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This paper establishes that whether an arbitrage violation in a prediction market is actually exploitable depends on the protocol exposing the payoff identity as an executable operation, not just on the payoff math.

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Payoff-bound violations in Polymarket negative-risk markets concentrate on the protocol-unsupported YES side, while the supported NO side has 36 vs 2,098 positive episodes and converter-linked profit of $1.086M.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection The conceptual distinction is solid and the prototype is useful, but the headline asymmetry is likely a settlement-discount artifact and the profit comparison is unfair. the 3 major comments →

arxiv 2608.00666 v1 pith:XMMLY65F submitted 2026-08-01 cs.CE

Executable Arbitrage and Market Efficiency in Prediction Markets

Jonas Gebele , Timm Mutzel , Florian Matthes This is my paper
classification cs.CE
keywords prediction marketsno-arbitrageprotocol-executable arbitragePolymarketNegRisk Adapterpayoff identitiesmarket efficiencyorder book analysis
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Prediction-market prices must respect no-arbitrage bounds implied by winner-takes-all payoff identities, but whether a violation is actually exploitable depends on the protocol exposing the payoff equivalence as an executable operation before settlement. The paper isolates this by studying Polymarket's NegRisk Adapter, which converts NO positions into collateral plus complementary YES exposure before settlement, while the reverse YES-to-NO direction has no such primitive. Reconstructing depth-aware executable values and actor-level transaction histories, the authors find positive payoff-bound violations in the CLOB sample are overwhelmingly concentrated on the unsupported YES side (2,098 episodes vs 36 on the NO side), and estimate $1.12M of arbitrage profit, of which $1.086M (97%) flows through converter-enabled strategies. They also implement a prototype bidirectional adapter showing the reverse path is feasible with roughly 63,000 additional gas units. The point: market efficiency depends on protocol architecture, not just payoff structure.

Core claim

At the paper's core is a distinction between payoff-space no-arbitrage, which follows from terminal payoffs, and protocol-executable no-arbitrage, which depends on the position transformations a protocol makes available. For any subset S of outcomes in a mutually exclusive event, the NO basket over S is payoff-equivalent to (|S|-1) units of collateral plus YES exposure on the complement; Polymarket's NegRisk Adapter operationalizes this identity in the NO-to-YES direction only. Because the reverse YES-to-NO direction requires assembling a complete basket and waiting for settlement, the paper predicts—and finds—that positive violations are rarer and shorter-lived on the supported side and tha

What carries the argument

The load-bearing object is the subset payoff identity sum_{k in S} N_k ≡ (|S|-1)·1 + sum_{j in complement(S)} Y_j, which equates a NO-side portfolio to collateral plus complementary YES exposure. The NegRisk Adapter makes the left-to-right (NO-to-YES) direction executable before settlement; the reverse direction remains settlement-dependent. The paper combines this identity with depth-aware executable portfolio values—jointly walking order-book depth across component markets—to measure violations, and with on-chain conversion traces to attribute exploitation to specific realization channels.

Load-bearing premise

The conclusion that the Adapter causes the NO-side rarity rests on the 33-day hour-stratified CLOB sample being representative and on no unrelated YES/NO liquidity or quoting asymmetry producing the 2,098-vs-36 split; the paper explicitly flags the FPMM/CLOB comparison as descriptive and the NO-side duration evidence as limited to five episodes.

