Summary of Findings: Collective Focus Theorem & Foculus Architecture
1. Exponential Optimality Under Constraint
- The exponential allocation principle explains why base-e distributions appear in least-action physics, maximum-entropy thermodynamics, and attention economics.
- The Collective Focus Theorem (CFT) is a special case: group attention over competing items decays exponentially with rank.
- Implication: Optimal cognitive and computational systems—like Cybergraph—should structure resource allocation to approximate base-e efficiency.
2. Collective Focus Theorem in Consensus
- CFT applied to consensus enables probabilistic attention finality instead of block ordering.
- Nodes model the network as a token-weighted directed graph; repeated random walks converge to a stable stationary distribution (π).
- Transactions finalize when their π-value exceeds a threshold τ, guaranteeing safety under honest-majority focus.
- This approach allows millions of TPS, sub-3s finality, and low communication overhead.
3. Foculus Consensus Protocol
- Graph-native, block-free consensus.
- GPU-accelerated sparse matrix × vector updates every ~100 ms.
- Particles = transactions/data, cyberlinks = weighted endorsements.
- Finality = πᵢ > τ, conflicts below τ are discarded.
- Safety: ≥50% honest π-mass prevents double finality.
- Liveness: Ergodicity ensures all honest transactions finalize.
4. Economic Model
- Minting rewards tied to Δπ(p) — measurable shift in collective focus caused by a proof particle.
- Only focus updates mint; all other useful proofs rewarded from transaction fees.
- Fee split: 50% burned, 50% funds auxiliary proofs.
- Stake delegation = attention delegation; long-term reputation from accumulated π-weight.
- Eternal weight via burn anchors critical knowledge permanently.
5. State Model for Superintelligence
- Graph-native state: particles (nodes) and cyberlinks (edges) as first-class citizens.
- Token-weighted attention determines significance.
- Hybrid architecture: integrates account-based deterministic execution with probabilistic, resource-based cognition.
- Suitable for AGI substrate—supports semantic emergence, modular knowledge, and scalable parallelism.
6. Data Availability & Trust Minimization
- Tiered DA stack:
- Tier 0: Ethereum calldata checkpoints (immutable, minimal bandwidth).
- Tier 1: Active graph focus blobs on Celestia, mirrored to IPFS/Filecoin.
- Tier 2: Archival erasure-coded storage.
- Phone-class light clients can verify via DAS sampling; future-proofed for FRIDA/FRI proofs.
- Governance knobs: min sampling confidence, max blob fee, checkpoint interval.
7. Authenticated Graph Data Structures (AGDS)
- Fully-authenticated focus cascading (FFC):
- Merkelized subgraphs with path-hash accumulators.
- Fractional cascading overlays for O(log n) cross-shard lookups.
- Sharding strategies: id-hash, neuron-centric, topic, community, geo/ownership, temporal, hybrid.
- Ensures every edge and weight shaping π is cryptographically verifiable.
8. Confidentiality Model
- 64-byte Blake3-XOF digests for quantum-resilient content addressing.
- Pedersen commitments for weights: perfectly hiding, homomorphic.
- Poseidon2 tags for zk efficiency.
- Default anonymization of node IDs; selective disclosure possible.
- Range proofs ensure bounded, valid weights.
9. Scalability & Sharding (Foculus v2)
- Two-tier commit:
- K committee shards each sign micro-roots.
- Beacon committee aggregates to a vector root.
- GPU-per-shard parallel focus computation.
- Throughput: up to 10⁷ links/s with K=50 while keeping per-node load constant.
- Safety: attack requires corrupting >1/3 committees and beacon in same slot.
10. Implementation Roadmap
- Phase 1: Prototype consensus & economic layers.
- Phase 2: Integrate lattice-based quantum-resilient checkpoints.
- Phase 3: Incentivize public-good computation.
- Phase 4: Enhance DA & bundling.
- Phase 5: Mainnet beta with adaptive RL optimization.
Conclusion: The integration of CFT, exponential optimality, authenticated/confidential graph structures, and a GPU-native, proof-weighted consensus protocol forms a cohesive design for an earth-scale decentralized superintelligence. The system is:
- Scalable: 10⁶–10⁷ TPS class.
- Secure: Honest-majority π-mass safety, quantum-resilient checkpoints.
- Economically aligned: Rewards tied directly to measurable contribution to collective cognition.
- Trust-minimized: Cryptographic proofs for all state, verifiable by light clients.
- Privacy-preserving: Confidential by default, selectively transparent.
This architecture is not just a blockchain—it is a substrate for global, convergent, verifiable cognition.