A compelling claim.
A checkable constraint.

A trading-math roadmap by Roan motivates combinatorial reasoning with two related events priced at 0.48 and 0.32. Accept its premise that the stronger event B implies event A. The implication requires P(B) ≤ P(A). These numbers satisfy that condition.

The three weights above construct a compatible probability model: P(B) = 0.32, P(A) = 0.32 + 0.16 = 0.48, and P(neither) = 0.52. Their complements are 0.68 and 0.52. Removing an impossible outcome therefore does not, by itself, demonstrate mispricing.

from fractions import Fraction as F

both, a_only, neither = F(32, 100), F(16, 100), F(52, 100)
assert both + a_only + neither == 1
assert both + a_only == F(48, 100)
assert both == F(32, 100)
assert min(both, a_only, neither) > 0
print("Compatible marginals; no demonstrated violation.")

At hypothetical frictionless prices equal to these expectations, every zero-cost portfolio of these claims has expected payoff zero. Because each allowed state has positive weight, it cannot pay nonnegatively everywhere and positively somewhere. This proves consistency of this finite example. Actual bids, asks, costs, and contract resolution terms were not supplied or evaluated.

Saguillo and colleagues (2025) estimate roughly $40 million of historical arbitrage profit during their study period. Their method analyzes recorded activity and uses heuristic and expert checks for related markets. That estimate is evidence about the studied participants and period; it does not establish a return for a new system.

Kroer and colleagues (2016) develop a combinatorial market maker using a Frank–Wolfe method, Bregman projection, and an integer-programming oracle. Their evaluation uses a basketball tournament outcome space of 2⁶³. This is a different experiment. Neither abstract establishes that the top participant in the later study used that optimizer.

The model also matters. A cost-function market maker and a limit order book expose different execution assumptions. Polymarket’s order-book documentation describes bids and asks. A displayed probability is not evidence that an entire multi-order position can be acquired at that price.

A second post describes a layered agent system, separating proposal, testing, validation, and risk enforcement. The useful design principle is independent checking. Its agent counts, cost reduction, and implied trading performance remain author-reported claims here.

Role separation helps organize a review, but several agents can share the same data error or assumption. My engineering requirement is a reproducible artifact at each handoff: immutable input revision, declared evaluation window, machine-readable exclusions, independently recomputed metrics, and a human-readable account of unresolved failures.

• Proposal: record the hypothesis and parameter search before inspecting the evaluation window.
• Validation: reproduce the result from frozen inputs and include all attempted variants in selection accounting.
• Review: challenge chronology, units, missing observations, and execution assumptions with counterexamples.
• Release: publish the exact validated artifact and its limits. A passing test does not authorize an account action.

A log row can represent a rejected candidate, an order response, a partial fill, or a settlement. Counting them all as trades overstates activity. An expired order can retain earlier fills. A successful submission is also distinct from settlement, as Polymarket’s lifecycle example makes explicit.

My reporting approach separates decision rows, identifiable order results, filled quantities, fees, and unresolved outcomes. A net account result additionally requires a consistent treatment of sales, settlements, open positions, external cash flows, and the reporting interval. Missing evidence remains missing rather than becoming a zero.