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Signals CLMSR Whitepaper

The Signals whitepaper is the canonical description of how our Continuous LMSR implementation works. It walks through the probability model, proves the bounded-loss guarantees that make the market safe to operate, and documents the practical constraints we enforce in Solidity. Keep it close whenever you audit the protocol or build integrations that rely on the exact economics of a range trade.

Download and version​

The latest release lives at Signals CLMSR Whitepaper (PDF). Version v1.0 matches the currently deployed contracts as of the 1.1.0 release train; when protocol upgrades affect the math or rounding rules we bump the whitepaper version and log the change in the Changelog.

What the paper covers​

  1. Mechanism derivation – Starting from the classic LMSR, the paper derives the continuous version used in Signals. It shows how the potential function generates prices, how α\alpha bounds maker loss by αln⁡n\alpha \ln n, and why every range shares the same convex surface.
  2. Outcome grid construction – It formalises the outcome spec (L, U, s, d) and proves that the half-open tick intervals keep probabilities normalised even when oracle data sits at the exact edge of a bin.
  3. Lazy multiplicative segment tree – The data structure that stores weights for millions of ticks is analysed in detail. You can trace how deferred factors propagate, why chunk sizes are capped, and which invariants must hold for every node.
  4. Rounding discipline – A full chapter justifies rounding costs up and proceeds down, quantifies the dust the system can tolerate, and enumerates the guards that block “free” positions. Upcoming Solidity changes around sell and claim rounding are also scoped here.

How to use the whitepaper effectively​

  • Refer to the derivations when you need formal justification for pricing or bounded-loss claims.
  • Use the notation section to keep dashboards and analytics consistent with the units described in the paper.
  • When validating behaviour on-chain, compare the recorded transactions with the scenarios outlined in the worked examples.
  • Mechanism Overview converts the whitepaper into narrative form for readers who prefer prose over proofs.
  • Cost & Rounding and Safety Parameters track implementation status so you can compare live behaviour with the model.
  • On-chain data can be retrieved directly from explorers or analysis tools when applying the whitepaper’s formulas.

Whenever you quote or extend Signals’ CLMSR implementation, reference the whitepaper directly. It is the single source of truth for the math that underpins every range trade.