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consensus-math-correctness

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L1 trigger - audits consensus arithmetic for truncation, unused bounds, EMA direction, and threshold edge errors.

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Injectable Skill: Consensus Math Correctness

L1 trigger: CONSENSUS flag AND (adjust_difficulty OR difficulty_adjust OR ema OR moving_average OR reward_curve OR target_time detected) Inject Into: depth-consensus-invariant or depth-edge-case Language: Go and Rust Finding prefix: [CM-N]

Consensus math bugs are small, deterministic, and load-bearing. They rarely need fancy exploit chains: one wrong operator, one dead bound, or one flipped EMA direction can permanently skew the chain.

1. Division-before-multiplication

For every expression of the form (A / B) * C, test whether A < B is possible. If so, the intermediate division truncates to zero before the multiplication and the protocol silently loses precision.

Questions:

  1. Can A < B happen at runtime?
  2. Is the intended formula mathematically (A * C) / B?
  3. If multiplication moves first, is there an overflow guard on the wider intermediate?

Tag: [CONSENSUS-MATH:DIV-FIRST]

2. Declared-but-unapplied bounds

Consensus configs often declare bounds that never influence runtime math.

Questions:

  1. Which config fields look like bounds or caps? Example names: max_difficulty_adjustment_factor, min_reward, max_step_count.
  2. Is each field used only during config parsing, or also in the live computation?
  3. If a field is declared but never applied at runtime, what unbounded state transition does that permit?

Tag: [CONSENSUS-MATH:UNUSED-BOUND]

3. EMA / moving-average direction

For each moving-average implementation, identify the prior sample, current sample, and smoothing factor.

Questions:

  1. Does the code use the same sample ordering as the design doc or comments?
  2. Is the "previous" state actually previous, or has the implementation swapped current and prior inputs?
  3. If the direction is flipped, does the chain overreact instead of smoothing?

Tag: [CONSENSUS-MATH:EMA-DIRECTION]

4. Threshold operators

Consensus edge cases often live at threshold-1, threshold, and threshold+1.

Questions:

  1. For every > / >= / < / <= gate in consensus math, what does the protocol text say should happen exactly at the threshold?
  2. Does the implementation match that boundary?
  3. What happens at threshold-1, threshold, and threshold+1?

Tag: [CONSENSUS-MATH:BOUNDARY-OP]

5. Ratio / fixed-point edge vectors

Difficulty and reward math often expresses "increase/decrease by X%" using integer ratios or fixed-point factors. Enumerate the exact vectors:

InputExpectedObserved
no changefactor = 1.0
minimum decreasefactor just below 1.0
maximum decreasee.g. 50% decrease
maximum increaseconfigured cap
denominator near zeroreject / clamp

Mandatory checks:

  1. If a config field is named max_*_adjustment_factor, prove it clamps both upward and downward movement at runtime.
  2. Test the exact human-readable boundary from docs/comments, not only random samples. If docs say "up to 50% decrease," test exactly 50%.
  3. Check whether integer truncation prevents the boundary from ever being reached.
  4. Check > vs >= at every clamp boundary.

Tag: [CONSENSUS-MATH:RATIO-EDGE]

6. Consensus floating point / platform dependence

If consensus math uses f32, f64, log, log10, pow, platform C math, SIMD, CUDA, or FFI:

  1. Determine whether the result affects any value that other nodes must agree on.
  2. Check cross-platform determinism: Linux vs Windows, CPU vs GPU, feature flags, and architecture word size.
  3. If a floating-point result is cast back into integer consensus state, emit a finding unless the implementation proves deterministic rounding.

Tag: [CONSENSUS-MATH:NONDET-FP]

Output guidance

  • Preferred evidence tags: [CONFORMANCE-PASS] > [NON-DET-PASS] > [LSP-TRACE] > [CODE-TRACE]
  • Severity baseline: Medium, upgrade when the math directly affects consensus safety, liveness, or issuance economics

Known class references

  1. Consensus clients and SDKs have repeatedly removed floating-point or precision-sensitive arithmetic from state-machine code after divergence incidents.
  2. Difficulty-adjustment and reward-curve bugs are historically dominated by truncation, unused bounds, and edge-threshold mistakes rather than complex exploit logic.