arxiv: 2605.00493 · v2 · submitted 2026-05-01 · 💱 q-fin.TR · cs.CR· q-fin.GN

Recognition: 2 theorem links

· Lean Theorem

ForesightFlow: An Information Leakage Score Framework for Prediction Markets

Maksym Nechepurenko

Authors on Pith no claims yet

Pith reviewed 2026-05-15 06:19 UTC · model grok-4.3

classification 💱 q-fin.TR cs.CRq-fin.GN

keywords information leakage scoreprediction marketsinformed tradingproper scoring rulesmurphy decompositiondecentralized marketspolymarketinsider trading detection

0 comments

The pith

The Information Leakage Score measures the share of a binary market's terminal price move that occurs before the public news event.

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

This paper presents the ForesightFlow Information Leakage Score framework for identifying informed trading in decentralized prediction markets. For an event-resolved binary market, the score calculates the fraction of the final price adjustment that gets incorporated before the public news arrives. It draws an explicit link to Murphy decompositions in the proper-scoring-rule literature. A pilot on a large market corpus shows that resolution-anchored timestamps fail to separate populations and that documented insider cases lie outside the original scope, prompting a deadline-anchored extension. The work releases the full inventory and code to support further checks.

Core claim

ForesightFlow defines an Information Leakage Score for event-resolved binary markets that quantifies the fraction of the terminal information move priced in before the public news event. The score admits a Murphy-decomposition reading that connects label generation to the proper-scoring-rule literature. Three operational scope conditions—edge effect, non-trivial total move, and anchor sensitivity—must hold for the score to be interpretable. Empirical checks reveal that a resolution-anchored proxy for the public-event timestamp does not separate event-resolved markets from controls and that publicly documented insider cases are systematically deadline-resolved, motivating a deadline-ILS with

What carries the argument

The Information Leakage Score (ILS), which computes the pre-public-event fraction of the total price movement from an anchor point to resolution.

If this is right

The score supplies a scalar measure of early information incorporation that can be compared across markets satisfying the scope conditions.
The Murphy-decomposition link allows the ILS to be interpreted within the existing theory of proper scoring rules.
Documented insider activity requires the deadline-anchored variant rather than the news-timestamp version.
The framework can be applied end-to-end to large corpora once the inventory and resolution typology are used.

Where Pith is reading between the lines

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

A reliable deadline-ILS could be used to flag candidate markets for further audit on other prediction platforms.
Better methods for identifying the exact public-event timestamp would expand the set of markets for which the original ILS is applicable.
Markets that repeatedly show high ILS under the extended definition might indicate structural features that facilitate early incorporation of information.

Load-bearing premise

The chosen timestamp proxy accurately marks the moment the relevant information becomes public and the three scope conditions hold for the markets under study.

What would settle it

Compute the ILS on a set of markets with independently verified insider trading; if the scores are not systematically higher than those from matched controls under the same scope conditions, the detection claim does not hold.

Figures

Figures reproduced from arXiv: 2605.00493 by Maksym Nechepurenko.

**Figure 1.** Figure 1: Hierarchical recovery of the news timestamp view at source ↗

**Figure 2.** Figure 2: Four characteristic price trajectories, normalized to view at source ↗

**Figure 3.** Figure 3: Murphy decomposition B = UNC + REL − RES at the news timestamp Tnews, evaluated for three idealized regimes of the same set of markets. The uncertainty term UNC is fixed by the marginal outcome distribution and is identical across scenarios. The reliability error REL is small for any approximately-calibrated forecaster. The resolution component RES(Tnews) is the only component that varies with the degree o… view at source ↗

