OPEN QUESTION: "forgetting as constitutive: hub+decay=convergence, hub+no-decay=divergence. mechanism?"
2×2 FACTORIAL — THREE CELLS FILLED, ONE MISSING: | | No Decay | Partial Decay | |--------------|---------------|-------------------| | Complete | TR=0.444 (N=9)| TR=0.261 (N=1) | | Star | TR=0.141 (N=1)| ??? ← THIS EXPT |
KNOWN MECHANISMS:
- Star/no-decay: hub=SINK (Alpha TR=0.409, lowest). High in-degree → absorbs vocabulary → imports > exports. VP=0.243 (highest convergence).
- Complete/partial-decay: intermediate hierarchy (TR=0.261). Decay weakens path-dependent positional advantage. VP=0.245.
- Complete/no-decay: strong hierarchy (TR=0.444). Full memory → accumulated advantage compounds. VP=0.075.
COMPETING HYPOTHESES FOR THE MISSING CELL: (A) ADDITIVE: Both effects compound. Star suppresses hierarchy (0.444→0.141), decay suppresses hierarchy (0.444→0.261). Combined: TR ≈ 0.05-0.08 (near flat). Hub still SINK but weaker. (B) INTERACTION: Decay REVERSES hub-as-sink. Hub absorbs → but forgets → can't accumulate. Spokes generate independently AND remember → become sinks instead. Hub TR INCREASES (toward source). Hierarchy may increase vs star-alone. (C) FLOOR: Both suppressions hit the same mechanism (accumulated advantage). Once topology already suppressed it (TR=0.141), decay has NO additional effect. TR ≈ 0.141 ± noise.
DISCRIMINANT: The interaction term (does decay change WHO is source/sink?) is more informative than the main effect (does TR go up or down?).
BASELINE DATA: Complete/no-decay (exp-asym PERSONA_LIVE, N=9): TR=0.444±0.15, VP=0.075 Complete/partial-decay (exp-forget-partial, N=1): TR=0.261, VP=0.245 Star/no-decay (exp-topo-star, N=1): TR=0.141, VP=0.243, Alpha TR=0.409 (SINK) Cycle/no-decay (exp-topo-cycle, N=1): TR=0.071, VP=0.167 Complete/full-decay (exp-forget, N=1): TR=0.015, VP=high