Note on uncertainties handling between operands with matching/non-matching and propagate_to_all keys.

[toqduj]

Some general rules on what to expect when operating with (multiple) uncertainty estimates (GPT used for formatting):

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1) When both operands only have propagate_to_all

• Output keys: only {"propagate_to_all": ...}
• Propagation: standard (uncorrelated) error propagation.

Example (mul):
R = A*B → σ_R^2 = (B σ_A)^2 + (A σ_B)^2
and store it under propagate_to_all.

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2) One side has only propagate_to_all, the other has specific keys (e.g. poisson)

• Output keys: only the specific keys (poisson, pixel_index, …).
  No propagate_to_all key in the result.
• Meaning: propagate_to_all acts as a fallback contributor into those specific keys.

So if a has only propagate_to_all and b has poisson, then result.uncertainties["poisson"] includes:

• a’s global uncertainty contribution
• plus b’s poisson contribution
  combined in quadrature (after proper unit handling).

This exactly matches your “apply propagate_to_all to it, as expected”.

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3) Both operands have matching non-propagate_to_all keys

• Output keys: the matching keys
• Propagation: by key, combining left+right contributions for that key (quadrature).

So poisson + poisson stays poisson and is combined correctly.

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4) Both operands have non-matching non-propagate_to_all keys

• Output keys: the union of keys (e.g. {"pixel_index", "poisson"})
• Propagation: each key is propagated from the operand that owns it, without inventing NaNs and without trying to merge unrelated keys.

Concretely:

• result["pixel_index"] comes only from the pixel_index source(s) (plus any global fallback if that operand only had propagate_to_all, per rule 2)
• result["poisson"] comes only from the poisson source(s)

No “matching” happens, so no cross-key quadrature sum between unrelated sources.