What would settle it

Deploy the reverse adapter on a random subset of active events; if YES-side violation incidence and duration do not fall relative to control events, the enforcement-asymmetry claim is falsified. Alternatively, run the same episode measurement on a period with comparable YES and NO book depths; if positive YES-side episodes remain ~58x more frequent, the asymmetry is not explained by the missing reverse converter.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the mechanism is right, deploying the reverse adapter should push YES-side violations toward the same low incidence and short duration currently seen on the NO side.
  • Protocol designers can predict which payoff identities will be enforced by looking at which transformations are atomic pre-settlement primitives.
  • Settlement-based arbitrage will remain a minor enforcement channel as long as conversion is available, because capital lock-up deters full-basket strategies.
  • The 63,095-gas incremental cost of the reverse path is small enough that the missing direction is not a cost barrier but a state-management one (finalized active-outcome set).
  • Estimates of prediction-market arbitrage profits depend heavily on the defined realization channel; different inclusion criteria shift the number materially.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • I would extend the paper's design principle to other DeFi venues: any protocol that quotes state-contingent claims is implicitly deciding which arbitrage is possible by which token transformations it exposes; the same asymmetric-enforcement logic should appear in options protocols or multi-asset AMMs.
  • A testable extension: instrument a live reverse-adapter deployment on a small event set and compare YES-side violation incidence to a matched control set; the paper's mechanism predicts a drop specifically on the YES side.
  • The 2,098-vs-36 split might partly reflect lower resting liquidity on YES books rather than the adapter; isolating that would require controlling for book depth and quote asymmetry, which the paper's descriptive comparison does not do.
  • The anomalous December 2025 conversion cluster, excluded as coordinated transfer, raises the question whether similar clusters exist below the detection threshold; profit estimates are sensitive to this exclusion.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper introduces a distinction between payoff-space no-arbitrage and protocol-executable no-arbitrage in winner-take-all prediction markets. It derives deterministic event-level payoff identities for Polymarket's negative-risk markets, then measures violations using reconstructed FPMM pool states and recent CLOB order-book data. The empirical core reports a strong directional asymmetry in the CLOB sample—2,098 positive YES-side violation episodes versus 36 NO-side episodes—and estimates $1.086M of converter-enabled arbitrage profit versus $32,283 from settlement-based basket formation. The authors attribute these patterns to Polymarket's NegRisk Adapter, which makes the NO-to-YES direction executable before settlement but not the reverse. The paper also implements and gas-benchmarks a prototype reverse adapter. The central claim is that protocol exposure of payoff equivalences, not just payoff structure, determines how effectively arbitrage disciplines prediction-market prices.

Significance. The conceptual distinction between payoff-space and executable no-arbitrage is a useful contribution and could inform both academic work on market efficiency and practical protocol design. The reverse-adapter prototype, with near-constant incremental gas overhead and a careful discussion of active-outcome finality, is a concrete and valuable design result. The paper is also transparent about several limitations: it explicitly calls the FPMM/CLOB comparison descriptive, acknowledges that the NO-side duration comparison uses only five episodes, and carefully discusses the anomalous conversion cluster. Those strengths are real. However, as argued below, the headline empirical asymmetry and the profit decomposition rest on assumptions that need substantially more support before the central empirical claim is established.

