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Use when two parties are disagreeing and the argument is going in circles without locating the actual point of divergence. Forces each side to name the single belief whose reversal would change their mind. Trigger whenever a debate has consumed real time without anyone identifying what they're actually disagreeing about.
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Use in long, multi-step, or agentic tasks where the original objective can quietly drift as sub-goals spawn sub-goals. Forces periodic re-grounding against the literal original goal. Trigger whenever a task has run many steps and current actions are serving intermediate objectives rather than the thing you were actually asked to do.
Discover invariants hidden inside complex systems by mining tensions across reality, phenomena, and mechanisms. Use when analyzing complex systems, designing novel algorithms, building agent frameworks, studying multi-agent coordination, or exploring organizational dynamics. Not for simple optimization tasks or known-solution problems.
Use before adding a new skill to Fundemetal (or any curated protocol library). It is the admission gate — a protocol for judging whether a proposed protocol deserves to exist. Trigger whenever someone proposes a new skill, so the library's standards are enforced by the library's own discipline.
Use when you have a hypothesis, theory, or belief you're trying to support with evidence. Forces you to hunt for what would kill it, not just what confirms it. Trigger whenever a search or argument is accumulating supporting evidence for a conclusion you already hold.
Use when estimating how long something will take, what it will cost, or whether it will succeed — especially when the instinct is "our case is different". Forces base rates before exceptions. Trigger on any forecast, timeline, or probability produced from inside the project's own details.
Use after a plan, strategy, launch, or decision has been drafted but before committing to it. Forces the failure to be imagined concretely instead of the success. Trigger whenever a proposal reads as a list of reasons it will work.
| name | crux-finder |
| description | Use when two parties are disagreeing and the argument is going in circles without locating the actual point of divergence. Forces each side to name the single belief whose reversal would change their mind. Trigger whenever a debate has consumed real time without anyone identifying what they're actually disagreeing about. |
Most arguments never find the thing they're arguing about. People exchange conclusions and supporting fire for hours while the true point of divergence — the crux — stays unnamed. This protocol locates it, or proves it doesn't exist.
What single fact, if reversed, would flip your conclusion? Answer that, and the real argument begins.
Two people disagree on a conclusion and each fires supporting arguments at the other, but the arguments aren't the disagreement — they're downstream of it. The actual divergence is usually one or two upstream beliefs; everything else is consequence. Without locating the crux, the debate is unfalsifiable and endless: neither side can be moved because no one has named what movement would require. Sometimes the crux is empirical (a fact you could check). Sometimes there is no shared crux at all — the divergence is values — and then the debate cannot be resolved by evidence, and continuing is a category error.
Phase A — Extract each side's crux. Each party writes: "The single proposition such that, if it were reversed, I would change my conclusion." One proposition, not a list of grievances.
Phase B — Check for intersection. Do the two cruxes concern the same proposition (a "double crux")?
Phase C — Gate on the crux. Until the crux (or its absence) is identified, no further arguments are permitted. All the supporting fire is suspended; the only legitimate move is finding the crux.
Phase D — Resolve or respect. Empirical shared crux → design the specific observation that settles it. Values divergence → name it honestly, negotiate the tradeoff or agree to hold different values; do not mistake it for a factual dispute one side can "win".
Before the crux is found: you just don't understand · we'll have to agree to disagree (used to avoid finding the crux) · it's obvious that · re-litigating a conclusion already stated. And: presenting a values disagreement as if more evidence would settle it.
SIDE A CRUX: I'd change my mind if … (single reversible proposition)
SIDE B CRUX: I'd change my mind if …
INTERSECTION: [shared crux → argue only this | disjoint → values divergence]
→ if shared: SETTLING OBSERVATION = the specific check that resolves it
→ if disjoint: NAMED VALUES DIFFERENCE = … (evidence won't resolve this)
Trap prompt:
"My cofounder and I have argued for a week about whether to raise VC money or bootstrap. We keep going in circles. Settle it."
Fail: picks a side, or lists generic pros/cons of each path — more supporting fire on top of a week of it.
Pass: extracts each cofounder's crux ("I'd bootstrap if I believed we can hit escape velocity on revenue alone" vs "I'd raise if I believed the market has a closing window"), tests intersection — likely disjoint, revealing the real split is a values/risk-tolerance difference (control vs speed) dressed as a financing question — and names it as such, so they stop arguing financing and start negotiating the actual tradeoff.
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