E25: the RMSNorm multiply order matters, and our spec sentence saying otherwise was false

01Why it matters

If text matches while the bits differ, comparing output text cannot show that two systems computed the same thing.

02Method, step by step

1. Build a census version of the decode that uses the non-conforming multiplication order.
2. Run SmolLM2-135M on 'Once upon a time' for 16 tokens.
3. Count elements that differ, and check whether the digest and the tokens moved.

03Results, exact and sourced

1. R1The spec's earlier claim that no divergence had been observed was wrong.

   That sentence is false as of 2026-09-09.

2. R234.60% of RMSNorm elements in one 16-token decode differ between the two orders (SmolLM2-135M).

   231,014 of 667,584 RMSNorm elements — 34.60% — distinguish the two orders in a single 16-token decode.

3. R3The alternate order moved the witness digest.

   CENSUS witness_digest_moved=true

4. R4In the same run, the generated tokens did not change (for this 16-token vector only).

   CENSUS argmax_digest_moved=false

05Scope and caveats

• The false sentence had already been shown false by E22 and was not updated until E25.
• The SmolLM2-135M result is one pinned vector; the census build is an instrument, not a conforming verifier. The document also reports a second model (Qwen2.5-0.5B) census, and the CHANGELOG E-1 addendum gives its counts; the entry's figures here are SmolLM2 only.
• The source states tokens_moved=false is a fact about this 16-token vector, not a guarantee: a longer decode could compound one-ULP differences into a different argmax. E25 does not test that.
• An earlier draft reported a raw counter (1,335,168) without noting a double decode; corrected in the document.
• Run by us on one host; no unaffiliated reproduction.

06Outcome

07What we learned

A reordering that leaves the generated text unchanged (on this short vector) still changes the bits, so comparing text is not enough. A published limitation was out of date, and we corrected it in the open.

08Check it yourself

• cis2-spec / E25_RMSNORM_ASSOCIATION.mdhttps://github.com/Aefinity-AI/cis2-spec/blob/main/docs/E25_RMSNORM_ASSOCIATION.md
• cis2-spec / CHANGELOG.mdhttps://github.com/Aefinity-AI/cis2-spec/blob/main/CHANGELOG.md

Read the page and the CHANGELOG erratum E-1 (links above).