Module witness 

Witness construction for the logUp* prover.

These helpers build the multilinears that the two fractional-addition circuits run over:

• the looker numerator eq_r, the equality indicator at the evaluation point,
• the looker denominator c - I, with I the embedded index column,
• the negated table denominator J - c, with J the embedded table positions,
• the pushforward Y = I_* eq_r, the looker numerator scattered onto table positions.

Functions

combined_lookers

Build each table’s gamma-scaled looker numerators and its combined pushforward Y.

embed_position

Embed a table position j into the field through the GF(2)-linear basis.

looker_denominator

Build the looker denominator c - I over the n-variable looker cube.

pushforward

Build the pushforward Y = I_* eq_r over the m-variable table cube.

table_denominator

Build the negated table denominator J - c over the m-variable table cube.