01 · Partition
Plan distinct evidence
Give each worker a non-overlapping shard that measures the same target.
Evidence-Aware MapReduce for Forkable Compute
Separate execution fan-out from independent evidence.
Fork workers freely. Each answer carries an estimate, its uncertainty, and where its evidence came from. Independent results then combine in proportion to the information they contain.
Estimate
Uncertainty
Provenance
Reduction lab
Interactive model
Worker Aθ̂
4.88
info
Worker Bθ̂
5.03
info
Worker Cθ̂
4.96
info
ΣP · q · c
Combined result
with uncertainty
4.98 ± 0.10
4.3estimate θ5.7
Disagreement energyLOW · 0.19
When workers agree, the combined estimate becomes more precise and moves very little. These illustrative curves assume independent, non-overlapping evidence.
The mathematics is established inverse-information pooling. This artifact turns it into an auditable worker contract and keeps declared evidence visible at the merge.
✓Unit tests
3Sanity paths
1Locked E2E
The idea at a glance
Keep the evidence with the answer.
A useful worker result says what the worker estimated, how uncertain that estimate is, and which evidence produced it. Declared identifiers expose repeated labels before they are counted twice.
02 · Emit
Return a complete result
Each worker returns its estimate, uncertainty, sample size, lineage, and evidence IDs.
03 · Reduce
Add compact summaries
Compatible Gaussian results merge by adding the small summaries P, q, and c.
04 · Audit
Report the result and conflict
Return the combined estimate, covariance, and exact disagreement energy.
Worker result contract
theta_hat
info_per_obs
n
lineage[]
evidence_ids[]
metadata{}
Live fusion explorer
Try the cases that matter.
Drag the worker estimates, change their uncertainty, remove a worker, stream new samples, or reuse an evidence ID. The reducer updates immediately and stops a merge when it sees a repeated ID.
Worker estimates · θ
ID check passed · declared IDs are distinct
Drag a colored handle horizontally · wider curves carry less information
Worker A
Worker B
Worker C
Worker D
Combined result
Combined θ̂4.99
95% interval[4.88, 5.10]
Disagreement Δ/20.42
Total precision P333.1
P = Σσₖ⁻² · q = ΣPₖθ̂ₖ · combined θ̂ = P⁻¹q
Why this matters
Every answer stays accountable to its evidence.
The reducer carries evidence strength, declared identity, lineage, and disagreement all the way from each worker to the combined result.
01
Evidence earns weight
Total precision Pₖ = nₖJₖ determines each estimate's contribution to the combined result.
02
Merging scales as a tree
The compact numeric state can merge in any tree shape. Evidence IDs are sorted, while lineage keeps first-seen order.
03
Conflict stays visible
A disagreement term records how far the workers lie from their combined estimate. Confident workers that point in different directions leave a clear signal.
Where the model applies
The experiment must establish independent evidence.
Combine worker summaries when they estimate the same target from independent, non-overlapping evidence. The number of workers alone says nothing about independence.
A good fit
Worker summaries have a defensible uncertainty model and genuinely distinct evidence.
- One shared parameter and compatible units
- Disjoint evidence or explicitly modeled dependence
- A sound Gaussian approximation, exact or asymptotic
Choose a broader model when
Workers share errors, may act adversarially, or estimate different local truths.
- Model-generated confidence needs calibration
- Adversarial workers need robust aggregation
- Shared snapshots need a dependence argument
Core requirementShared prompts, models, repositories, tests, or fork ancestors can produce the same error in many workers. Declared IDs expose repeated labels; a covariance model must cover subtler shared sources.
Auditable artifact
Read it, rerun it, and challenge it.
The tests cover the Gaussian calculation, its closed-form integral, tree-shaped merges, serialized records, repeated evidence IDs, and three deterministic statistical examples. Platform logs document the execution paths exercised so far. A controlled cross-provider benchmark remains future work.
MeanInformation-pooled 4.9542 versus centralized 4.9546 on twelve synthetic shards.
0.033Coefficient gap to centralized OLS in the committed linear-regression sanity check.
8 seedsUnequal-size IID logistic check, with limitations stated alongside the result.
4 shardsNamed-snapshot islo execution path exercised end to end.
Citation
Cite the published arXiv record.
Yossi Eliaz. “Boltzmann MapReduce: A Partition-Function Reduce for Forkable Sandboxes.” arXiv:2607.09689 [cs.AI], 2026. doi:10.48550/arXiv.2607.09689.
Version note: This citation follows arXiv v2, revised 14 July 2026. The repository PDF is the candidate next revision, titled “Evidence-Aware MapReduce for Forkable Compute: Separating Execution Fan-Out from Independent Evidence.” ArXiv will continue to show the v2 title and abstract until that revision is uploaded.
@misc{eliaz2026boltzmann,
title = {Boltzmann MapReduce: A Partition-Function
Reduce for Forkable Sandboxes},
author = {Yossi Eliaz},
year = {2026},
eprint = {2607.09689},
archivePrefix = {arXiv},
primaryClass = {cs.AI},
doi = {10.48550/arXiv.2607.09689},
url = {https://arxiv.org/abs/2607.09689}
}Reproduce locally
One command checks the artifact from tests to paper.
The locked workflow checks the Python package, local demos, generated figures, paper build, release PDFs, and website contract.
$ git clone https://github.com/zozo123/boltzmann-mapreduce $ cd boltzmann-mapreduce $ uv sync --locked $ uv run --locked python scripts/verify_e2e.py ✓ Python · package · demos · paper · website