From craftwork-reasoning
Applies limit thinking to trace system behavior as variables approach extremes (zero, infinity, 100%) for scaling, rollout, and growth decisions.
How this skill is triggered — by the user, by Claude, or both
Slash command
/craftwork-reasoning:limit-thinkingThe summary Claude sees in its skill listing — used to decide when to auto-load this skill
Don't ask "what is the value at this point?" — ask "what does this converge to as we push the variable toward its extreme?" Most planning failures evaluate a snapshot instead of a trajectory. The mathematical concept of a limit — what a function *approaches* rather than where it *is* — exposes asymptotes, phase transitions, and convergence traps hiding inside seemingly linear plans.
Don't ask "what is the value at this point?" — ask "what does this converge to as we push the variable toward its extreme?" Most planning failures evaluate a snapshot instead of a trajectory. The mathematical concept of a limit — what a function approaches rather than where it is — exposes asymptotes, phase transitions, and convergence traps hiding inside seemingly linear plans.
For the system or decision being evaluated, identify the key variables that could be pushed toward an extreme.
LIMIT ANALYSIS SETUP
System: [what's being evaluated]
Variables to push:
- Variable 1: [what is it?] → Push toward: [0 / ∞ / 100% / boundary]
- Variable 2: [what is it?] → Push toward: [0 / ∞ / 100% / boundary]
- Variable 3: [what is it?] → Push toward: [0 / ∞ / 100% / boundary]
For each: What does intuition say happens? (Naive expectation to test.)
Good variables to push:
Vague prompts ("scale AI across the org") generate 5+ candidates. Tracing all is exhaustive but overwhelming. Identify candidates, then select 2-3 using:
List all candidates, mark the 2-3 you'll trace, briefly note why others were deprioritized.
Don't jump to the extreme — approach incrementally and watch what happens.
CONVERGENCE TRACE: [Variable] → [Extreme]
Current state: [where things are now]
↓ Push slightly...
Incremental: [what improves or changes — usually positive]
↓ Push further...
Midpoint: [secondary effects — first sign of non-linearity]
↓ Push toward extreme...
Near-limit: [what breaks, saturates, or reverses — the real finding]
↓ At the limit...
Convergence: [variable] → [extreme] means [outcome] → [what it converges to]
Does outcome converge to what intuition predicted? YES / NO
If NO — what's the actual limit, why is it counterintuitive?
Patterns to watch for:
| Pattern | What it looks like | Example |
|---|---|---|
| Asymptotic ceiling | Returns diminish and flatten. Approach a max but never reach it. | More engineers: productivity asymptotes, then declines (Brooks's Law) |
| Phase transition | System changes state entirely at a threshold. No incremental change prepares for the discontinuity. | Water at 100°C: more heat → steam, not "hotter water". Org maturity at L4: tools don't help, structural change needed |
| Reversal / collapse | Variable's effect flips sign. What helped starts hurting. | Context in an agent: more helps until it doesn't, then success drops (ETH Zurich finding). Review automation: reduces burden until reviewers disengage |
| Convergence to zero | A human quality (attention, responsibility, skill) atrophies as the system takes over. | Pilots and autopilot: more autopilot → less manual skill. Limit of pilot skill as automation → 100% is dangerously low |
| Divergence | No stable limit. System oscillates or explodes. | Feedback loops without damping: over-correction → under-correction → chaos |
The value of limit thinking is the delta between naive expectation and actual convergence. State it explicitly:
LIMIT INSIGHT
Naive expectation: "If we push [variable] toward [extreme], [outcome] will [improve]."
Actual convergence: As [variable] → [extreme], [outcome] → [surprising result].
The delta: [Why actual differs from expectation. What force, feedback loop, or
phase transition causes the divergence?]
Implication for the decision: [What should change about plan/strategy/design
given the trajectory leads somewhere unexpected?]
If the convergence trace shows diminishing returns, reversal, or collapse past a point, that inflection is the practical operating target.
OPERATING POINT ANALYSIS
Variable: [what we're tuning]
Benefit curve: [how benefit changes as variable increases]
Inflection point: [where marginal benefit starts declining significantly]
Recommended range: [where to operate — range, not precise number]
Signal to watch: [early indicator you've pushed past optimal]
Each variable being pushed and toward what extreme.
For each variable, the incremental trace from current state to limit:
For each trace where actual ≠ expected:
Where to operate if the limit reveals diminishing returns or reversal:
What changes about plan/strategy/design given these convergence findings.
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Fetches up-to-date documentation from Context7 for libraries and frameworks like React, Next.js, Prisma. Use for setup questions, API references, and code examples.
npx claudepluginhub andurilcode/craftwork --plugin craftwork-reasoning