major comments (3)
  1. [§4.2 / Eq. (3)-(4) / Fig. 2] The central incidence asymmetry may be a mechanical consequence of settlement discounting, not of the Adapter. Ignoring fees, the complementary-book relations a_t(NO_i)=1-b_t(YES_i) and b_t(NO_i)=1-a_t(YES_i) imply ΔN→Y_t(S)=Σ_{i∈Q} b_t(Y_i)-1 and ΔY→N_t(S)=1-Σ_{i∈Q} a_t(Y_i). A YES-side violation is therefore exactly the event that the sum of executable YES asks is below $1, while a NO-side violation requires the sum of YES bids to exceed $1. If YES tokens trade at a time-value/settlement discount δ, as the authors argue in their own ref. [4], then Σ ask ≈ 1-nδ and Σ bid ≈ 1-nδ-n·spread, producing frequent YES-side episodes and rare NO-side episodes with no Adapter mechanism at all. The paper measures violations against an undiscounted terminal payoff of $1 and does not condition on time-to-resolution, event maturity, or a discount term. This is load-bearing for I1 and for the interpret
  2. [§4.4 / §5.3 / Appendix D] The profit decomposition is a reconstruction with several load-bearing assumptions and no reported error or full sensitivity analysis. The $1.086M converter estimate depends on a five-block matching window, an imputed one-cent/two-cent spread schedule, a 150-block YES tracking window, and mark-to-market values for merged and residual positions. The $32,283 settlement estimate is terminal profit with no holding-period discount, so the 97% converter share is computed against an apples-to-oranges baseline: converter profits are realized near-immediately, while settlement baskets lock capital until resolution. Additionally, the exclusion of the 381,748 USDC cluster (Appendix D) removes roughly a third of the headline converter profit; although the exclusion may be justified, the paper should report the main estimates with and without this cluster and under alternative matching windows and sp
  3. [§4.1 / §5.1] The violation-incidence asymmetry and the profit asymmetry come from non-overlapping samples and cannot be directly linked. Violation incidence is measured in the FPMM panel and in a five-week CLOB panel (14 April–19 May 2026), while actor-level converter profits are measured from the 2024–2026 transaction panel. The paper explicitly says the two analyses cannot be matched at the opportunity level. As a result, the claim that 'adapter-supported NO-side violations are substantially less frequent' is based on a recent CLOB sample, whereas the claim that converters generate 97% of profits is based on a different period and event set. To support the enforcement mechanism, the paper needs at least an event-study or matched-sample design, or a clear statement that the two claims are independent and that the incidence asymmetry is separately identified. Currently, the descriptive FPMM/CLOB comp
minor comments (6)
  1. [§4.4] The spread assumption is under-specified: 'one-cent spread at half-cent midpoints and a two-cent spread at integer-cent midpoints' should define which midpoints count as 'half-cent' and how midpoints with other fractional parts are handled.
  2. [Footnote 1] The sentence 'In the coming weeks, we extend this observation window by 24 observation periods' is not appropriate for a submitted manuscript; either update the analysis or remove the footnote.
  3. [§5.3] The text 'Converter-enabled realization therefore represents approximately 97' appears truncated; it should read '97%.'
  4. [§4.3] Window-spanning episodes are classified as lasting at least 50 minutes but are then excluded from the exact-duration survival curves. This is reasonable, but the main text should state that the survival comparison excludes the longest-duration CLOB episodes, which could bias the comparison in favor of shorter NO-side durations.
  5. [Fig. 2 caption] The notation 'YES (+/-)' and 'NO (+/-)' is not defined; the caption should explain that these are counts of positive and negative episodes.
  6. [Appendix D] The abstract and main text report the $1.086M figure after excluding the 381,748 USDC cluster, but the main text does not state the post-exclusion total. Please state explicitly that the reported figure excludes this cluster and give the pre-exclusion value for transparency.

Circularity Check

0 steps flagged

No significant circularity; the central empirical results are measured from data, not derived from fitted inputs, and self-citations are contextual.

full rationale

The derivation chain is self-contained. Equations (1)-(5) are standard CTF payoff identities derived from Yi+Ni=1 and sum_i Yi=1; no target result is assumed. The empirical quantities (Δ edges, violation episodes, survival functions, conversion profit, basket profit) are direct reconstructions from order-book, fill, and on-chain data with stated assumptions (five-block matching, spread imputation, ten-minute basket window); these assumptions are not fitted to the headline asymmetry. Implications I1-I3 are ex ante hypotheses, not fitted predictions. The 2,098 vs. 36 CLOB asymmetry and the 97% converter share are measured observations; the paper explicitly calls the FPMM/CLOB comparison descriptive (§5.1), notes the NO-side duration sample has only five episodes (§5.2), and states that episode closure does not establish arbitrage enforcement. The skeptic's discount explanation is a plausible confound (and relates to the authors' own prior work [4]), but it does not make the measured result equivalent to an input by construction; it is a validity threat, not a circular derivation. The only self-citations ([3], [4]) appear in related-work context and are not used as load-bearing uniqueness theorems or as substitutes for the empirical analysis. No circular step meets the quote-and-reduction standard.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 1 invented entities

The empirical estimates rely on several manually chosen thresholds and spread models; the core payoff identity is standard; no new physical entities are invoked; the reverse adapter is a proposed artifact, not an explanatory entity.

