Level 11.9 — Scaled KG + Planning Prototype

Date: 2026-02-16 Cycle: Level 11 Cycle 10 Version: Level 11.9 Chain Link: #119

Summary

Level 11.9 scales the knowledge graph to 225 triples across 3 domains, adds a planning prototype (path queries through multi-hop chains), and stress-tests chains to 6 hops and memories to 25 entities. Three results:

1. 225-Triple Multi-Domain KG: 100% single-hop (225/225). Three domains (geography, people, science), each with 15 entities and 5 relations. Associative memory pattern scales cleanly. Hierarchical superposition reveals capacity wall: domain attribution only 34.7% with 75 triples per domain (exceeds sqrt(1024) ~ 32 capacity).

2. Planning Prototype: 16/16 forward, 16/16 reverse, 4/4 convergence. Four chains (Paris, Berlin, Tokyo, Cairo) each traverse city → country → continent → hemisphere → Earth. All paths compose and decompose with sim=1.0000. Reverse planning (Earth → which city?) also works perfectly.

3. Stress Test: 6-hop chains 100%, memory capacity curve. Bipolar chains exact at all depths 1-6. Memory holds 100% up to 20 entities, degrades to 92% at 25 (approaching sqrt(1024) capacity). Noise curve: 100%/100%/80%/66.7%/40%.

353 total tests (349 pass, 4 skip). Zero regressions.

Key Metrics

Metric	Value	Notes
Integration Tests	81/81 pass	+3 new (Tests 79-81)
Total Tests	353 (349 pass, 4 skip)	+3 from Level 11.8
KG Total Triples	225	3 domains × 15 ents × 5 rels
Single-Hop Accuracy	100.0% (225/225)	All 3 domains
Planning Forward	100.0% (16/16)	sim=1.0000 all paths
Planning Reverse	100.0% (16/16)	Bidirectional exact
6-Hop Chains	100.0%	sim=1.0000
Memory at 20 ents	100.0%	Below capacity limit
Memory at 25 ents	92.0%	Approaching sqrt(1024)
Hierarchical Super	34.7%	Capacity wall at 75/domain
Noise=2 Retrieval	80.0%	Signal fraction 33%
minimal_forward.zig	~13,500 lines	+~400 lines

Test Results

Test 79: Scaled KG 225 Triples + Hierarchical Superposition

=== SCALED KG: 200+ TRIPLES + HIERARCHICAL SUPERPOSITION (Level 11.9) ===
Domains: 3, Entities/domain: 15, Relations/domain: 5
Triples/domain: 75, Total triples: 225

--- Single-Hop Queries Per Domain ---
Domain    | Correct | Total | Accuracy
----------|---------|-------|--------
Geography |      75 |    75 | 100.0%
People    |      75 |    75 | 100.0%
Science   |      75 |    75 | 100.0%

Total single-hop: 225/225 (100.0%)

--- Hierarchical Superposition ---
Domain discrimination from mega: 3/3
Superposition recall (domain attribution): 26/75 (34.7%)

Analysis:

The single-hop result proves the associative memory pattern scales: 15 entities per memory, 5 memories per domain, 3 domains — all 225 queries resolve correctly. Each per-relation memory stores only 15 pairs (well within capacity).

The hierarchical superposition result is the valuable negative finding: bundling 75 triples per domain (5 memories × 15 entities each) into a single domain vector, then bundling 3 domain vectors into a mega vector, dilutes individual triple signals below the discrimination threshold. At 75 items per domain, capacity is exceeded: sqrt(1024) ~ 32.

Domain-level discrimination (3/3) works because each domain super has distinct overall character. But triple-level attribution (34.7%) fails because the query bind(entity, relation) represents 1/75 of the domain signal.

Lesson: Hierarchical superposition needs intermediate indexing. Store domain→relation→entities, not domain→all_triples.

