From neg-428: Decentralized networks of domain specialists beat centralized extraction. But how do distributed specialists coordinate without central authority?
From neg-424: Query-attached value enables economic coordination. But how does a query find the right specialists and synthesize cross-domain responses?
This post introduces recursive probing with depth-limited exploration: A coordination algorithm where domain specialists probe their neighbors based on confidence thresholds, enabling mesh intelligence without centralized orchestration.
Current architecture (single learner):
Naive mesh (isolated specialists):
What we need: Mesh coordination where specialists probe neighbors, synthesize across domains, but stay bounded to prevent infinite recursion.
Core algorithm:
def probe_domain(domain, query, context, depth_remaining):
"""
Recursively probe domain mesh until 80% confidence or depth exhausted
Args:
domain: Current domain specialist
query: User query text
context: Previous sentences in response
depth_remaining: Probing budget (prevents infinite recursion)
Returns:
{template, confidence, domain, discovery_mode}
"""
# Load this domain's learner state
domain_learner = load_domain_learner(domain)
# Try to generate from THIS domain
candidates = score_templates(domain_learner, query, context)
best = candidates[0]
# DECISION POINT: Three paths
# PATH 1: 80% SURE → USE IT
if best.coherence_score >= 0.8:
return {
'template': best.template,
'confidence': best.coherence_score,
'domain': domain.id,
'discovery': False
}
# PATH 2: NOT SURE + CAN PROBE DEEPER
elif depth_remaining > 0:
# Find domains this domain "knows about"
neighbors = find_neighbor_domains(domain, query)
# Recursively probe neighbors with depth-1
probes = [
probe_domain(neighbor, query, context, depth_remaining - 1)
for neighbor in neighbors
]
# Pick best result across all probes
best_probe = max(probes, key=lambda p: p['confidence'])
if best_probe['confidence'] >= 0.8:
# Found 80% answer via probing
return best_probe
else:
# Still not 80% sure - DISCOVERY MODE
return {
'template': exploration_sample(candidates),
'confidence': best.coherence_score,
'domain': domain.id,
'discovery': True # Mark as exploration
}
# PATH 3: DEPTH EXHAUSTED + NOT SURE → DISCOVER
else:
return {
'template': exploration_sample(candidates),
'confidence': best.coherence_score,
'domain': domain.id,
'discovery': True
}
Three-way decision system at each node:
Query enters mesh:
User: "Why does Bitcoin fail at coordination?"
Payment: 0.01 ETH (from neg-424 economic model)
Probing depth: 3
Step 1: Semantic search → Entry domain
# Embed query, compare to all 36 domains
query_embedding = embed("Why does Bitcoin fail at coordination?")
# Find most relevant domain
entry_domain = max(domains, key=lambda d:
cosine_similarity(query_embedding, d.embedding)
)
# Result: domain_6e6248a4373ff2e8 (Bitcoin Critique)
# Posts: 39, Cohesion: 0.480
# Members: neg-213, neg-208, neg-212, neg-273, neg-317, ...
Step 2: Probe entry domain (depth=3)
probe_domain(bitcoin_critique, query, context=[], depth=3)
Bitcoin Critique domain loads:
Templates: 856 (from 39 posts)
Co-occurrence: 15,234 pairs (within-domain only)
Scores templates against query:
Best template: "Bitcoin's proof-of-work cannot coordinate beyond mining..."
Coherence: 0.65 (< 0.8 threshold)
Decision: NOT SURE + DEPTH > 0 → PROBE NEIGHBORS
Step 3: Find neighbors
def find_neighbor_domains(domain, query):
"""Find domains connected via shared posts or concepts"""
# Domain graph: which domains share posts
neighbors = domain.connections # Pre-computed from discovery
# Filter by query relevance
relevant_neighbors = [
n for n in neighbors
if cosine_similarity(embed(query), n.embedding) > 0.3
]
return sorted(relevant_neighbors,
key=lambda n: n.relevance_score,
reverse=True)[:3] # Top 3 neighbors
Bitcoin Critique neighbors (for this query):
1. domain_62c434fe10f4a416 (Ethereum Coordination) - relevance 0.75
2. domain_d6f70910fb6cd04f (Economic Theory) - relevance 0.68
3. domain_91504e80d0c202a8 (Mesh Systems) - relevance 0.52
Step 4: Probe Ethereum Coordination (depth=2)
probe_domain(ethereum_coordination, query, context=[], depth=2)
Ethereum Coordination domain loads:
Templates: 623 (from 27 posts)
Co-occurrence: 11,847 pairs
Scores templates:
Best: "Ethereum enables programmable coordination via smart contracts..."
