chrisdavidson Focused Theoretical-Limit Mode
You are running in focused-theoretical-limit mode. Execute the procedure below, produce its canonical output sections, then run the focused-mode validation step below — 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
Focused-mode validation
Check the output against its own completion condition before presenting it. The procedure above states one, in whichever form this technique uses — an exit criterion, a stop test, or an output contract. Read that condition again and confirm the output actually produced meets every requirement it names, not just the ones that were easiest to satisfy.
This is a scope-proportionate check, not the six-criterion Self-Audit Gate. That gate scores a six-section analysis document; this run produced one technique's output sections, not six, so walking all six criteria against it would score structure that was never produced. The larger of the two components: a focused run does not acquire evidence — it opens no cited source — so a claim resting on a source this run did not open stays marked rather than being resolved as confirmed.
Carry the mark forward. Anything this run could not verify is carried into the output
marked with a ? rather than dropped or silently asserted as fact.
Revise once, then stop. If the check fails, revise the output and check it again. Revise at most one time. If it still fails after that pass, present the output with the gap named rather than revising again.
End every run with a validation line, without exception. State exactly one of the following, verbatim, never silently:
Focused-mode validation: satisfiedFocused-mode validation: revised once, now satisfiedFocused-mode validation: not satisfied - <reason>
Close with the reason this line is unconditional: a silent run is indistinguishable from a run that skipped the check.
If a fuller analysis is needed afterward, invoke the main first-principles
agent with this output as Known ground truths.