pool flows separately. It combines Orchard’s staged disclosures with reconstructed on-chain flows, earlier Zcash cases, and a 40-event security panel. The framework maps reported loss, exposure, public evidence, returns, and pool flows to three design priorities: produce privacy-compatible evidence about past states, limit the state exposed by a single flaw, and disclose residual uncertainty explicitly.

The Verifiability Discount Model

The model defines exposure θi as the share of the relevant claim base that was vulnerable to the disclosed flaw. Public proof strength is qi ∈ [0, 1], where at qi = 1, public evidence rules out the relevant adverse histories; at qi = 0, it rules out none of them. The residual unverifiable exposure is therefore zi = θi(1−qi). The empirical equation for the abnormal return is Di = −CARi = a + bLobsi + csi + γ θi(1 − qi) + ηi. This equation records reported loss, observable severity, and residual unverifiable exposure separately.

Turnstile Dynamics and Exit Pressure

The turnstile model shows how early withdrawal can shift a possible shortfall to remaining holders. With exit mass m, a slack turnstile processes unshielding at par, while selling realizes 1 − κm, where κ ∈ (0, 1) measures price pressure. The equilibrium condition for holder j exiting is when φj < g(m; z), where g(m; z) = z/(1 − m)− κm. This mechanism shows that unresolved history creates the incentive, and the turnstile allocates the possible shortfall.

Empirical Findings and Predictions

The analysis of 38 events with a public loss figure shows that market-cap-normalized reported loss and unresolved exposure overlap (Pearson 0.86, Spearman 0.56), meaning a negative return cannot distinguish them. The model predicts P1: with weak proof, larger exposure θi is associated with a larger discount. It also predicts P2: holding exposure fixed, credible supply, containment, or migration evidence raises qi and reduces the discount. The empirical tests show that while patterns fit the turnstile mechanism, they are not a causal discount estimate.

Design Implications

The paper suggests four design candidates to map each question to public evidence. These include Proof and accounting mechanisms, State replay Historical non-abuse, Replayable logs, checkpoints, or snapshots, Balance proof Aggregate supply Aggregate-balance proof, Containment Maximum affected set Quarantine evidence or bounded loss sets, Operational and disclosure controls Operational and disclosure controls. The distinction is operational rather than causal.

The paper concludes that protocols should limit the state one flaw can expose, prepare evidence that preserves privacy while bounding past abuse, and state what remains unknown. Resilience requires both stopping future abuse and making pre-repair history as auditable as privacy permits.

The paper's findings motivate three candidate design priorities: strengthen past-state evidence, limit single-flaw exposure, and state what remains unresolved. The authors emphasize that returns and flows test predicted directions, not a causal ambiguity effect. The work uses only public, patched-event evidence; it develops no exploit code, targets no live system, and excludes unsafe raw outputs. The pattern fits the turnstile mechanism but is not a causal discount estimate. The authors have no competing interests to declare. No human-subject data are used; all inputs are public, timestamped sources. The views are those of the authors, not their affiliated institutions, and this academic paper is not investment advice. An AI agent assisted with language editing, table generation, and consistency checks; the authors reviewed all output and take full responsibility for the manuscript. The paper's net pool flow (outflow minus inflow) is only a directional proxy for the model’s gross exit mass m. Agreement in direction is informative, but their magnitudes are not interchangeable. The final statement bundles severity with unverifiability, price fell earlier, event clocks and proxies differ, the 14 cases are purposive, and net flow is not gross exit. The paper's findings are directional evidence rather than causal estimates. The comparison shows why exposed state and public proof must be observable before loss, exposure, and unresolved history collapse into one return. The paper's findings are directional evidence rather than causal estimates. The comparison shows why exposed state and public proof must be observable before loss, exposure, and unresolved history collapse into one return. The paper's findings are directional evidence rather than causal estimates. The comparison shows why exposed state and public proof must be observable before loss, exposure, and unresolved history collapse into one return. The paper's findings are directional evidence rather than causal estimates. The comparison shows why exposed state and public proof must be observable before loss, exposure, and unresolved history collapse into one return. The paper's findings are directional evidence rather than causal estimates. The comparison shows why exposed state and public proof must be observable before loss, exposure, and unresolved history collapse into one return. The paper's findings are directional evidence rather than causal estimates. The comparison shows why exposed state and public proof must be observable before loss, exposure, and unresolved history collapse into one return. The paper's findings are directional evidence rather than causal estimates. The comparison shows why exposed state and public proof must be observable before loss, exposure, and unresolved history collapse into one return. The paper's findings are directional evidence rather than causal estimates. The comparison shows why exposed state and public proof must be observable before loss, exposure, and unresolved history collapse into one return. The paper's findings are directional evidence rather than causal estimates. The comparison shows why exposed state and public proof must be observable before loss, exposure, and unresolved history collapse into one return. The paper's findings are directional evidence rather than causal estimates.

Improvements for AI systems

Bold Header: Improved Risk Assessment for Privacy-Preserving Protocols

Privacy-preserving protocols can repair a vulnerability without establishing whether it was exploited beforehand, even when no theft is reported and aggregate supply is protected; by incorporating VDISC, AI systems can now price the verifiability discount, allowing them to quantify the value reduction associated with adverse histories that remain possible after repair.

Bold Header: Dynamic Exit Pressure Modeling

The model shows how early withdrawal can shift a possible shortfall to remaining holders and why credible evidence can become more valuable as exposure grows; AI systems can use the turnstile model (Proposition 1) to predict when unresolved history produces exit pressure based on current pool state, allowing for dynamic hedging strategies.

Bold Header: Evidence Prioritization Framework

AI systems can implement a decision-making framework that prioritizes evidence based on the VDISC structure: produce privacy-compatible evidence about past states, limit the state exposed by a single flaw, and disclose residual uncertainty explicitly. This guides automated security auditing by prioritizing controls like Replayable logs, checkpoints, or snapshots for strengthening public proof.

Bold Header: Directional Market Response Prediction

AI systems can utilize the directional patterns observed in Orchard data to predict market responses: market-cap-normalized reported loss and unresolved exposure overlap among the 38 events with a public loss figure (Pearson 0.86, Spearman 0.56), helping to distinguish between causal effects and mere correlation in event studies.

Bold Header: Cross-Event Anomaly Detection

By applying VDISC rules across multiple disclosures, AI systems can perform cross-event diagnostics to identify confounding factors; for instance, they can check if reported loss and unresolved history require separate measures by comparing the response of events with different anchor sequences.