tier1
plain-language theorem explainer
Tier-1 weight is set to the reciprocal of phi to represent casual contacts in the multi-tier social model. Researchers deriving bandwidth-limited group sizes cite this term when summing the geometric series to bound stable relationships. The definition is a direct assignment from the imported phi constant.
Claim. The weight for Tier-1 (casual contacts) is defined by $1/phi$, where $phi$ is the golden ratio satisfying $phi^2 = phi + 1$.
background
The DunbarFromBandwidth module partitions social relationships into five tiers whose weights form a geometric series with common ratio $1/phi$. This ratio encodes the coordination dividend from upstream GameTheory results. Tier-0 carries weight 1 for close contacts, Tier-1 carries $1/phi$ for casual contacts, and subsequent tiers continue the descent to Tier-4 at $1/phi^4$. The per-agent sigma-budget is fixed at the consciousness gap value 45, so the mean stable group size is obtained by multiplying this budget by the partial sum of the first three or five tier weights.
proof idea
One-line definition that directly assigns tier1 to the expression 1 divided by phi, drawing the constant from the imported Constants module.
why it matters
The definition supplies the second summand in totalWeight, which is required by the positivity theorem tier_weights_pos and the bound totalWeight_lt_5. It instantiates the phi-ladder scaling that converts the recognition budget into the observed Dunbar band of roughly 100-250. The construction closes the link between the foundational phi fixed point and the sociological application of the Recognition Composition Law.
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