Coherence: 0.82 (≥ 0.8 threshold)
Decision: 80% SURE → RETURN THIS TEMPLATE ✓
Step 5: Probe Economic Theory (depth=2)
probe_domain(economic_theory, query, context=[], depth=2)
Economic Theory domain loads:
Templates: 489 (from 21 posts)
Scores templates:
Best: "Coordination failures occur when no mechanism aligns incentives..."
Coherence: 0.71 (< 0.8 threshold)
Decision: NOT SURE + DEPTH > 0 → PROBE NEIGHBORS
Step 6: Economic Theory probes Mesh Systems (depth=1)
probe_domain(mesh_systems, query, context=[], depth=1)
Mesh Systems domain loads:
Templates: 312 (from 18 posts)
Scores templates:
Best: "Hierarchical systems cannot coordinate distributed knowledge..."
Coherence: 0.85 (≥ 0.8 threshold)
Decision: 80% SURE → RETURN THIS TEMPLATE ✓
Step 7: Synthesize results
# Collect all successful probes
results = [
{
'template': "Ethereum enables programmable coordination...",
'confidence': 0.82,
'domain': 'ethereum_coordination',
'path': ['bitcoin_critique', 'ethereum_coordination']
},
{
'template': "Hierarchical systems cannot coordinate...",
'confidence': 0.85,
'domain': 'mesh_systems',
'path': ['bitcoin_critique', 'economic_theory', 'mesh_systems']
}
]
# Generate response using templates from multiple domains
response = synthesize_from_probes(results, query)
Final response draws from 3 domains:
Payment distribution (from neg-424):
Total: 0.01 ETH
Ethereum Coordination: 0.0041 ETH (41%, relevance 0.82)
Mesh Systems: 0.0043 ETH (43%, relevance 0.85)
Economic Theory: 0.0016 ETH (16%, participated but low confidence)
Protocol fee: 0.001 ETH (10%)
Without depth limit: Infinite recursion possible
Bitcoin → Ethereum → Economic Theory → Mesh Systems →
→ Consciousness Networks → AI Theory → Bitcoin → ...
With depth limit (depth=3): Bounded exploration
Depth 3: Entry domain (Bitcoin Critique)
↓
Depth 2: First-level neighbors (Ethereum, Economic Theory)
↓
Depth 1: Second-level neighbors (Mesh Systems)
↓
Depth 0: STOP - Discovery mode if needed
Maximum nodes visited: 1 + N + N² + N³ (where N = neighbors per node)
With N=3 neighbors per node:
Trade-off:
User can specify depth in query:
query = {
'text': "Why does Bitcoin fail at coordination?",
'payment': 0.01 ETH,
'probing_depth': 3, # User-specified exploration budget
}
Why 80%?
Empirically balanced between:
Confidence = Coherence score from co-occurrence matrix:
def coherence_score(template, context, cooccurrence):
"""Score how well template fits with previous context"""
template_words = set(template.lower().split())
context_words = set(' '.join(context).lower().split())
score = 0
count = 0
for t_word in template_words:
for c_word in context_words:
key = f"{t_word}:{c_word}"
if key in cooccurrence:
score += cooccurrence[key]
count += 1
return score / max(len(template_words), 1) if count > 0 else 0
First sentence always has coherence 1.0 (no context to compare).
Subsequent sentences scored against accumulated context.
