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Concept · Paying for the intermediate

Contraction and bond limits

A contraction plan is an order in which tensors are multiplied. The quality of that order dominates runtime. Lumen Weave exists so Data-T can show the order, the peak, and the discarded weight instead of hiding them inside a black-box ‘simulate’ call.

What is being multiplied

Every index is either open or summed. Summing an index is the contraction. Open indices are the answer: a vacuum-to-vacuum amplitude has none; a reduced density on k wires has 2k open indices. The planner’s only freedom is the order of sums and which summed index to slice.

A bad order builds a tensor whose rank is the number of wires crossing a cut. Rank 30 is a gigabyte-class intermediate even when the final answer is one complex number. The byte forecast is that rank, not the final answer’s rank. Callers should budget against the forecast.

Slicing

Slicing fixes one summed index, repeats the smaller problem, and adds the slices. It is exact. It multiplies latency by the slice count and divides the heavy intermediate by that count, in the ideal case where the sliced index sat on the heavy cut. The planner slices the index that most reduces the peak, not the first index in the gate list.

Nested slicing is capped. Depth-two is the 1.0 maximum so a job cannot quietly turn into a swarm without the caller’s slice budget.

Bond limits are approximate

A bond limit keeps the largest singular values on a cut and drops the rest. The discarded weight is the error indicator Data-T will sign. It is not a rigorous diamond-norm bound on a later expectation. Model cards that need a guaranteed envelope must stay in exact mode or move the question to Lumen Trace with a coefficient cutoff they can defend.

Repeated truncation along a long ladder accumulates. Weave reports discarded weight per cut and the maximum. The maximum is the number a reviewer should read first.

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