Boltzmann MapReduce: A Partition-Function Reduce for Forkable Sandboxes

[Submitted on 17 Jun 2026 (v1), last revised 17 Jul 2026 (this version, v3)]

View PDF HTML (experimental)

Abstract:Snapshot-backed sandboxes make branching cheap while leaving evidence dependence unchanged. Branches can reuse a model, prompt, repository, tests, observations, or execution ancestor, so counting outputs can amplify one repeated error into high-confidence consensus. We introduce an \emph{evidence-aware reduction contract}: each worker reports an estimate, estimated information, evidence identifiers, fork lineage, and execution metadata. For independent workers estimating one common parameter, we use standard inverse-information pooling in its Gaussian/Wald form. The fixed-dimensional numeric summary can merge in any tree order; evidence IDs and lineage follow separate rules. The residual $\Delta$ measures disagreement, becomes Cochran’s $Q$ in the scalar inverse-variance case, and appears in the product integral. A reference implementation validates serialized records, rejects repeated nonempty evidence identifiers, carries evidence and lineage through tree reduction, and uses Cholesky-based numerical linear algebra. Unit tests and seeded synthetic checks exercise the algebra, unequal information, and forged precision; one four-worker named-snapshot trace exercises the end-to-end path. Platform logs document the exercised execution paths. A central open systems challenge is to turn evidence identity and fork lineage into a dependence model for correlated and adaptively selected AI branches.

Submission history

From: Yossi Eliaz [view email]
[v1] Wed, 17 Jun 2026 16:26:18 UTC (538 KB)
[v2] Tue, 14 Jul 2026 20:12:20 UTC (57 KB)
[v3] Fri, 17 Jul 2026 06:58:06 UTC (13 KB)