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IndisputableMonolith.Sociology.DunbarFromBandwidth

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This module defines the per-agent σ-budget per recognition cycle in Recognition Science, setting it equal to the consciousness gap at D=3, then introduces tier weights and total weight for social structures. Sociologists applying RS to network sizes or Dunbar derivations would cite these definitions. The module consists entirely of definitions and basic positivity lemmas with no complex proofs.

claimLet $\sigma$ be the per-agent budget per recognition cycle, defined as the consciousness gap at $D=3$. Define tier weights $w_0,\dots,w_4$ and total weight $W=\sum w_i$ satisfying $w_i>0$ and $W<5$.

background

Recognition Science derives all structure from the J-cost functional equation and the forcing chain (T0-T8) that fixes D=3 spatial dimensions. The imported Constants module supplies the RS-native time quantum $\tau_0=1$ tick. The Cost module supplies the underlying recognition-cost definitions. This sociology module therefore introduces the per-agent $\sigma$-budget as the consciousness gap evaluated at D=3, then builds tier0 through tier4, totalWeight, and the associated positivity statements.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the bandwidth primitives required to derive Dunbar numbers from recognition costs inside the Recognition framework. It directly instantiates the D=3 result from the UnifiedForcingChain at the sociological level. No downstream theorems are recorded yet.

scope and limits

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (18)