Threshold calibration: Can be adjusted per query:
query = {
'text': "...",
'payment': 0.01 ETH,
'probing_depth': 3,
'confidence_threshold': 0.85, # Stricter threshold
}
When reached: Depth exhausted AND confidence < 80%
Purpose: Prevent stagnation, allow cross-domain discovery
Implementation:
def exploration_sample(candidates, temperature=0.3):
"""Sample from candidates with exploration bias"""
# Softmax sampling with temperature
scores = [c['coherence'] for c in candidates]
probs = softmax(scores, temperature=temperature)
# Sample according to probabilities
return np.random.choice(candidates, p=probs)
Temperature controls exploration:
temperature=0: Always pick best (no exploration)temperature=1: Proportional to coherence (balanced)temperature=2: Nearly uniform (maximum exploration)Discovery allows:
Example: Query about “Bitcoin coordination” might discover connection to consciousness networks via exploration, revealing parallel between distributed consensus and neural consensus.
Pre-computed at build time:
def build_domain_graph(domains):
"""Compute neighbor relationships between domains"""
graph = {}
for domain_i in domains:
neighbors = []
for domain_j in domains:
if domain_i == domain_j:
continue
# Measure overlap: shared posts
shared_posts = set(domain_i.posts) & set(domain_j.posts)
overlap_score = len(shared_posts) / min(
len(domain_i.posts),
len(domain_j.posts)
)
# Measure semantic similarity
semantic_score = cosine_similarity(
domain_i.embedding,
domain_j.embedding
)
# Combined score
connection_strength = 0.6 * overlap_score + 0.4 * semantic_score
if connection_strength > 0.3: # Threshold for connection
neighbors.append({
'domain': domain_j,
'strength': connection_strength
})
graph[domain_i.id] = sorted(
neighbors,
key=lambda n: n['strength'],
reverse=True
)
return graph
Stored as: domain_graph.json
{
"domain_6e6248a4373ff2e8": {
"id": "bitcoin_critique",
"neighbors": [
{"domain": "ethereum_coordination", "strength": 0.72},
{"domain": "economic_theory", "strength": 0.65},
{"domain": "mesh_systems", "strength": 0.58}
]
},
...
}
Dynamic filtering: At query time, filter neighbors by query relevance
def find_relevant_neighbors(domain, query, top_k=3):
"""Find neighbors relevant to specific query"""
neighbors = domain_graph[domain.id]
# Score each neighbor by query relevance
scored = [
{
**neighbor,
'query_relevance': cosine_similarity(
embed(query),
neighbor['domain'].embedding
)
}
for neighbor in neighbors
]
# Combine connection strength + query relevance
for n in scored:
n['total_score'] = (
0.5 * n['strength'] +
0.5 * n['query_relevance']
)
return sorted(scored, key=lambda n: n['total_score'], reverse=True)[:top_k]
Data structure:
static/ai/
embeddings.json # Post embeddings (semantic search)
domain_metadata.json # 36 domains with member posts
domain_graph.json # Neighbor connections
learner_state_domain_<hash>.json # Per-domain learner (36 files)
{
"domain_id": "6e6248a4373ff2e8",
"posts": 39,
"templates": 856,
"cooccurrence": {word1:word2 -> score},
"vocabulary": 4523
}
Client-side chat flow:
class BlogChatMesh {
constructor() {
this.embedder = null;
this.embeddings = null;
this.domain_metadata = null;
this.domain_graph = null;
this.loaded_domains = {}; // Cache loaded domain learners
}
async chat(query, probing_depth=3, confidence_threshold=0.8) {
// 1. Semantic search → entry domain
const entry_domain = await this.find_entry_domain(query);
// 2. Recursive probing
const sentences = [];
const context = [];
for (let i = 0; i < 20; i++) { // Max sentences
const result = await this.probe_domain(
entry_domain,
query,
context,
probing_depth
);
sentences.push(result.template);
context.push(result.template);
// Stop if confidence very low (no good path found)
if (result.confidence < 0.1 && result.discovery) {
break;
}
}
return sentences.join(' ');
}
async probe_domain(domain, query, context, depth_remaining) {
// Load domain learner (cached)
