tier0
plain-language theorem explainer
Base tier weight for close ties equals 1 in the bandwidth cost model. Sociologists deriving mean stable group sizes from recognition ledgers cite this as the anchor for the geometric tier series 1 + φ^{-1} + .... The definition is introduced by direct constant assignment.
Claim. The weight of the innermost social tier is $1$.
background
The model assigns costs to social tiers decreasing geometrically by the golden ratio φ, where φ satisfies φ² = φ + 1 from the self-similar fixed point. Tier 0 represents close ties maintained at full bandwidth cost of 1. This setup uses the total σ-budget per agent bounded by the consciousness gap of 45 units, as defined in the module's derivation of stable group size. The approach builds on the recognition composition law for multi-agent ledgers and the phi-ladder structure.
proof idea
One-line definition that sets the base tier weight to the constant 1.
why it matters
This base weight feeds the totalWeight definition and the positivity result for all tiers. It enables the closed-form Dunbar bound via summation of the series up to 1/φ⁴, connecting to the phi-ladder and the T6 fixed point in the forcing chain. The structure yields a band of group sizes consistent with empirical ranges 100-250.
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