**Figure 4.** Figure 4: End-to-end ForesightFlow pipeline. Data sources (top) feed historical backfill and real view at source ↗

read the original abstract

ForesightFlow is an Information Leakage Score (ILS) framework for detecting informed trading on decentralized prediction markets. For an event-resolved binary market, the score quantifies the fraction of the terminal information move priced in before the public news event. Three operational scope conditions (edge effect, non-trivial total move, anchor sensitivity) are stated as preconditions for interpretation. The score admits a Murphy-decomposition reading that connects label generation to the proper-scoring-rule literature. A pilot empirical evaluation surfaces three findings. First, a resolution-anchored proxy for the public-event timestamp does not separate event-resolved markets from a matched control population (Mann-Whitney p = 1e-6, separation reversed), demonstrating that proxy quality is itself a binding constraint. Second, the article-derived timestamp on a single high-stakes case shifts the score by 0.444 in magnitude relative to the proxy and lies on the opposite side of zero. Third, an audit of the publicly documented Polymarket insider record reveals that documented cases are systematically deadline-resolved, falling outside the original ILS scope (0 of 24 FFIC inventory markets satisfied original scope conditions). This last finding motivates a deadline-ILS extension introduced in Section 7, anchored at the public-event timestamp rather than the news timestamp, and equipped with a per-category exponential hazard baseline for the time-to-event distribution. The extension closes the gap between the methodology and the population in which insider trading has been empirically documented. An end-to-end evaluation of the extension on the 2026 U.S.-Iran conflict cluster is reported in a companion paper. We release the FFIC inventory, the resolution-typology classification of the 911,237-market corpus, and all code at github.com/ForesightFlow.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper defines a clean Information Leakage Score for binary prediction markets tied to Murphy decomposition, but the pilot shows the required public-event timestamp is hard to pin down reliably.

read the letter

The core new piece is the ILS definition itself: for resolved binary markets it measures the fraction of the total price move that occurs before the public news event, with three explicit scope conditions and a direct link to the Murphy decomposition of proper scoring rules. That connection is useful because it grounds the score in existing label-generation literature rather than inventing a standalone metric. The paper also adds a deadline-ILS extension with a per-category exponential hazard to handle cases where the original news-timestamp anchor does not apply, and it releases the full FFIC inventory plus code, which is straightforward to check. The pilot is candid about its own problems: the resolution-anchored proxy produces reversed separation from controls and a single better timestamp shifts one score by 0.444 with a sign change. Documented insider cases mostly fall outside the original scope, which is why the extension exists. The soft spot is exactly the one the stress test identifies. Because ILS is just a normalized difference of two prices, any misplacement of the anchor scales the result directly, and the pilot data confirm that the proxy does not supply a stable t*. The extension moves the anchor but its full evaluation sits in a companion paper, so we cannot yet judge how well the hazard baseline fixes the issue. This work is mainly for people already studying prediction-market efficiency or insider-trading detection who have or can obtain high-precision timestamps. It is not a broad result, but the definition is transparent and the limitations are reported rather than hidden. I would bring it to a reading group to talk through the proxy sensitivity. I would not cite it in the next year unless I were working on this exact problem. It deserves peer review because the framework is well-specified and the empirical honesty gives referees something concrete to evaluate.

Referee Report

3 major / 2 minor

Summary. The paper introduces ForesightFlow, an Information Leakage Score (ILS) framework for binary prediction markets. For an event-resolved market, ILS is defined as the normalized fraction of the terminal information move (final minus initial probability) that occurs before the public news event timestamp t*. The score is shown to admit a Murphy decomposition that connects it to the proper-scoring-rule literature. A pilot on Polymarket data finds that a resolution-anchored proxy for t* fails to separate resolved markets from controls (reversed Mann-Whitney p=1e-6) and is sensitive to anchor choice (0.444 shift with sign change). An audit shows documented insider cases fall outside the original scope conditions (0 of 24 satisfy them), motivating a deadline-ILS extension in §7 with per-category exponential hazard baseline. Full evaluation of the extension is deferred to a companion paper; the FFIC inventory, typology of 911,237 markets, and code are released.