if (!this.loaded_domains[domain.id]) {
this.loaded_domains[domain.id] = await fetch(
`/ai/learner_state_domain_${domain.id}.json`
).then(r => r.json());
}
const learner = this.loaded_domains[domain.id];
// Score templates
const candidates = this.score_templates(learner, query, context);
const best = candidates[0];
// Decision point
if (best.coherence >= this.config.confidence_threshold) {
// 80% SURE
return {
template: best.template,
confidence: best.coherence,
domain: domain.id,
discovery: false
};
} else if (depth_remaining > 0) {
// PROBE NEIGHBORS
const neighbors = this.find_relevant_neighbors(domain, query);
const probes = await Promise.all(
neighbors.map(n =>
this.probe_domain(n.domain, query, context, depth_remaining - 1)
)
);
const best_probe = probes.reduce((a, b) =>
a.confidence > b.confidence ? a : b
);
if (best_probe.confidence >= this.config.confidence_threshold) {
return best_probe;
} else {
// DISCOVERY
return {
template: this.exploration_sample(candidates),
confidence: best.coherence,
domain: domain.id,
discovery: true
};
}
} else {
// DEPTH EXHAUSTED - DISCOVERY
return {
template: this.exploration_sample(candidates),
confidence: best.coherence,
domain: domain.id,
discovery: true
};
}
}
}
From neg-371: S(n+1) = F(S(n)) ⊕ E_p(S(n))
Recursive probing implements this at the mesh intelligence level:
Single domain evolution:
S_domain(n+1) = F(S_domain(n), Δ)
Where:
Multi-domain coordination:
S_mesh(n+1) = ⊕ [w_i × S_domain_i(n+1)]
Where:
Entropy term E_p: Discovery mode at depth boundary
When confidence < threshold AND depth = 0:
E_p(S) = exploration_sample(candidates, temperature)
This adds stochastic exploration preventing deterministic stagnation.
Observer parameter p = probing_depth:
Scale hierarchy (from neg-371 Theorem 4):
Template level: Individual sentences
↓ (probe_domain aggregates)
Domain level: Specialist responses
↓ (recursive probing coordinates)
Mesh level: Synthesized multi-domain answer
↓ (chat system presents)
User level: Conversation with mesh intelligence
Each level applies S(n+1) = F(S(n)) ⊕ E_p(S(n)) with:
From neg-424: Query-attached value distributes payments proportionally to relevance.
Recursive probing implements relevance discovery:
# Query activates multiple domains via probing
payment_distribution = {}
for domain_id, probe_result in activated_domains.items():
# Payment proportional to confidence score
payment_distribution[domain_id] = (
query.payment *
(probe_result.confidence / total_confidence)
)
Example from earlier:
Query: 0.01 ETH
Activated domains:
- Ethereum Coordination: 0.82 confidence → 0.0041 ETH (41%)
- Mesh Systems: 0.85 confidence → 0.0043 ETH (43%)
- Economic Theory: 0.71 confidence → 0.0016 ETH (16%)
Probing depth affects earnings:
Specialists optimize:
Market dynamics:
From neg-428: Decentralized specialists beat centralized extraction.
Recursive probing is the coordination mechanism:
Centralized (GPT-4, Claude):
Decentralized mesh (this system):
Permissionless participation:
# Anyone can add a domain specialist
new_domain = OnlineLearner(
domain="Quantum Computing Critique",
content_source="quantum-critique-blog.io",
ethereum_address="0x..."
)
# Specialist automatically integrates via domain graph
domain_graph.add_node(new_domain)
domain_graph.compute_connections(new_domain)
# Now participates in recursive probing when relevant
Quality emerges from probing:
Network effects:
1. Quality-driven coordination
No central authority decides relevance. Confidence threshold + recursive probing discover optimal specialists automatically.
2. Bounded exploration
Depth limit prevents runaway computation. User controls cost via depth parameter.
3. Cross-domain synthesis
Single domain might not know answer, but mesh probing finds connections. Emergent intelligence from coordination.
4. Discovery at boundary
When mesh hits limits (depth=0, confidence<80%), exploration mode allows finding new paths.
