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Proteus: Continuous-Gradient Prediction Markets via On-Chain Levenshtein Distance

On the Information-Theoretic Collapse of Binary Markets and the Case for Metric-Scored Text Prediction Sean McDonald
with many AI models February 2026

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Abstract

Binary prediction markets encode exactly one bit of information per contract. As AI forecasting systems approach superhuman calibration, the marginal edge any participant can capture in a binary market collapses toward zero — the correct answer becomes trivially computable, and spreads vanish. We propose an alternative market structure in which participants predict the exact text a public figure will post, scored by Levenshtein edit distance. Text prediction over a 95-character printable ASCII alphabet with strings up to length 280 yields an outcome space of approximately 95^280 ≈ 10^554 possibilities, encoding roughly 1,840 bits of information per market versus 1 bit for binary contracts — a 1,840:1 improvement in information density. Levenshtein distance induces a proper metric on this space (satisfying identity, symmetry, and the triangle inequality), which means payoffs are not a binary cliff but a continuous gradient surface where every character of precision is rewarded. We demonstrate this with a thesis example: given the same prompt and public training corpus, Claude predicts a Satya Nadella post at edit distance 1 while GPT achieves distance 8 — a 7-edit gap that determines the entire pool. In a binary market, both models “predicted correctly” and split nothing.

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Key Contributions

Formal Analysis

Proofs of metric properties, outcome space analysis, and payoff surface characterization

Working Prototype

Deployed on BASE Sepolia with on-chain Levenshtein computation in 513 lines of Solidity

Worked Examples

Six demonstrations spanning AI roleplay, insider advantage, null prediction, and bot filtration

Attack Vector Analysis

Self-oracle exploits, insider dynamics, AI-induced behavior modification, Sybil resistance

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The Commoditization Problem

Prediction markets are no longer a niche experiment. Polymarket and Kalshi combined processed approximately 40billioninvolumein2025.Industryprojectionsestimate445billioncontractsand40 billion in volume in 2025. Industry projections estimate 445 billion contracts and 222.5 billion in notional volume for 2026, representing 47% annual growth. These markets all operate on the same simple primitive: a contract resolves to 0 or 1, and participants trade shares priced between 0and0 and 1 reflecting the market’s collective probability estimate. This structure has a fundamental limitation. As AI forecasting systems improve along what appears to be an exponential capability curve, the edge available in binary markets shrinks. When every sophisticated participant’s model outputs “87% yes” on the same question, the spread vanishes and the market becomes commoditized. The information content of a binary outcome is exactly 1 bit — there is no room for gradations of skill once the probability estimate converges.

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Text Prediction as Richer Outcome Space

Consider predicting not whether something happens, but the exact words a public figure will use to describe it. The outcome space changes dramatically: 
Outcome space: {0, 1}
Information content: 1 bit
This is not a marginal improvement. The text prediction space contains roughly 10^554 possible outcomes, a number that exceeds the estimated number of atoms in the observable universe by over 470 orders of magnitude. No AI system, no matter how capable, will exhaust this space.
Information Density Ratio: Text prediction markets encode approximately 1,840 times more information than binary prediction markets.

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Mathematical Foundations

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Levenshtein Distance as Metric

The Levenshtein distance d_L(a, b) between two strings is the minimum number of single-character edit operations (insertions, deletions, substitutions) required to transform one string into another. Theorem: d_L is a proper metric on the space of strings, satisfying:
  1. Identity of indiscernibles: d_L(a, b) = 0 if and only if a = b
  2. Symmetry: d_L(a, b) = d_L(b, a)
  3. Triangle inequality: d_L(a, c) ≤ d_L(a, b) + d_L(b, c)

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Payoff Surface

The Proteus payout mechanism is winner-take-all: 
fee = ⌊pool × 700 / 10000⌋       // 7% platform fee
payout = pool − fee                 // 93% to winner
winner = argmin_{s ∈ submissions} d_L(s.predictedText, actualText)
Lipschitz Continuity: The expected payoff is Lipschitz-continuous with respect to prediction quality — marginal improvements in distance always translate to marginal improvements in expected payout. There is no “close enough” threshold below which improvements stop mattering. Every edit counts.

