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book: Use M for number-of-circuit-instances in proof encoding
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@ -58,27 +58,27 @@ In the encoding description below, we will use the following circuit-specific co
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- $Q_A$ - the number of advice column queries.
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- $Q_F$ - the number of fixed column queries.
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- $Q_I$ - the number of instance column queries.
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- $N$ - the number of instances of the circuit that are being proven simultaneously.
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- $M$ - the number of instances of the circuit that are being proven simultaneously.
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As the proof encoding directly follows the transcript, we can break the encoding into
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sections matching the Halo 2 protocol:
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- PLONK commitments:
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- $A$ points (repeated $N$ times).
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- $2L$ points (repeated $N$ times).
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- $P$ points (repeated $N$ times).
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- $L$ points (repeated $N$ times).
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- $A$ points (repeated $M$ times).
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- $2L$ points (repeated $M$ times).
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- $P$ points (repeated $M$ times).
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- $L$ points (repeated $M$ times).
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- Vanishing argument:
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- $D - 1$ points.
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- $Q_I$ scalars (repeated $N$ times).
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- $Q_A$ scalars (repeated $N$ times).
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- $Q_I$ scalars (repeated $M$ times).
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- $Q_A$ scalars (repeated $M$ times).
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- $Q_F$ scalars.
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- $D - 1$ scalars.
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- PLONK evaluations:
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- $(2 + \textsf{Col}_P) \times P$ scalars (repeated $N$ times).
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- $5L$ scalars (repeated $N$ times).
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- $(2 + \textsf{Col}_P) \times P$ scalars (repeated $M$ times).
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- $5L$ scalars (repeated $M$ times).
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- Multiopening argument:
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- 1 point.
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