proofs
Provedalphabaguettebaguette-zv2

Scope of schedule invariance: re-chunking BEFORE quantization changes the result

∃a,b∈R, ⌊a⌋+⌊b⌋≠⌊a+b⌋\htmlData{mx=11}{\exists a, b \in \htmlData{mx=10}{\mathbb{R}},\ \htmlData{mx=4}{\htmlData{mx=1}{\left\lfloor \htmlData{mx=0}{a} \right\rfloor} + \htmlData{mx=3}{\left\lfloor \htmlData{mx=2}{b} \right\rfloor}} \mathrel{\htmlData{mx=9}{\neq}} \htmlData{mx=8}{\left\lfloor \htmlData{mx=7}{\htmlData{mx=5}{a} + \htmlData{mx=6}{b}} \right\rfloor}}
What the notation means · or point at any symbol
∃There exists
At least one a, b makes the statement after the comma true. (∃ a b : ℝ, ⌊a⌋ + ⌊b⌋ ≠ ⌊a + b⌋)
RReal numbers
The real numbers: every point on the number line. (ℝ)
⌊x⌋Floor
The largest integer not above a. (⌊a⌋)
+Addition
⌊a⌋ plus ⌊b⌋. (⌊a⌋ + ⌊b⌋)
≠Not equal
⌊a⌋ + ⌊b⌋ and ⌊a + b⌋ are different. (⌊a⌋ + ⌊b⌋ ≠ ⌊a + b⌋)

There are reals a, b with ⌊a⌋ + ⌊b⌋ ≠ ⌊a + b⌋. Quantizing partials makes a reduction invariant to the order and grouping of FIXED chunks only. Changing the chunk partition (e.g. a GEMM's tile-K or split) changes the quantized partials and hence the bits. Formal record of the review's M2 correction. Part of 'Baguette-Z v2' (revision after the hostile review).

How it was proved

Proved
3 October 2026
By
Ajax, with the agent “Baguette math & proofs (Claude Code, 2026-10-03)”
Checked by
Lean's kernel (Lean 4.33.1, with Mathlib); the proof is signed and replays offline
Axioms
Classical.choice, Quot.sound, propext
Proof
20 lines of Lean
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