Theoretical limit

<!-- DO NOT EDIT — generated from shared/skills/theoretical-limit/SKILL.md by sync-content.py -->

Focused Theoretical-Limit Mode

You are running in focused-theoretical-limit mode. Execute only the procedure below and produce only its canonical output sections — do not run the full 5-phase first-principles analysis. Skip Step 0 technique selection; the user has already chosen this technique by invoking the slash command directly.

When to reach for this

Use theoretical-limit when a decision hinges on whether a current figure is close to what the laws permit or whether there is substantial headroom the convention has not captured. The question you are really asking is: "If every convention were removed, what do the laws actually permit here — and how far below that ceiling are we operating?"

Good fit: a conventional figure exists (industry practice, historical precedent, accepted engineering default) and you suspect it may embed a convention — a rule of thumb, a legacy design choice, a practical constraint — rather than a hard physical limit; you want to know the upper bound on what is achievable; a claim about performance or cost rests on an assumption that current practice is near-optimal.

Not a good fit: the question is "what would cause this claim to fail?" — that is inversion, which enumerates necessary preconditions for failure rather than deriving what the laws permit. It is also not the right tool when the primary need is to rebuild a magnitude from constituent unit-factors — that is estimate (Fermi / dimensional analysis), which reconstructs HOW BIG a quantity is from its units, not what ceiling the fundamentals impose on it.

Decision rule — separating the upper-bound move from its neighbours:

• Theoretical-limit = what the laws permit once conventions are stripped: what is the ceiling the fundamentals allow? Names the governing law, derives the bound it imposes, brackets the gap between that bound and the conventional figure.
• Inversion = adversarial attack on a claim/plan: what would guarantee failure? Enumerates necessary preconditions for collapse — the closest neighbour and the real collision risk; theoretical-limit asks what is possible, inversion asks what is fatal.
• Estimate = quantitative magnitude rebuild from units: how big is this quantity? Reconstructs a target number from constituent unit-factors (dimensional analysis).

A single analysis often uses all three: apply theoretical-limit to find the law-permitted ceiling, estimate to rebuild the conventional figure from unit-factors, and inversion to surface which assumptions would need to break for the ceiling to be unreachable.

---

Procedure

Name the conventional figure and its embedded conventions (a performance metric, efficiency, or cost ceiling) before stripping anything.

Strip each convention back to a governing physical law, definition, or direct measurement. Name the law explicitly (e.g., "the Second Law of Thermodynamics," "Carnot efficiency bound"). Do not reason by analogy to what others currently achieve — the ceiling is set by the laws, not by the best incumbent.

Derive the limit the fundamentals permit, using the governing law and first-principles values (constants, definitions, direct measurements). This is the law-permitted ceiling: the highest the figure can go if every convention is removed and only physics remains as a constraint.

Bracket the gap between the law-permitted ceiling and the conventional figure. State explicitly:

• Law-permitted ceiling: the value the governing law allows.
• Conventional figure: the figure in current practice.
• Gap: the headroom between current practice and what the laws permit.

Identify how much of the gap is irreducible (the laws impose it — a process converting X → Y can never be 100% efficient under the Second Law) versus how much is convention (headroom the laws allow but practice has not reached).

Apply the stop criterion. The analysis is complete when: (1) the governing law is named explicitly, (2) the limit is derived from first-principles values — not from what competitors achieve — and (3) the gap to the conventional figure is stated explicitly. A theoretical-limit analysis that names a ceiling without bracketing that gap is incomplete — the bracket, not the ceiling alone, is the deliverable.

Read theoretical-limit-detail.md when you need:

• a worked example of this technique
• the failure modes and how to avoid them
• handoff guidance to another technique

---

If a fuller analysis is needed afterward, invoke the main first-principles agent with this output as Known ground truths.