Whitepaper · public by design

The load-bearing math

Everything below is published in full — composition, scores, and changelogs included. Radical transparency is the trust substitute for a human index committee.

§1Per-market scoring

Each (market, theme) pair gets a scoring triple against the theme's axis charter— a one-paragraph, value-neutral definition of what "+" means:

sign s ∈ {−1, +1} — discrete; the direction must be crisp and auditable.
relevance w ∈ (0, 1] — centrality × magnitude, continuous.
confidence c ∈ [0, 1] — used only as a gate(include iff c ≥ 0.8), never as a weight shader. A wrong sign isn't a small error; it's betting against your own theme.

§2Aligned probability

A market's YES price p is converted to a theme-aligned probability:

q_i = p_i        if s_i = +1
q_i = 1 − p_i    if s_i = −1

q is "the market-implied probability that this leg resolves in the theme's + direction."

§3The gauge (0–100)

G = 100 · Σ(w_i · q_i) / Σw_i

The storytelling number. It may step when the composition changes (a leg added, removed, or resolved) — every step is annotated in the public changelog, never smoothed away.

§4The share-weighting identity

Baskets allocate by relevance-weighted shares, not dollars: buy n_i = λ·w_i shares of each leg's aligned side, with λ set by your stake. Since each share pays $1 if it wins:

NAV = Σ n_i · q_i = λ · Σ w_i · q_i ∝ gauge numerator

The basket is the gauge, scaled — what you buy tracks the published number by construction; tracking difference is pure frictions (fees, slippage, caps). And because YES + NO = $1 on a binary market, shorting the theme = buying the complement side of every leg — exact, with no borrow. You hold those positions directly; nothing is rebalanced on your behalf.

§5Eligibility gates & caps

Curation is fully automated, so safety is encoded as data rules:

Relevance≥ 0.3

Confidence≥ 0.8 (ensemble self-consistency)

Price∈ [0.03, 0.97]

Resolution1–18 months out

Liquidityfloor · max spread ceiling

Per-leg cap≤ 15% effective weight

Per event group≤ 20% (one leg per negRisk event)

One-month resolution≤ 40% of weight

Correlated cluster≤ 25% of weight

Sign disagreementany → excluded

Marks use a 1-hour time-weighted median of the bid/ask mid for manipulation resistance; a market under UMA dispute is frozen at its pre-dispute TWAP.

§6On history & carry

The gauge is a statistic, not a chained return. Each historical day is simply the relevance-weighted average (§3) of the markets that were live for the theme that day — including thousands of since-resolved markets, scored on their questions alone under the same rubric as live ones (winners and losers alike, so the history carries no survivorship bias). A resolving leg takes its final 0/1 settlement on its last day and then leaves the set. There is no divisor and no chain: a daily average has no composition-change discontinuity to neutralize, so adding or dropping a market never fabricates a move.
Reconstruction caveats. Historical liquidity data does not exist, so pre-live membership applies a volume floor instead of the live liquidity gate; and days with fewer than three priced members are omitted — an honest gap where the theme barely existed yet, never smoothed over.
Carry / deadline decay. "X by DATE" legs bleed mechanically toward 0 as the deadline approaches even when nothing happens — so part of an index's drift is carry, not the theme moving. Each index discloses weighted average time-to-resolution and carry tilt.