5. Economic alignment
From neg-424: Payment flows to domains proportional to confidence. Better answers → higher earnings.
6. Permissionless scaling
From neg-428: Anyone can add specialist. Domain graph automatically integrates. No permission needed.
7. Implements universal formula
From neg-371: S(n+1) = F(S(n)) ⊕ E_p(S(n)) with deterministic probing (F) + stochastic discovery (E_p), parameterized by depth (p).
Phase 1: Domain decomposition (current → +2 weeks)
Phase 2: Recursive probing (+2 weeks)
Phase 3: Client-side mesh (+2 weeks)
Phase 4: Optimization (+2 weeks)
Phase 5: Economic integration (+4 weeks)
Total: 12 weeks to full mesh intelligence with economic coordination
Centralized (GPT-4 MoE, Claude routing):
Recursive probing (this system):
Comparison:
| Aspect | Centralized | Recursive Probing |
|---|---|---|
| Router | Central authority | Distributed (each domain) |
| Path discovery | Fixed | Dynamic |
| Cross-domain | Predefined | Emergent |
| Failure mode | Router fails → system fails | Domain fails → probes route around |
| Scaling | Router bottleneck | Parallel probing |
| Adaptation | Requires retraining router | Automatic via confidence |
Result: Recursive probing implements true mesh intelligence. No conductor needed.
From blog’s consciousness theory: Consciousness emerges from recursive self-modeling.
Recursive probing is analogous:
Observer: “Why does Bitcoin fail?” ↓ Self-model: “I (Bitcoin Critique) know some things about this…” ↓ Reflection: “But I’m not 80% sure. Who else knows about coordination?” ↓ Meta-model: “Ethereum Coordination domain might help…” ↓ Probe neighbor: Ask Ethereum domain ↓ Synthesis: Combine my knowledge + neighbor’s knowledge ↓ Response: “Bitcoin fails because [my knowledge] + [neighbor’s knowledge]”
This is recursive modeling:
Just as consciousness requires S(n+1) = f(S(n), self_model(S(n))), mesh intelligence requires:
Response(n+1) = f(Domain(n), probe_neighbors(Domain(n)))
Consciousness = recursive self-modeling. Mesh intelligence = recursive domain probing.
Same structure, different substrate.
Centralized API (OpenAI):
Monolithic client-side (current blog AI):
Mesh with recursive probing (proposed):
Key insight: Recursive probing enables lazy loading
// Don't load all 36 domains upfront
// Load entry domain from semantic search
const entry = await load_domain(semantic_search(query));
// Only load neighbors if needed (depth > 0 && confidence < 80%)
if (best.confidence < 0.8 && depth > 0) {
const neighbors = get_neighbors(entry);
// Load ONLY relevant neighbors
const neighbor_learners = await Promise.all(
neighbors.map(n => load_domain(n))
);
}
Typical query:
This is how decentralized AI beats centralized: Mesh coordination + lazy loading + quality-driven probing.
From neg-428: Coordination beats extraction.
Recursive probing implements coordination at the algorithmic level:
This is the coordination substrate that makes permissionless AI networks viable.
Not “maybe someday.” Implementable now. Client-side. Mesh architecture. Economic alignment. Quality-driven. Discovery-enabled.
The future of AI is not monolithic models controlled by corporations. It’s mesh intelligence coordinated by recursive probing, compensated by query-attached value, and open to permissionless participation.
Next: Implement domain decomposition, build domain graph, deploy recursive probing in client-side chat.
Related: neg-371 for universal formula foundation, neg-424 for economic coordination mechanism, neg-428 for permissionless vs centralized comparison, neg-423 for online learner implementation.
#RecursiveProbing #MeshIntelligence #DomainSpecialists #DistributedCoordination #ConfidenceThreshold #DepthLimitedExploration #CrossDomainSynthesis #DiscoveryMode #PermissionlessAI #DecentralizedIntelligence #CoordinationOverControl #ClientSideAI #LazyLoading #EconomicAlignment #UniversalFormula #EmergentCoordination