Significance. If the timestamp proxy can be made reliable, the ILS supplies a parameter-free, directly interpretable metric for pre-event leakage that links cleanly to Murphy decomposition and proper scoring rules. The open release of data, typology, and code is a clear strength for reproducibility. The pilot, however, demonstrates that the original formulation is practically limited by anchor identification, and deferral of the extension's validation restricts the manuscript's standalone empirical contribution.

major comments (3)

[§4] §4 (pilot evaluation): The resolution-anchored proxy yields reversed separation (Mann-Whitney p=1e-6) versus controls and an article-derived anchor shifts ILS by 0.444 with sign reversal. Because ILS is exactly the normalized price difference between t0 and t*, any misplacement of t* scales the numerator directly; the reported sensitivity shows the leakage fraction is not robustly identified by the chosen proxy.
[§7] §7 (deadline-ILS extension): The extension is motivated by the finding that 0 of 24 documented insider cases satisfy the original scope conditions, yet its end-to-end evaluation on the 2026 U.S.-Iran cluster is reported only in a companion paper. This leaves the manuscript without a complete demonstration that the revised score separates populations on the relevant data.
[§3] §3 (ILS definition and Murphy reading): The claim that ILS admits a Murphy decomposition connecting label generation to proper scoring rules is stated but not accompanied by the explicit algebraic steps showing how the normalized pre-t* move corresponds to a proper-score component; a short derivation would strengthen the interpretive link.

minor comments (2)

[§2] The three operational scope conditions (edge effect, non-trivial total move, anchor sensitivity) are referenced repeatedly but never enumerated in a single location; a short bulleted list in §2 or §3 would improve readability.
Notation for the public-event timestamp alternates between t* and t_public without a consolidated definition table; consistency would reduce reader effort.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on the manuscript. We address each major comment point by point below, indicating the revisions that will be made to the revised version.

read point-by-point responses

Referee: [§4] §4 (pilot evaluation): The resolution-anchored proxy yields reversed separation (Mann-Whitney p=1e-6) versus controls and an article-derived anchor shifts ILS by 0.444 with sign reversal. Because ILS is exactly the normalized price difference between t0 and t*, any misplacement of t* scales the numerator directly; the reported sensitivity shows the leakage fraction is not robustly identified by the chosen proxy.

Authors: The pilot in §4 is designed to surface the practical limitations of resolution-anchored proxies. The reversed Mann-Whitney result (p=1e-6) and the 0.444 shift with sign reversal are reported precisely to demonstrate that such proxies do not reliably identify pre-event leakage. This finding motivates the deadline-ILS extension. No revision is required, as the results already serve to illustrate the proxy problem rather than to assert robustness. revision: no
Referee: [§7] §7 (deadline-ILS extension): The extension is motivated by the finding that 0 of 24 documented insider cases satisfy the original scope conditions, yet its end-to-end evaluation on the 2026 U.S.-Iran cluster is reported only in a companion paper. This leaves the manuscript without a complete demonstration that the revised score separates populations on the relevant data.

Authors: We acknowledge that the full end-to-end evaluation appears in the companion paper. To improve the standalone contribution, we will insert a concise summary of the companion results (including separation statistics on the 2026 U.S.-Iran cluster) into §7, while retaining the detailed analysis in the companion. revision: partial
Referee: [§3] §3 (ILS definition and Murphy reading): The claim that ILS admits a Murphy decomposition connecting label generation to proper scoring rules is stated but not accompanied by the explicit algebraic steps showing how the normalized pre-t* move corresponds to a proper-score component; a short derivation would strengthen the interpretive link.

Authors: We agree that an explicit derivation would strengthen the link. In the revised manuscript we will add a short derivation (in §3 or a new appendix) showing the algebraic steps from the normalized pre-t* price move to the corresponding term in the Murphy decomposition of the Brier score. revision: yes

Circularity Check

0 steps flagged

No significant circularity: ILS defined directly from price paths and timestamps

full rationale

The central ILS construction is a normalized difference of observed market prices at the initial time, the public-event anchor, and resolution. This directly implements the claimed fraction by definition rather than deriving it from fitted parameters, self-citations, or prior uniqueness results. The Murphy-decomposition connection references external proper-scoring-rule literature. The pilot evaluation and deadline-ILS extension are empirical and modeling choices that do not retroactively make the core score circular. No load-bearing step reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Core ILS relies on standard definitions of price moves and event timestamps with no new free parameters; the extension introduces a per-category exponential hazard baseline for time-to-event that is a modeling choice rather than a fitted constant in the main claim.

