Hyperbolic Bulk Skill

Hyperbolic Bulk Skill

Status: ✅ Production Ready
Trit: 0 (ERGODIC - mediates bulk ↔ boundary)
Principle: AdS/​CFT correspondence for entropy
Chain: Aptos (Move language)

---

Overview

The Hyperbolic Bulk implements on-chain entropy storage with GF(3) conservation. Named after the AdS/​CFT bulk-boundary correspondence:

• BULK (interior): Entropy records, triads, reafference proofs
• BOUNDARY (observable): Agents, skills, colors

         BOUNDARY (Observable)
    ┌─────────────────────────────┐
    │  Agents  │  Skills  │ Colors │
    └─────────────┬───────────────┘
                  │ project
                  ▼
    ┌─────────────────────────────┐
    │      HYPERBOLIC BULK        │
    │  ┌─────────────────────┐    │
    │  │  EntropyRecord      │    │
    │  │  drand ⊕ eeg ⊕ vrf  │    │
    │  └──────────┬──────────┘    │
    │             ▼               │
    │  ┌─────────────────────┐    │
    │  │  EntropyTriad       │    │
    │  │  GF(3) = 0 conserved│    │
    │  └──────────┬──────────┘    │
    │             ▼               │
    │  ┌─────────────────────┐    │
    │  │  ReafferenceProof   │    │
    │  │  predict = observe  │    │
    │  └─────────────────────┘    │
    └─────────────────────────────┘

---

Entropy Sources

Combination: combined = drand_seed ⊕ eeg_seed ⊕ onchain_rand

---

GF(3) Conservation

Triads must sum to 0 mod 3:

MINUS (-1) ≡ 2 (mod 3)  — Verification/​Constraint
ERGODIC (0)             — Coordination/​Balance  
PLUS (+1)               — Generation/​Exploration

Conservation: trit_1 + trit_2 + trit_3 ≡ 0 (mod 3)

Strict Mode: form_conserved_triad() reverts if not conserved.

---

Move Contract

module hyperbolic_bulk::entropy_triads {
    
    struct EntropyRecord has store, drop, copy {
        drand_round: u64,
        drand_seed: u256,
        eeg_seed: u256,
        combined_seed: u256,
        timestamp: u64,
        trit: u8,
        color_hex: vector<u8>,
    }

    struct EntropyTriad has store, drop, copy {
        record_id_1: u64,
        record_id_2: u64,
        record_id_3: u64,
        gf3_sum: u8,
        gf3_conserved: bool,
        skill_1: vector<u8>,
        skill_2: vector<u8>,
        skill_3: vector<u8>,
    }

    struct ReafferenceProof has store, drop, copy {
        seed: u256,
        predicted_color: vector<u8>,
        observed_color: vector<u8>,
        matched: bool,
        loop_type: vector<u8>,  // "loopy_strange" or "exafference"
    }

    #[randomness]
    entry fun store_entropy(...) { /​* combines drand ⊕ eeg ⊕ vrf */ }
    
    entry fun form_conserved_triad(...) { /​* enforces GF(3) = 0 */ }
    
    entry fun record_reafference(...) { /​* proves prediction = observation */ }
}

---

Integration with World-Memory-Worlding

The loop closes when worlded triads become new memory records.

---

Reafference Proofs

On-chain proof that prediction matched observation:

struct ReafferenceProof {
    seed: u256,
    predicted_color: vector<u8>,
    observed_color: vector<u8>,
    matched: bool,           // prediction == observation
    loop_type: vector<u8>,   // "loopy_strange" iff matched
}

Loopy Strange: Generator ≡ Observer when same seed produces same color.

---

GF(3) Triads

bisimulation-game (-1) ⊗ hyperbolic-bulk (0) ⊗ gay-mcp (+1) = 0 ✓
duckdb-timetravel (-1) ⊗ hyperbolic-bulk (0) ⊗ world-hopping (+1) = 0 ✓
spi-parallel-verify (-1) ⊗ hyperbolic-bulk (0) ⊗ operad-compose (+1) = 0 ✓

---

Python Integration

from drand_skill_sampler import DrandSkillSampler, EEGEntropySource

# Create entropy sources
eeg = EEGEntropySource(
    delta=0.15, theta=0.25, alpha=0.35, 
    beta=0.20, gamma=0.05
)

# Sample skills with DRAND entropy
sampler = DrandSkillSampler(drand_seed=10770320150143512701, eeg_source=eeg)

# Generate Aptos transaction
tx = sampler.to_aptos_transaction()
# {
#   "function": "hyperbolic_bulk::entropy_triads::store_entropy",
#   "arguments": [drand_round, drand_seed, eeg_seed, color_hex]
# }

---

Ruler Configuration

[entropy]
drand_round = 24634579
eeg_dominant = "alpha"
aptos_module = "hyperbolic_bulk::entropy_triads"

[mcp]
enabled = true
servers = ["gay", "drand", "localsend"]

[agents.codex]
trit = 0
bulk_address = "0x..."

---

Commands

# Deploy contract
aptos move publish --package-dir hyperbolic_bulk

# Store entropy
aptos move run --function-id 'hyperbolic_bulk::entropy_triads::store_entropy' \
  --args u64:24634579 u256:0x9577dd1cea89307d u256:0x8219ed722cbf7d6a

# Form conserved triad
aptos move run --function-id 'hyperbolic_bulk::entropy_triads::form_conserved_triad' \
  --args u64:0 u64:1 u64:2 'vector<u8>:skill1' 'vector<u8>:skill2' 'vector<u8>:skill3'

# Query stats
aptos move view --function-id 'hyperbolic_bulk::entropy_triads::get_stats'

---

The Bulk-Boundary Insight

Why "hyperbolic"?

In AdS/​CFT, the hyperbolic (anti-de Sitter) bulk contains more information than the flat boundary. Similarly:

• Bulk: Full entropy (drand × eeg × vrf), all triads, all proofs
• Boundary: Projected observables (colors, skill names, agent states)

The boundary is a lossy projection of the bulk. But GF(3) conservation is preserved across the projection—it's a geometric invariant.

Reafference as Holography:

• When prediction = observation, the boundary faithfully represents the bulk
• "Loopy strange" = holographic consistency (no information loss)
• "Exafference" = external perturbation (bulk ≠ boundary)

---

See Also

• world-memory-worlding — Autopoietic loop
• gay-mcp — Deterministic color generation
• drand_skill_sampler.py — Entropy sampling

---

Skill Name: hyperbolic-bulk
Type: On-Chain Entropy / GF(3) Conservation
Trit: 0 (ERGODIC - bulk-boundary mediation)
Chain: Aptos Move
Contract: hyperbolic_bulk::entropy_triads

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/​claude-scientific-skills ecosystem:

Graph Theory

• networkx [○] via bicomodule
  • Universal graph hub

Bibliography References

• general: 734 citations in bib.duckdb

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 10. Adventure Game Example

Concepts: autonomous agent, game, synthesis

GF(3) Balanced Triad

hyperbolic-bulk (+) + SDF.Ch10 (+) + [balancer] (+) = 0

Skill Trit: 1 (PLUS - generation)

Secondary Chapters

• Ch1: Flexibility through Abstraction
• Ch4: Pattern Matching
• Ch2: Domain-Specific Languages
• Ch7: Propagators

Connection Pattern

Adventure games synthesize techniques. This skill integrates multiple patterns.

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.