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Algorithmic Complexity

The standard Wagner-Fischer dynamic programming algorithm computes d_L(a, b) in O(mn) time using O(min(m, n)) space. Gas costs on BASE L2 (approximate):
String LengthGas Cost
50 characters~400,000
100 characters~1,500,000
280 characters~9,000,000
The contract enforces MAX_TEXT_LENGTH = 280 (tweet length) to prevent block gas limit denial-of-service.

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System Design

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Architecture

All market data lives on-chain. There is no database. Redis is used only for caching RPC responses, authentication nonces and OTPs, and rate limiting.

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Contract Constants

ConstantValuePurpose
PLATFORM_FEE_BPS700 (7%)Fee taken from winning pool
MIN_BET0.001 ETHMinimum stake per submission
BETTING_CUTOFF1 hourNo submissions within 1 hour of market end
MIN_SUBMISSIONS2Minimum entries for valid resolution
MAX_TEXT_LENGTH280Character limit (tweet length, gas cap)

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The Null Sentinel

The contract reverts on empty strings. To express the prediction “this person will not post,” participants submit the sentinel value __NULL__. When resolution also uses __NULL__: 
d_L("__NULL__", "__NULL__") = 0
This creates a market primitive that binary contracts cannot express: betting on silence. AI roleplay agents always generate text — they cannot predict inaction.

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X as Resolution Infrastructure

Text prediction markets require a resolution source: a public, timestamped, attributable record of what a person actually said. X (formerly Twitter) is uniquely suited to this role.

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Why X Specifically

X posts have four properties that make them suitable for market resolution:
Posts are visible without authentication. No scraping or privileged access is required for verification.
Each post carries a server-side timestamp accurate to the second, enabling dispute resolution about whether a post fell within a market’s resolution window.
The handle-to-person mapping is well-established for public figures, and X’s verification system provides a baseline identity layer.
While posts can be edited or deleted after the fact, edits are detectable via the X API, and third-party archival services provide independent records.

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Market-Moving Speech

X posts are financial events:
  • Elon Musk’s tweets have produced approximately 3% price moves in DOGE on multiple occasions
  • Donald Trump’s Truth Social posts in March 2025 naming specific cryptocurrencies triggered a $300 billion crypto market rally
  • Sam Altman’s statements on X have moved AI sector sentiment, with Microsoft stock reaching all-time highs on key announcements
API Update (Feb 2026): X now offers pay-per-use API access — no subscriptions, no monthly caps, just credit-based billing. This makes independent, multi-oracle tweet verification economically viable for the first time.

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Economic Opportunity

Prediction markets represent a 40billionmarketin2025,withprojectionsof40 billion market in 2025, with projections of 222.5 billion in notional volume by 2026 and a total addressable market exceeding $100 billion within the decade.

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Adjacent Markets

  • Sports betting: 100.9billionin2024,projectedtoreach100.9 billion in 2024, projected to reach 187 billion by 2030 (11% CAGR)
  • Creator economy: Monetizing attention and influence
  • Corporate communications monitoring: Market-moving executive statements

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Full Paper

The complete whitepaper includes:
  • Detailed prediction market landscape analysis (boom and bust history)
  • Related work on scoring rules and string metrics
  • Complexity-theoretic framing of text prediction as AI capability proxy
  • Market lifecycle dynamics and limiting cases
  • Fast takeoff considerations

Read the Full Whitepaper

Access the complete research paper with formal proofs, extended economic analysis, and technical appendices.

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Citation

@article{mcdonald2026proteus,
  title={Proteus: Continuous-Gradient Prediction Markets via On-Chain Levenshtein Distance},
  author={McDonald, Sean},
  year={2026},
  month={February}
}

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