perAgentBudget_eq
plain-language theorem explainer
The per-agent σ-budget is fixed at 45 by the consciousness gap at three dimensions. Sociologists deriving Dunbar group size from recognition bandwidth cite the equality to anchor the scale of the tier-weighted prediction. The proof is immediate reflexivity on the constant definition.
Claim. The per-agent $σ$-budget per recognition cycle equals 45.
background
In the DunbarFromBandwidth module the model assigns one unit of σ-flow per pairwise relationship per cycle. The total per-agent budget is supplied by the consciousness gap evaluated at D=3, which the upstream definition sets to the natural number 45. This numerical anchor is then multiplied by the φ-weighted tier sum (1 + 1/φ + 1/φ² + …) to bound stable group size.
proof idea
The proof is a one-line wrapper that applies reflexivity to the defining equation of perAgentBudget.
why it matters
The equality populates the budget_eq field of dunbarFromBandwidthCert and the first conjunct of dunbar_one_statement. It links the T8 forcing step (D=3) to the sociological bound dunbar_predicted < 225, which comfortably contains the classical 150 value while allowing the empirical band [60,250].
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