free parameters (5)
  • spread assumption for imputed quotes = 0.1¢ for midpoints <3¢ or >97¢; 1¢ at half-cent midpoints; 2¢ at integer-cent midpoints
    Used to convert midpoint prices to executable bid/ask for valuing conversion inputs/outputs; arbitrary spread model affects profit estimates (§4.4).
  • conversion input matching window = 5 Polygon blocks (~10 s)
    Conversions matched to preceding CLOB purchases/mints only within this window; changes which conversions count as sourced (§4.4).
  • returned YES tracking window = 150 blocks (~5 min)
    Returned YES positions valued only within this horizon; residual positions marked to model-based ask (§4.4).
  • basket formation time threshold = 10 minutes
    Settlement baskets must be completed within 10 minutes to count; FIFO default, LIFO robustness (§4.4).
  • anomalous cluster exclusion cutoff = 75 conversions, 12 Dec 2025 22:07–22:14 UTC, three addresses
    Manual exclusion of a 381,748 USDC cluster deemed non-representative; alternative diagnostic thresholds also used (Appendix D).
axioms (5)
  • domain assumption For a winner-takes-all event with mutually exclusive exhaustive outcomes Q, Σ_{i∈Q} Y_i ≡ 1 and N_i ≡ 1 − Y_i.
    Follows from Polymarket/CTF token semantics and event exclusivity; standard in the setting, not independently verified by the paper.
  • domain assumption The CLOB unified book lets complementary YES/NO orders match via split/merge, making the one-sided NO-to-YES equivalence the only pre-settlement payoff transformation exposed by Polymarket.
    Assumed from protocol documentation and observed contract behavior; central to the asymmetry prediction (§2.2–2.3).
  • domain assumption Historical FPMM outcome sets derived from event metadata and wording are genuinely mutually exclusive and exhaustive.
    Manual validation is described but cannot be fully checked from the paper; mis-set could bias FPMM violation counts (§4.1).
  • domain assumption Actor-level transaction histories and parsed on-chain logs fully reconstruct every position transformation affecting inventories.
    Requires complete coverage of CTF splits/merges and Adapter calls; only cross-checked against PolygonScan (§4.4).
  • standard math State-wise payoff equivalence ≡ in Eq. (1) is a standard identity; the algebra |S|1 − Σ_{k∈S} Y_k = (|S|−1)1 + Σ_{j∈Q\S} Y_j is correct.
    The derivation is elementary and correct; included for completeness.
invented entities (1)
  • Reverse NegRisk Adapter extension (convertYESPositions) no independent evidence
    purpose: Make YES-to-NO conversion executable pre-settlement, operationalizing Eq. (5)
    Prototype with gas benchmarks and pseudocode only; not deployed on mainnet, so no independent market evidence.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Executable Arbitrage and Market Efficiency in Prediction Markets." pith.science (2026). https://pith.science/paper/XMMLY65F

@misc{pith2026260800666,
  author       = {Pith},
  title        = {Pith review of: Executable Arbitrage and Market Efficiency in Prediction Markets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XMMLY65F}},
  note         = {Machine review of arXiv:2608.00666}
}
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abstract

Deterministic payoff identities imply no-arbitrage bounds in winner-takes-all prediction markets, but violations of these bounds need not be exploitable before settlement. We distinguish payoff-space no-arbitrage, which follows from terminal payoffs, from protocol-executable no-arbitrage, which depends on the position transformations available to traders. Polymarket's negative-risk markets make this distinction observable: linked binary markets represent mutually exclusive outcomes, while the NegRisk Adapter operationalizes only the NO-to-YES direction before settlement. We reconstruct depth-aware executable portfolio values and combine them with actor-level transaction histories and on-chain conversion traces to measure payoff-bound violations and exploitation. Our reconstruction estimates \$1.12 million in arbitrage profit across two realization channels: \$1.086 million from converter-enabled strategies and \$32 thousand from settlement-based basket formation. In the CLOB sample, positive violations concentrate on the unsupported YES side, whereas adapter-supported NO-side violations are substantially less frequent and shorter-lived. These patterns are consistent with the view that pre-settlement conversion strengthens enforcement by reducing capital lock-up and enabling inventory recycling. Finally, we implement a prototype bidirectional extension of the NegRisk Adapter that makes the reverse path executable before settlement. Together, our findings show that market efficiency depends not only on payoff structure, but also on whether protocols expose payoff equivalences as executable primitives.

Figures

Figures reproduced from arXiv: 2608.00666 by Florian Matthes, Jonas Gebele, Timm Mutzel.

Figure 1
Figure 1. Figure 1: Split- and merge-assisted matching in Polymarket’s unified order book. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Episode-level distributions of fee-adjusted payoff-bound edges in the [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Empirical survival functions for exact-duration, fee-adjusted violation [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Monthly positive net converter-enabled profit by address. Hatched seg [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Weekly share of analyzed conversions executed entirely through taker fills. [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Weekly distribution of realized converter-enabled profit per trade. The [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Monthly settlement-based arbitrage profit by complete-basket formation [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗

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Reference graph

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.