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def

oneStepMobilityCost

definition
show as:
module
IndisputableMonolith.Sociology.SocialStratificationFromConfigDim
domain
Sociology
line
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papers citing
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plain-language theorem explainer

The definition sets the one-step upward mobility cost to phi minus three halves. Sociologists applying Recognition Science to stratification models cite it when assigning J-cost values to transitions between the five predicted strata. It is supplied as a direct constant definition.

Claim. The one-step upward mobility cost equals $phi - 3/2$, where this value coincides with $J(phi)$ and $J$ denotes the cost function satisfying the Recognition Composition Law.

background

The module models social stratification as five layers forced by configDim equal to 5, matching other five-fold divisions such as Köppen zones and Big Five factors. The J-cost for adjacent stratum transitions satisfies the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$, and reduces to $J(phi)$ for the base step. This definition supplies the explicit constant for that base case.

proof idea

The declaration is a direct definition of the real number phi minus three halves. No lemmas are applied; the value is introduced explicitly to match the J-cost at phi.

why it matters

It supplies the positive cost value required by the SocialStratificationCert structure, which certifies the five-stratum model with nonnegative transition costs. This completes the instantiation of the J-cost mechanism for sociology, consistent with T5 J-uniqueness and T6 phi as self-similar fixed point in the forcing chain. The module notes a falsifier in the form of surveys showing stratum counts other than 5.

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