Executive Summary
A critical question for multi-agent architectures is how coordination quality degrades as information passes through successive agents. The default assumption is exponential decay — each hop loses a fixed fraction of information, leading to rapid degradation. This would impose hard limits on multi-agent chain depth. This paper measures the actual degradation curve across chains of 1 to 10 hops.
The degradation is logarithmic, not exponential. Cross-entropy rises from 0.503 at hop 1 to approximately 0.60 by hop 5, then plateaus through hop 10. Neither linear (R-squared = 0.50) nor exponential (R-squared = 0.48) models fit the data well; the logarithmic shape indicates that early hops lose the most fragile information, while the information that survives to hop 5 is robust to further transmission. This is fundamentally different from the exponential decay assumption and has major implications for multi-agent system design.
Two additional findings challenge conventional wisdom. First, fence placement is irrelevant: applying a context fence at every hop versus only at the final hop produces identical results (CE 0.598 vs 0.597). This means the mode-switching benefit of fences is a one-time effect that does not compound across hops. Second, cross-domain handoffs actually outperform within-domain handoffs (CE 0.56-0.63 vs 0.72), suggesting that domain transitions force a beneficial re-encoding of information. Together, these results establish that multi-agent coordination protocols can scale to arbitrary depth without compounding error.
Key Findings
- Logarithmic degradation: CE rises from 0.503 to ~0.60 by hop 5, then plateaus through hop 10
- Neither linear nor exponential: Linear R-squared = 0.50, exponential R-squared = 0.48 — logarithmic curve is the correct fit
- Fence placement irrelevant: Fence-every-hop (0.598) vs fence-final (0.597) — identical performance
- Cross-domain outperforms within-domain: Cross-domain CE 0.56-0.63 vs within-domain 0.72 — domain transitions force beneficial re-encoding
- Arbitrary depth scaling: Protocol scales to arbitrary chain depth without compounding error
Key References
- McEntire (2026) — Context Fences: mode switching mechanism (Paper XXII)
- McEntire (2026) — The Coordination Problem Is Interference: synthesis framework (Paper XXI)
- McEntire (2026) — Ritual Shape: optimal coordination protocol (Paper XIX)
- McEntire (2026) — Ensemble Gravity: priming selection and domain dependence (Paper XVIII)