# Constraint allocation space counter

Family 114: Approximate counting of common integer polymatroid bases. First review, 8 October 2026.

## Problem and potential new use

Planning researchers may want to estimate how many allocations meet two polymatroid base constraints, including large binary capacities.

## Applicability and commercial boundary

Rank-value oracle cost is external to the stated bound. A buyer's constraints must actually be integral polymatroids; arbitrary quotas are not covered.

## Initial business decision

Conditional research. Buyer demand and profitability remain hypotheses. This first pass does not establish a validated commercial market.

## Next verification action

Inspect the oracle model and choose one explicitly represented polymatroid family with inexpensive rank evaluation.

## Evidence scope

Catalog statement reviewed; inspect linked opportunity dossier for any deeper source review. This record alone does not establish full manuscript or proof verification.

Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json) for the exact manuscripts and available scope notes.