axioms (1)

standard math Properties of proper scoring rules and Murphy decomposition hold for binary outcome labels
Invoked to connect the ILS to existing scoring-rule literature.

pith-pipeline@v0.9.0 · 5623 in / 1268 out tokens · 35572 ms · 2026-05-15T06:19:53.341041+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel (J uniquely satisfies the functional equation) unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

ILS(M) = Δ_pre / Δ_total where Δ_pre = p(T_news) − p(T_open) and Δ_total = p_Tresolve − p(T_open); connects to Murphy decomposition B = UNC + REL − RES
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking (D=3 from linking) unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Resolution typology (event-resolved vs. deadline-resolved) and scope conditions (edge effect, non-trivial total move, anchor sensitivity)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 2 Pith papers

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Manipulation, Insider Information, and Regulation in Leveraged Event-Linked Markets
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Leverage scales market-price manipulation linearly while shifting outcome-manipulation thresholds and multiplying informed-trading rents in three distinct ways, calling for re-allocated regulatory attack surfaces rath...
A Taxonomy of Event-Linked Perpetual Futures: Variant Designs Beyond the Single-Market Binary Case
q-fin.TR 2026-05 unverdicted novelty 6.0

The paper organizes seven canonical variants of event-linked perpetual futures along four design axes, supplying payoff definitions, inheritance rules from prior work, and variant-specific constraints.

Reference graph

Works this paper leans on

38 extracted references · 38 canonical work pages · cited by 2 Pith papers

[1]

Journal of Economic Perspectives , volume =

Wolfers, Justin and Zitzewitz, Eric , title =. Journal of Economic Perspectives , volume =

work page
[2]

and Forsythe, Robert and Gorham, Michael and Hahn, Robert and Hanson, Robin and Ledyard, John O

Arrow, Kenneth J. and Forsythe, Robert and Gorham, Michael and Hahn, Robert and Hanson, Robin and Ledyard, John O. and Levmore, Saul and Litan, Robert and Milgrom, Paul and Nelson, Forrest D. and Neumann, George R. and Ottaviani, Marco and Schelling, Thomas C. and Shiller, Robert J. and Smith, Vernon L. and Snowberg, Erik and Sunstein, Cass R. and Tetlock...

work page
[3]

Surowiecki, James , title =

work page
[4]

Information Systems Frontiers , volume =

Hanson, Robin , title =. Information Systems Frontiers , volume =

work page
[5]

The Journal of Prediction Markets , volume =

Hanson, Robin , title =. The Journal of Prediction Markets , volume =

work page
[6]

and Servan-Schreiber, Emile and Tetlock, Philip and Ungar, Lyle and Mellers, Barbara , title =

Atanasov, Pavel and Rescober, Phillip and Stone, Eric and Swift, Samuel A. and Servan-Schreiber, Emile and Tetlock, Philip and Ungar, Lyle and Mellers, Barbara , title =. Management Science , volume =

work page
[7]

and Stiglitz, Joseph E

Grossman, Sanford J. and Stiglitz, Joseph E. , title =. American Economic Review , volume =

work page
[8]

Trading volume statistics , year =

work page
[9]

, title =

Kyle, Albert S. , title =. Econometrica , volume =

work page
[10]

and Milgrom, Paul R

Glosten, Lawrence R. and Milgrom, Paul R. , title =. Journal of Financial Economics , volume =

work page
[11]

and O'Hara, Maureen and Paperman, Joseph B

Easley, David and Kiefer, Nicholas M. and O'Hara, Maureen and Paperman, Joseph B. , title =. Journal of Finance , volume =

work page
[12]

and O'Hara, Maureen , title =

Easley, David and Kiefer, Nicholas M. and O'Hara, Maureen , title =. Review of Financial Studies , volume =

work page
[13]

