[AdaWorldAPI]

One scratch document, for later examination: .claude/plans/nan-exclusion-mindmap-scratch.md. No code; nothing in it is built, measured or decided.

It is a follow-up to #378. A masked statistic (n, mean, variance) can meet a NaN, and the failure to avoid is dilution: the sums and the sample count stop describing the same rows, with no signal that it happened.

The document contains:

• Mindmap (Mermaid): purposes, NaN policies, carriers, the determinism requirements, and the players involved.
• Purposes:
  • P1 missing value: skip it;
  • P2 computation error: surface it;
  • P3 replay: same bits on every realization;
  • P4 audit: report what was excluded;
  • P5 cost: stay a mask fold.
• Payoff table, NaN policy by purpose:
  • Skip and Propagate are each best for one NaN meaning, and both are honest.
  • The two "keep n" policies (replace with 0, or drop from the sum but keep n) are never best on any purpose. They are only cheaper to write.
• Game-theory reading: the dilution policy is the locally cheapest strategy, and its cost lands silently on whoever reads the variance later. Four design moves change those payoffs:
  • a policy-free kernel;
  • making the honest options the cheapest to write;
  • reporting n_excluded;
  • deriving n from the same mask that selects the sums, so dilution cannot be expressed through the API.
• Carrier comparison: raw power sums, against mergeable (n, mean, M2), against compensated sums.
• Determinism ladder: single-rounding mul_add is done (simd: mul_add rounds once on every backend (wasm emulation, exact scalar FMA, no libm) #374/simd(wasm): certify the F64x8::mul_add domain, keep exact-product lanes in the vector #378); a fixed summation order and a fixed merge tree are still open.
• Candidate steps S1–S4, and open questions for the operator.

---

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