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Building one bipartite child network for each group and mode tuple

Fix a feasible tuple beta and group g. Put all current vertices labeled g, from BOTH sides of the current network, on one side of the child. On the other side, add one vertex for each packet. Connect each retained real port to its packet vertex, preserving the old tensor port order. The new packet tensor receives exactly the row bits Y and column bits X belonging to group g. Padding adds no ports. Retained tensor entries use their fixed creation-time representatives, reduced to the child precision p_t. This reorganizes the summation variables; it does not identify all bits in one group.

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Updated 2026-11-08

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Math