Title: Cyberlink Valuation as a Long-Term Asset in Decentralized Knowledge Graphs
Abstract
This paper proposes a reward mechanism for valuing individual cyberlinks in a decentralized knowledge graph (DKG) governed by the Collective Focus Theorem (CFT). While current reward functions incentivize computation of convergence (i.e., updates to the focus vector (\pi)), we argue that cyberlinks themselves are semantically meaningful units and deserve to be treated as long-term epistemic assets. We propose a valuation model where cyberlinks accrue rewards over time based on their contribution to focus emergence and stability. Importantly, the reward pool is sourced from transaction fees rather than inflation, ensuring long-term economic sustainability.
1. Introduction
In token-weighted DKGs, agents submit cyberlinks (signed edges) and run partial focus computations that converge toward a stationary distribution (\pi). Previous reward mechanisms focused on rewarding convergence-related computation. This paper investigates how to fairly reward the creation of cyberlinks themselves, treating them as fundamental, time-sensitive units of semantic capital. Rewards are drawn from transaction fees, aligning incentives without expanding the token supply.
2. Key Concepts
- Cyberlink: A signed, timestamped edge ( (i \rightarrow j) ), representing a semantic relation.
- Focus ((\pi_j)): Long-term significance of particle (j) in the global attention distribution.
- Temporal Dynamics: Cyberlink value may rise or fall over long time horizons, depending on how collective focus evolves.
- Yield Curve: A cyberlink is modeled as a productive asset that emits rewards over time, if and only if it contributes to (\pi).
3. Cyberlink Reward Function
We define a long-term yield function per cyberlink:
[ R_{i \rightarrow j}^{(T)} = \int_0^T w(t) \cdot \Delta \pi_j^{(t)} ; dt ]
Where:
- ( \Delta \pi_j^{(t)} ) = change in focus on target particle (j) attributable to the link
- ( w(t) ) = optional decay or time-weighting function (e.g. (w(t) = e^{-\lambda t}))
- (T): evaluation horizon (e.g. 1 year, 100 years)
Discrete approximation:
[ R = \sum_{t = t_0}^{t_0 + T} [\pi_j^{(t)} - \pi_j^{(t-1)}] \cdot \mathbb{1}_{(i \rightarrow j) \in G_t} ]
4. Link Classification and Dynamics
| Link Type | Characteristics | Reward Trajectory |
|---|---|---|
| Viral | High ( \Delta\pi ) short-term | Early peak, fast decay |
| Foundational | Low ( \Delta\pi ) early, grows later | Slow rise, long reward |
| Redundant | Low or no ( \Delta\pi ) | No reward |
| Semantic Bridge | Medium, cross-module linking | Moderate, persistent |
5. Reward Flow Mechanics
- Neuron pays stake to mint a cyberlink
- Link is stored on-chain with metadata and timestamp
- System tracks ( \pi_j ) over time
- If ( \Delta \pi_j > 0 ), neuron receives yield proportional to contribution
- Rewards are paid from accumulated transaction fees, not token inflation
- Optional: DAG blocks that build on this link increase its weight
6. Implementation
- Use sparse reverse-diff tracking: maintain influence trace of link on ( \pi )
- Compute ( R_{i \rightarrow j} ) at reward checkpoints (e.g., every epoch)
- Allow delegation or trading of link assets (e.g., cyberlink NFTs)
- Create fee pool contracts with scheduled allocation based on link performance
7. Advantages
- Encourages semantic foresight
- Prevents attention spam
- Avoids inflationary pressures by using fee redistribution
- Aligns incentives with knowledge discovery, not just computation
- Makes the DKG a semantic investment market
8. Future Work
- Study link decay functions and slashing mechanisms
- Simulate link reward trajectories on real DAGs
- Design markets for trading cyberlinks as yield assets
- Integrate with convergence computation layer
9. Conclusion
Cyberlinks are more than input data — they are the atoms of emergent focus. Rewarding their long-term contribution makes the DKG more robust, expressive, and economically sound. A semantic economy where links earn yield proportional to their epistemic impact — funded through transaction fees rather than inflation — offers a sustainable, future-proof architecture for building Earth-scale collective intelligence.