Test 80: Planning Prototype — Path Queries Through KG

=== PLANNING PROTOTYPE: PATH QUERIES (Level 11.9) ===
Chains: 4, Max depth: 4, Dim: 1024

--- Planning Queries ---
Chain  | From  | To         | Hops | Path                                      | Sim
-------|-------|------------|------|-------------------------------------------|------
Paris  | city  | country    |    1 | capital_of                                | 1.0000
Paris  | city  | continent  |    2 | capital_of->continent                     | 1.0000
Paris  | city  | hemisphere |    3 | capital_of->continent->hemisphere         | 1.0000
Paris  | city  | Earth      |    4 | capital_of->continent->hemisphere->planet | 1.0000
Berlin | city  | country    |    1 | capital_of                                | 1.0000
Berlin | city  | continent  |    2 | capital_of->continent                     | 1.0000
Berlin | city  | hemisphere |    3 | capital_of->continent->hemisphere         | 1.0000
Berlin | city  | Earth      |    4 | capital_of->continent->hemisphere->planet | 1.0000
Tokyo  | city  | country    |    1 | capital_of                                | 1.0000
Tokyo  | city  | continent  |    2 | capital_of->continent                     | 1.0000
Tokyo  | city  | hemisphere |    3 | capital_of->continent->hemisphere         | 1.0000
Tokyo  | city  | Earth      |    4 | capital_of->continent->hemisphere->planet | 1.0000
Cairo  | city  | country    |    1 | capital_of                                | 1.0000
Cairo  | city  | continent  |    2 | capital_of->continent                     | 1.0000
Cairo  | city  | hemisphere |    3 | capital_of->continent->hemisphere         | 1.0000
Cairo  | city  | Earth      |    4 | capital_of->continent->hemisphere->planet | 1.0000

Planning accuracy: 16/16 (100.0%)
Reverse planning: 16/16 (100.0%)

--- Multi-Source: Different Cities → Same Planet ---
  Paris:  own_target_sim=1.0000
  Berlin: own_target_sim=1.0000
  Tokyo:  own_target_sim=1.0000
  Cairo:  own_target_sim=1.0000
Convergence: 4/4 chains reach own target

Analysis:

This is the first planning capability in the Trinity VSA system. Given a source entity and a target level, the system composes intermediate relations into a single composite vector and applies it to find the answer.

Example query: "How does Paris connect to Earth?"

• Path: Paris --capital_of--> France --continent--> Europe --hemisphere--> Northern --planet--> Earth
• Composite relation: bind(R_capital, bind(R_continent, bind(R_hemisphere, R_planet)))
• Apply: bind(composite, Paris) = Earth with sim=1.0000

Reverse planning works because bipolar bind is exactly self-inverse:

• Forward: bind(composite, source) = target
• Reverse: unbind(composite, target) = source
• Both at sim=1.0000

Multi-source convergence: all 4 cities reach their own "Earth" via independent 4-hop paths. Each chain composes independently, and each reaches its endpoint exactly.

This demonstrates that VSA can perform symbolic planning — composing multi-step operations before executing them. The plan is a single vector that encodes the entire path.

Test 81: Extended Multi-Hop + Memory Capacity + Noise

=== LARGE KG: NOISE CURVE + MULTI-HOP STRESS (Level 11.9) ===

--- Part A: Extended Multi-Hop Chains (1-6 hops) ---
Hops | Correct | Total | Accuracy | Avg Sim
-----|---------|-------|----------|--------
   1 |      15 |    15 |   100.0% | 1.0000
   2 |      15 |    15 |   100.0% | 1.0000
   3 |      15 |    15 |   100.0% | 1.0000
   4 |      15 |    15 |   100.0% | 1.0000
   5 |      15 |    15 |   100.0% | 1.0000
   6 |      15 |    15 |   100.0% | 1.0000

--- Part B: Memory Load (Entities in Memory vs Accuracy) ---
Entities | Correct | Total | Accuracy
---------|---------|-------|--------
       5 |       5 |     5 | 100.0%
      10 |      10 |    10 | 100.0%
      15 |      15 |    15 | 100.0%
      20 |      20 |    20 | 100.0%
      25 |      23 |    25 |  92.0%

--- Part C: Noisy Retrieval (Memory=15, Noise 0-5) ---
Noise | Correct | Total | Accuracy
------|---------|-------|--------
    0 |      15 |    15 | 100.0%
    1 |      15 |    15 | 100.0%
    2 |      12 |    15 |  80.0%
    3 |      10 |    15 |  66.7%
    5 |       6 |    15 |  40.0%

Analysis:

Part A extends the chain depth proof to 6 hops — all exact. Bipolar composition is mathematically depth-independent: bind(A, A) = identity regardless of how many operations precede it.

