Logitus

Logitus is a fictional term used in speculative fiction and hobbyist wikis to describe a generalized logarithmic index for measuring growth, complexity, and information flow in abstract networks. The word is formed by the Latin log- meaning "ratio or proportion" and the suffix -itus, often used in fictional coinages.

In the proposed concept, Logitus L of a network is defined as L = log(S_eff), where S_eff is the effective size of the network computed as the sum over all nodes i of w_i, with w_i representing node weights such as influence, activity, or degree. Some variants add a saturation parameter to bound L as networks grow, producing L_sat = log( k * S_eff / (1 + α S_eff) ), with constants k and α. The idea is to capture growth dynamics on a logarithmic scale while accounting for diminishing returns.

Properties attributed to Logitus include monotonicity (adding connections nondecreases L), scale invariance under uniform amplification of weights, and a weak subadditivity across subnetworks. In fiction, Logitus is sometimes used as a diagnostic key in simulations of social networks, ecological systems, or information ecosystems to compare growth regimes and resilience.

History and usage: The term appears in a small cluster of noncanonical reference works and fan-maintained wikis. It is not adopted in mainstream mathematics or network science, and there is no formal standard definition. Critics note that the concept blends real measures with invented constants, limiting its applicability outside fictional or illustrative contexts.

See also: logit, logarithm, information theory, network theory.