ADR 0006: Detailed balance per sample

• Status: Accepted (2026-11-10)
• Date: 2026-11-10
• Deciders: Vincent Mader
• Related: Dullemond notes section 1.3.4; ADR 0005

Context

Mass conservation to round-off is the property that keeps long integrations stable. A sampled RHS must not trade conservation for speed. Dullemond’s notes require that each sampled pair contributes to all k it affects.

Decision

A drawn pair always contributes its complete recipe (all k entries, loss and gain) with one common weight. Sampling over k inside a fragmentation recipe (to reduce cost for long recipes) is allowed only if the sampled sub-recipe is itself mass conserving (e.g. a sampled fragment set renormalized to the pair’s mass). Every sampled step is checked for mass conservation like a full step.

Alternatives considered

• Independent samples per k (one option in the notes): breaks conservation per step; kept only as a comparison variant in E8, never as default.
• Post-hoc rescaling to restore mass (as fix_negative_densities did): hides errors (finding F7).

Consequences

• Mass conservation is independent of estimator quality, so errors in experiments are purely estimator bias and variance.
• Recipe length L enters the cost per draw; the cost-aware proposal accounts for it.