Asymptotic Claim Review¶
Protocol — instantiates Dominant-Term Regime Modeling
A review protocol for claims that invoke long-run, at-scale, or limiting behavior.
Asymptotic Claim Review is a qualitative governance protocol — a fixed set of questions applied to any verbal claim that leans on "at scale," "in the long run," or "in the limit." It computes nothing. Instead it forces a piece of rhetoric to expose its structure: which variable is supposed to be growing, when the invoked regime actually begins and whether that is inside the decision's horizon, what is being quietly treated as negligible residue, and what decision the claim is being used to license. A claim that cannot answer those questions is not necessarily false — but it is not yet reviewable, and the protocol sends it back until it is. This is the mechanism for settings where formal notation is unavailable or beside the point, and where the danger is not a wrong calculation but an uncalculated assertion dressed up as inevitability. Its home is language, not mathematics.
Example¶
A legislative committee is handed a proposal claiming a new program "pays for itself at scale." The reviewer runs the protocol rather than the arithmetic. Which variable is scaling — enrollment, or years elapsed? The claim never says. When does "at scale" begin, and is it inside the funded horizon? Pressed, the sponsors' own projection puts the break-even past year twelve — beyond the program's funded lifespan. What is being treated as negligible? Near-term costs concentrated on a small affected group, which the aggregate metric buries. What decision does the claim license? Full appropriation now. None of the answers required a single equation, yet together they show the claim's regime boundary sits past the point where the money runs out and its "negligible" residue carries real distributional weight. The proposal is returned — not because the math is wrong, but because its scale variable, boundary, and residuals were hidden.
How it works¶
- Apply a fixed question set to the prose claim, one question per hidden assumption.
- Force the scale variable to be named, the regime boundary to be stated and located relative to the decision horizon, the discarded terms to be listed with any protected status flagged, and the licensed decision to be made explicit and tested.
- Withhold approval until each question has a substantive, evidence-cited answer; convert rhetoric into reviewable structure.
Tuning parameters¶
- Strictness — advisory annotation versus a blocking gate; a hard gate catches more but slows every claim through it.
- Trigger scope — which claims must undergo review; a broad trigger catches more asymptotic rhetoric but taxes routine work.
- Evidence bar — how much backing the regime-boundary answer must cite; raising it forces real analysis but can stall genuine long-run cases.
- Sign-off — who must accept the answers; independent review guards against self-serving replies.
When it helps, and when it misleads¶
Its strength is catching the failures the quantitative tools never see, because those tools are never invoked: unbounded long-run promises and ethical elision, where a real harm to a small group is dismissed as lower-order in an aggregate. Keynes's line that "in the long run we are all dead"[n1] is the classic warning this protocol operationalizes — against decisions that lean on a limit reached too late to matter.
Its failure mode is box-ticking: the questions get plausible-sounding answers with no substance behind them, and the review launders a weak claim into an approved one. The guarding discipline is the evidence bar — the answers must cite an actual ratio test, benchmark, crossover calculation, or finite-size check, not mere assertion, so the protocol demands evidence rather than merely eliciting confident prose.
How it implements the components¶
scale_variable_definition— it forces the claim to name the variable it assumes is moving toward a limit.limiting_regime_boundary— it forces an explicit, located regime boundary and checks it against the decision horizon.residual_risk_register— it forces disclosure of what is being discarded, flagging any residue that carries rights, safety, or fairness weight.decision_translation_rule— it forces the decision the claim licenses into the open, where it can be tested against the answers.
It does not compute any order, ratio, or crossover — those quantitative fills come from Ratio Limit Test and Crossover-Point Calculation; its nearest kin is Finite-Size Correction Check, which puts a number on the residue this protocol only forces you to name.
Related¶
- Instantiates: Dominant-Term Regime Modeling — the governance layer that keeps at-scale rhetoric honest.
- Consumes: Ratio Limit Test, Crossover-Point Calculation, and Finite-Size Correction Check — supply the quantitative evidence its answers are required to cite.
- Sibling mechanisms: Big-O / Landau Notation · Ratio Limit Test · Log-Log Scaling Plot · Dominant Balance Table · Scale-Sweep Benchmark · Crossover-Point Calculation · Finite-Size Correction Check
Editorial Notes¶
Form Classification¶
Form family: Assessment, Review & Assurance
Rationale: A review protocol for claims that invoke long-run, at-scale, or limiting behavior, making its operative form a bounded evaluation of existing evidence or work that produces a finding or disposition.
Independent corroboration: The frozen evidence defines Asymptotic Claim Review as 'A review protocol for claims that invoke long-run, at-scale, or limiting behavior', so its operative form is Assessment, Review & Assurance.
Review outcome: Independent reviewer agreement; high confidence.
Origin Attribution¶
Primary origin: Mathematics
Origin pattern: Cross-disciplinary synthesis
Present-day reach: Multi-domain
Rationale: Asymptotic analysis supplies the formal meaning of long-run, at-scale, and limiting-regime claims.
Related originating lineages:
- Computer Science & Software Engineering — Algorithm analysis institutionalized review of asymptotic at-scale claims in computational practice.
- Rhetoric — Argument review contributes scrutiny of how limit language licenses practical conclusions.
Review resolution: Mathematics is the agreed primary lineage for asymptotic claims. Computer-science complexity analysis and rhetorical qualification both materially shape the review, whose evidence-and-language protocol is an Encyclopedia synthesis rather than ordinary theorem checking alone.
Encyclopedia synthesis: The exact catalogued form synthesizes established practice rather than reproducing a single standard historical label.
Review outcome: Reconciled after independent review; high confidence.
Notes¶
[n1] John Maynard Keynes's remark that "in the long run we are all dead" was a rebuke to reasoning that defers to a distant equilibrium while ignoring what happens in the interim — the paradigmatic caution against a claim whose invoked limiting regime arrives too late to be decision-relevant. ↩