tier2
plain-language theorem explainer
Tier-2 weight assigns 1/φ² to acquaintance-level ties in the five-tier social model. Researchers deriving Dunbar bounds from σ-flow budgets cite this constant when summing the geometric series of tier weights. The definition is a direct assignment using the golden-ratio scaling fixed by upstream constants.
Claim. The tier-2 weight is defined as $1/φ²$, where $φ$ denotes the golden ratio satisfying $φ² = φ + 1$.
background
The DunbarFromBandwidth module partitions stable social relationships into five tiers whose weights form a geometric sequence decreasing by successive factors of 1/φ. Tier 2 corresponds to acquaintances and is assigned weight 1/φ². The module sets the per-agent σ-budget to consciousnessGap 3 = 45 and obtains the mean stable group size as 45 · (1 + 1/φ + 1/φ²) ≈ 72.8; the classical Dunbar value ≈ 145 follows by extending the sum to five tiers.
proof idea
One-line definition that directly sets tier2 equal to the reciprocal of phi squared.
why it matters
This definition supplies the acquaintance-tier term to totalWeight and to the positivity theorem tier_weights_pos. It participates in the structural derivation of the Dunbar bound gap · (1 + 1/φ + 1/φ²) and the five-tier classical value. The 1/φ scaling originates from the RS coordination dividend established in GameTheory/CooperationFromSigma.
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