Thresholds Conceal Nonlinear Fragility
Claim
Analytical rule
Thresholds conceal nonlinear fragility behind stable averages.
This is a bounded hypothesis derived from several game mechanics. It is published before historical cases so its assumptions, scope, and failure conditions are visible before evidence is selected.
Mechanism chain
- Housing and Carrying Capacity supplies a threshold phase change step.
- Loyalty Pressure and Defection supplies a threshold phase change step.
- Golden and Dark Ages with Dedications supplies a threshold phase change step.
- Carbon Accumulation and Global Temperature supplies a accumulation depletion step.
Together the dossiers expose a sequence: conditions make a conversion possible; the conversion creates capability; capability alters later choices; and feedback changes the cost of repeating the sequence. The rule abstracts that shared structure without claiming that the game supplies historical proof.
The chain should be tested at a consistent unit and timescale. A city-level conversion cannot silently become a civilization-wide cause, and a short-run response cannot establish a long-run equilibrium. Where the mechanism crosses levels, the transmission step must be shown rather than assumed.
Scope conditions
The claim is most plausible systems with stocks, thresholds, nonlinear response, or feedback that remains weak until a boundary. It should not be exported to a case merely because the vocabulary sounds familiar. A case must show that the relevant stock, flow, threshold, network, or institutional conversion actually operated at the proposed scale.
Scope also includes actor incentives and available alternatives. If the historical actors did not control the relevant input, could not observe the threshold, or possessed substitutes that the game excludes, then the rule may describe the wrong decision problem even when the eventual outcome looks similar.
Countervailing mechanisms
early-warning indicators, gradual adaptation, and redundancy can make transitions less abrupt
Countervailing forces are part of the rule rather than exceptions hidden after the fact. Their presence may weaken the effect, reverse it, or define a different regime in which another rule is more useful.
A strong case should therefore compare the proposed mechanism with at least one rival explanation. The rule earns confidence when it explains intermediate changes and difficult observations better than those rivals, not when it can be attached retrospectively to any outcome.
Failure and falsification
The rule would be weakened or rejected by response remaining proportional and reversible across claimed thresholds. Evidence that only restates the outcome cannot test the mechanism; the intermediate links and plausible alternatives must be observable.
Evidence needed
Useful historical inquiry would require high-frequency observations around boundary crossings, including leading indicators and recovery paths. Sources must be independent scholarship or primary evidence appropriate to the case. Civilopedia historical-context prose is excluded from this role.
Comparison should include negative and deviant cases, not only celebrated examples that make the rule look intuitive. Where measurement is impossible, the case should state uncertainty rather than translate game numbers into invented historical precision.
Mechanics
- Housing and Carrying Capacity
- Loyalty Pressure and Defection
- Golden and Dark Ages with Dedications
- Carbon Accumulation and Global Temperature
Future cases and frameworks
No historical case or formal framework is required for v0.1. Future cases may support, qualify, counter, or revise this rule; frameworks may define a unit of analysis and combine it with other rules. Revisions should preserve the original mechanism mapping and record why the claim changed.