Fan-out

Part of the methodology series. Builds on Blind, Blind, Merge and The Spec Is a Hypothesis.

In 1890, T.C. Chamberlin warned geologists about what he called “parental affection” — the tendency to fall in love with your own hypothesis. His fix: hold multiple hypotheses simultaneously and let the evidence choose. In 1964, John Platt sharpened this into Strong Inference: devise alternatives, design a crucial experiment that kills at least one, run it, repeat with the survivors.

Both methods assume the same person generates the hypothesis and designs the test that might kill it. That takes a kind of intellectual honesty most people can’t sustain. You don’t interrogate your own children the way a stranger would.

What if the generator and the interrogator were different?

The method

Fan-out is Blind, Blind, Merge applied to research questions instead of code. The structure:

1. Fan out. Launch k hypotheses in parallel, each exploring a different approach to the same question. Each gets the same context and a distinct angle.

2. Converge. Send each result to an adversarial reviewer — a different model whose only job is to find what’s wrong. Two rounds max.

3. Prune. Kill what the reviewer proved wrong, what turned out to be known results under new names, and what failed to produce a concrete statement. Record cause of death. The failures are findings.

4. Extend. Take the survivors and go deeper. Harder examples, edge cases, generalizations. Repeat the converge/prune cycle.

5. Report. The research log is the deliverable: what survived, what died, why.

The tree narrows. Each cycle prunes branches and lowers uncertainty on the survivors. Hypotheses that look plausible in isolation but fail under adversarial review are the ones that get pruned. (For the categorically inclined: the funnel narrows a presheaf of candidates to a sheaf of validated claims. Local sections that don’t globalize get cut. This is decoration, but it hints at why the method composes with other skills in the pipeline.)

Why the role separation matters

The generator builds hypotheses. The critic tears them apart. A model evaluating its own output is a parent grading its own child’s homework.

Blind, Blind, Merge showed that two different models make complementary mistakes on code. Fan-out extends this: on research questions, one model generates candidates worth testing, the other decides which survive. The generator needs breadth and ambition. The critic needs precision and skepticism. Optimizing for both in one pass produces mush.

What Chamberlin was missing

One scientist holding multiple hypotheses is fighting confirmation bias with willpower. Separated roles between a generator and a critic is fighting it with structure.

Platt had the crucial experiment — the test designed to kill. Fan-out has the adversarial reviewer — a model that earns its keep by finding what breaks. The adversarial review runs in seconds instead of waiting for a lab result. The recursion (“recycle with survivors”) can happen in the same session.

The part neither Chamberlin nor Platt had: cause-of-death recording. When a hypothesis dies, the reason it died is a finding. “H¹ is the wrong invariant because cyclic monotonicity is a weighted inequality, not a cohomological vanishing condition” is more useful than the hypothesis that produced it. The dead-end archive is half the deliverable.

The funnel property

Fan-out is not exponential search. It’s a funnel. Each verification cycle prunes branches. k hypotheses become k·p survivors where p < 1. After n cycles: k·pⁿ, decaying toward convergence.

But the surviving branches extend further than the originals could. Verification lowers the uncertainty on survivors — you eliminated the inconsistent alternatives. Lower uncertainty means longer chains before the next checkpoint. Breadth shrinks, depth grows.

A session might start with five hypotheses and end with one finding plus four documented dead ends. That’s not failure. You traded five shallow guesses for one deep result backed by four reasons the alternatives don’t work.

The human in the loop

The human Attends between cycles. The models Filter. This distinction is load-bearing.

Without the human between fan-out cycles, the tree grows without sharpening. Subagents can check whether a computation is correct. They can’t check whether a question is interesting. “Should we explore relaxing the unanimity condition in Mishra-Nath-Roy?” is a judgment call that requires understanding the research program, not just the mathematics.

The models prune by correctness. The human prunes by relevance. Both are necessary. Neither is sufficient.

What it looks like

I tested fan-out on a question I’d already answered manually: does DSIC compose? Three hypotheses launched in parallel: domain restrictions, hedging mechanisms, sheaf cohomology. Results:

• Domain restriction: rediscovered the known answer (additive separability is the boundary). Useful bibliography, no new result.
• Hedging: the concept exists under known names (linked mechanisms, dynamic VCG). Dead on arrival as novelty.
• Sheaf reading: generated an interesting-looking cohomological framing. The adversarial reviewer killed it — H¹ is the wrong invariant for weighted inequality conditions. The kill was the most valuable output of the session.

Three hypotheses in, one documented failure worth keeping, twenty minutes. The manual version took days and reached the same conclusion without the sheaf detour. The automatic version tried a riskier hypothesis, failed faster, and documented why.

When to use it

When you have multiple plausible approaches to a question and don’t know which will land. Research questions, theorem attempts, design alternatives. Not for tasks with known solutions — that’s just search. Fan-out is for problems where the solution space is underspecified and you need to explore before you can commit.

The cost is k model calls per cycle. The benefit is breadth you couldn’t achieve alone, pruning you couldn’t trust yourself to do, and a dead-end archive that prevents re-exploring paths already shown not to work.

Chamberlin was right in 1890. Hold multiple hypotheses. Let the evidence choose. He just didn’t have the staff.

Written via the double loop. The fan-out skill: skill definition. Prior work: Blind, Blind, Merge.