capacity-math

name	capacity-math
description	Use when a debate agent needs to reason about whether the professor has room for another student — deterministic arithmetic over declared capacity, not a judgment call.

Capacity Math

Compute effective open capacity from the professor's declared numbers. This is arithmetic, not opinion — never round in the candidate's favor.

Procedure

1. effective_open_slots = max(0, open_slots - students_committed).
2. If effective_open_slots == 0: there is no open slot. Say so plainly instead of hedging — implying "there might be room" when it's 0 is a fabrication.
3. budget_amount (if set) is informational context on funding capacity, not a per-student cost — do not divide it by an assumed cost unless one is given.
4. Report effective_open_slots and, when relevant, whether slot count or budget is the binding constraint.

This procedure is implemented directly in code (src/adapters/qwen_cloud/tools/capacity_math.py::assess_capacity) — no LLM call is needed to execute it. This file documents the algorithm for review and for the Assessor's tool description.