Convergence-Weighted Aggregation of Cross-Exchange Prediction Markets: A Dependency-Aware Index for Combining Prices Across Kalshi, Polymarket, Manifold, Metaculus, and Long-Tail Venues

Version 2 (2026-08-19). The version of this paper deposited in May 2026 promised a forward cross-exchange evaluation of the Index of Convergence Multi-epistemic (ICM) aggregator and its lead-lag dependency penalty, and retired itself on the grounds that forward collection had not started. That evaluation has now been executed retrospectively, on markets that had already resolved, which required no waiting - and it returns a null. On 125 frozen cross-venue market families (SHA-256 e87c977d..., all two-venue) drawn from 132,486 in-universe resolved markets across Kalshi, Polymarket and Manifold, ICM is statistically indistinguishable from equal weighting at one and seven days and significantly worse at thirty days (Brier delta +0.00072, cluster-bootstrap 95% CI [+0.00006, +0.00126]). The magnitude is economically negligible, the sign is against the aggregator, and the direction is stated in the abstract because the evaluation protocol was frozen before the matched set was built and required reporting whatever the sign came out. That comparison is the protocol's secondary stratum: the pre-registered primary stratum of three or more venues contains zero families, so the pre-registered headline cell is empty. The structural reason is printed rather than inferred - at two venues the median equals the mean by construction and rank-normalised volumes cancel exactly out of both weights, leaving the lead-lag penalty as the aggregator's only degree of freedom, near-inert on the typical family and occasionally catastrophic (on 16 of 119 rows the penalty hits its cap and the aggregate discards a venue entirely; dropping those rows removes every directional signal in the table, in both directions). Two further results are, the author thinks, worth more than the null. First, the matcher is the binding methodological problem and is here measured rather than assumed: a deterministic token-overlap matcher was refused by its own gold-set gate twice, at false-positive rates of 87.88% and then 70.00% on the accepted band, forcing an architecture change in which blind three-vote adjudication becomes the matcher and the similarity score is demoted to candidate generation; the freeze gate then passed at 2.06% [0.57, 7.21] on an independent fresh panel. Both refused rounds ship. Because that adjudicated matcher is stochastic, its test-retest reliability is reported from two independent realisations of the same panels (0.70% of 3,990 votes flip; the frozen-list hash is a realisation of a stochastic instrument rather than a deterministic anchor, and the headline is invariant to the perturbation). Second, and most consequentially: of 17 hand-built cross-venue reference event families, 9 contain no proposition-equivalent contract pair at all, and two families that a blind three-vote panel judged to be the same proposition resolved in opposite directions - equivalence lives in settlement rules, not titles. Cross-venue aggregation at contract granularity is therefore structurally bounded, and that bound applies to any title-level matcher including this one. What the text below no longer describes accurately. The closing sentence below announces a forward-looking evaluation with rolling collection from May 2026. That evaluation was not run forward; it was run retrospectively on already-resolved markets, and this version reports its result - a null. The V=2 degeneracy noted below is no longer an observation but a proved structural property: at two venues the median equals the mean by construction and rank-normalised volumes cancel out of both weights, leaving the lead-lag penalty as the aggregator's only remaining degree of freedom. The earlier text is left standing unedited as the record of what that version said. The manuscript's own title in this version is: Convergence-Weighted Aggregation of Cross-Exchange Prediction Markets: A Measured Matcher, a Null Result at V=2, and the Contract-Non-Equivalence Bound on Cross-Venue Aggregation. The record title above is retained unchanged so that the concept DOI keeps a stable citation string across versions. Modern prediction-market venues increasingly host overlapping markets on identical world events. Naive aggregation methods treat each venue as a conditionally independent source given the resolution outcome; this assumption is violated by three documented mechanisms (cross-exchange copy-trading bots, shared news flow, arbitrageur compression). Adapts the Index of Convergence Multi-epistemic (ICM) framework to the prediction-market setting. Within Pi, the lead-lag primitive Pi_L is the load-bearing component for the empirical bias-reduction result. Synthetic experiments confirm bias-reduction direction under Mechanism I (copy-trading) but not under Mechanisms II (common factor) or III (arbitrage compression); result is regime-targeted rather than uniformly dominant. Strict cross-exchange backtest at V=2 listing venues degenerates ICM to equal-weighted naive mean. Reference implementation released open-source. Forward-looking evaluation across additional exchanges (Kalshi via authenticated API, plus Metaculus and long-tail venues) planned with rolling collection from May 2026.