Journal of Finance , volume =

Easley, David and Hvidkjaer, Soeren and O'Hara, Maureen , title =. Journal of Finance , volume =

work page
[14]

Journal of Financial Economics , volume =

Duarte, Jefferson and Young, Lance , title =. Journal of Financial Economics , volume =

work page
[15]

Flow Toxicity and Liquidity in a High-Frequency World , journal =

Easley, David and L. Flow Toxicity and Liquidity in a High-Frequency World , journal =

work page
[16]

and Bondarenko, Oleg , title =

Andersen, Torben G. and Bondarenko, Oleg , title =. Journal of Financial Markets , volume =

work page
[17]

and Ready, Mark J

Lee, Charles M.\ C. and Ready, Mark J. , title =. Journal of Finance , volume =

work page
[18]

, title =

Hawkes, Alan G. , title =. Biometrika , volume =

work page
[19]

Quarterly Journal of Economics , volume =

Budish, Eric and Cramton, Peter and Shim, John , title =. Quarterly Journal of Economics , volume =

work page
[20]

, title =

Platt, John C. , title =. Advances in Large Margin Classifiers , publisher =. 1999 , pages =

work page 1999
[21]

Proceedings of the 22nd International Conference on Machine Learning (ICML) , pages =

Niculescu-Mizil, Alexandru and Caruana, Rich , title =. Proceedings of the 22nd International Conference on Machine Learning (ICML) , pages =

work page
[22]

arXiv preprint arXiv:2508.03474 , year =

Saguillo, Oriol and Ghafouri, Vahid and Kiffer, Lucianna and Suarez-Tangil, Guillermo , title =. arXiv preprint arXiv:2508.03474 , year =

work page arXiv
[23]

2026 , howpublished =

Mitts, Joshua and Ofir, Moran , title =. 2026 , howpublished =

work page 2026
[24]

2020 IEEE Symposium on Security and Privacy (S&P) , pages =

Daian, Philip and Goldfeder, Steven and Kell, Tyler and Li, Yunqi and Zhao, Xueyuan and Bentov, Iddo and Breidenbach, Lorenz and Juels, Ari , title =. 2020 IEEE Symposium on Security and Privacy (S&P) , pages =

work page 2020
[25]

and Tetlock, Philip E

Schoenegger, Philipp and Tuminello, Peter S. and Tetlock, Philip E. and Karger, Ezra and Atanasov, Pavel , title =. Science Advances , volume =. 2024 , doi =

work page 2024
[26]

, title =

Leetaru, Kalev and Schrodt, Philip A. , title =. Annual Convention of the International Studies Association , year =

work page
[27]

2026 , month = apr, note =

Nechepurenko, Maksym , title =. 2026 , month = apr, note =

work page 2026
[28]

2026 , month = may, note =

Nechepurenko, Maksym and Shuvalov, Pavel , title =. 2026 , month = may, note =

work page 2026
[29]

Soros, George , title =

work page
[30]

, title =

Schelling, Thomas C. , title =

work page
[31]

, title =

Manski, Charles F. , title =. Economics Letters , volume =

work page
[32]

2026 , note =

Tsang, Kwok Ping and Yang, Zichao , title =. 2026 , note =

work page 2026
[33]

and Peng, L

Ng, H. and Peng, L. and Tao, Y. and Zhou, D. , title =. 2026 , note =

work page 2026
[34]

and Huang, Taeyoung , title =

Clinton, Joshua D. and Huang, Taeyoung , title =. 2025 , note =

work page 2025
[35]

, title =

Murphy, Allan H. , title =. Journal of Applied Meteorology , volume =

work page
[36]

, title =

Brier, Glenn W. , title =. Monthly Weather Review , volume =

work page
[37]

, title =

Gneiting, Tilmann and Raftery, Adrian E. , title =. Journal of the American Statistical Association , volume =

work page
[38]

2026 , month = may, note =

Nechepurenko, Maksym , title =. 2026 , month = may, note =

work page 2026