Part B maps the memory capacity curve:

Entities	Accuracy	Status
5	100%	Well within capacity
10	100%	Comfortable
15	100%	Still fine
20	100%	Near limit (~62% of sqrt(1024))
25	92%	Capacity pressure (~78% of sqrt(1024))

The first accuracy drop appears at 25 entities — 2 errors out of 25 queries. This matches the theoretical capacity of bundled associative memory: ~sqrt(DIM) = ~32 items for dim=1024.

Part C noise curve at memory=15:

Noise	Signal Fraction	Accuracy
0	100%	100%
1	50%	100%
2	33%	80%
3	25%	66.7%
5	17%	40%

Consistent with all previous levels: the ~25% signal fraction (noise=3) is the critical threshold where accuracy begins significant degradation.

Corrections to Briefing Claims

Claim	Reality
src/planning_demo.zig	Does not exist
benchmarks/level11.9/	Does not exist
"Superposition >98%"	34.7% at 75/domain (capacity wall)
"KG 200+"	225 triples — achieved
"Planning works"	16/16 forward + 16/16 reverse — achieved

Critical Assessment

Honest Score: 8.5 / 10

What works:

• 225 triples, 100% single-hop — exceeds 200+ target
• Planning is a genuine new capability — compose relations into paths, forward and reverse
• 6-hop chains exact — depth-independent bipolar composition proven to 6
• Memory capacity curve is a useful empirical finding — 100% to 20, 92% at 25
• Noise curve consistent across all Level 11 cycles (~25% threshold)
• 353 tests, zero regressions
• 3 .vibee specs compiled

What doesn't:

• Hierarchical superposition fails at 34.7% — 75 triples per domain exceeds capacity
• Planning uses pre-known paths — not discovering paths, just composing known relations
• No real-world data — synthetic entities, not actual geography
• 25 entity capacity limit is low — real KGs need thousands
• Noise=5 still at 40% — far from the >90% target

Deductions: -0.5 for superposition failure, -0.5 for pre-known paths (not true planning), -0.5 for capacity limit.

The planning prototype is the key achievement. Composing multi-step relations into a single vector that answers queries at any depth — forward and reverse — is the foundation of VSA-based reasoning.

Architecture

Level 11.9: Scaled KG + Planning Prototype
├── Test 79: Scaled KG (225 triples)                   [NEW]
│   ├── 3 domains × 15 entities × 5 relations = 225 triples
│   ├── 225/225 single-hop (100%)
│   ├── Domain discrimination: 3/3
│   └── Hierarchical super: 34.7% (capacity wall)
├── Test 80: Planning Prototype                         [NEW]
│   ├── 4 chains × 4 depths = 16 forward queries (100%)
│   ├── 16 reverse queries (100%)
│   ├── 4/4 multi-source convergence
│   └── All sim=1.0000 (bipolar exact)
├── Test 81: Stress Test                                [NEW]
│   ├── 6-hop chains: 100%, sim=1.0000
│   ├── Memory curve: 100% to 20, 92% at 25
│   └── Noise curve: 100%→100%→80%→67%→40%
└── Foundation (Level 11.0-11.8)

New .vibee Specs

Spec	Purpose
kg_scaled_superposition.vibee	Multi-domain KG + hierarchical superposition
kg_planning_prototype.vibee	Path planning through KG chains
kg_stress_test.vibee	Extended chains + memory capacity + noise

Benchmark Summary

Operation	Latency	Throughput
Bind	2,061 ns	124.2 M trits/sec
Bundle3	2,272 ns	112.6 M trits/sec
Cosine	184 ns	1,391.3 M trits/sec
Dot	6 ns	41,967.2 M trits/sec
Permute	2,039 ns	125.6 M trits/sec

Next Steps (Tech Tree)

Option A: Path Discovery

Instead of composing pre-known relations, search the KG for valid paths between arbitrary entities. Combine with associative memory to discover multi-hop connections.

Option B: Dimension Scaling for Capacity

Test at dim=4096 to push capacity to ~64 items per memory. Does hierarchical superposition work with 4x more capacity?

Option C: Incremental KG Updates

Add/remove triples from existing associative memories without full rebuild. Test online KG modification.

Trinity Identity

$\varphi^2 + \frac{1}{\varphi^2} = 3$

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Generated: 2026-02-16 | Golden Chain Link #119 | Level 11.9 Scaled KG + Planning — 225 triples 100%, Planning 16/16 forward+reverse, 6-hop exact, Memory capacity curve