Conflicting Supervision Moves Commitment, Not Capability: A 12.29{\sigma} arrangement effect that is exactly zero under a convention-agnostic score

arXiv cs.AIOctober 2, 2026en

arXiv:2610.00234v1 Announce Type: new Abstract: "Train a model on the same problems written under two incompatible conventions, both correct, and ask what the ordering of that data writes into the parameters. The learning-rate schedule is not a background condition for that question. It is the averaging operator, and it decides the answer. We prove a bound in which the arrangement and the schedule enter the ordering effect as separate multiplied factors: the arrangement only as a block period, the schedule only as how much weight the endpoint can place on any one moment of the run. A decaying schedule cannot put a large step size and an uncontracted remainder at the same moment; a constant o

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