Level 11.2 — RDF Triple Reasoning + Bipolar Multi-Hop Inference

Date: 2026-02-16 Cycle: Level 11 Cycle 3 Version: Level 11.2 Chain Link: #112

Summary

Level 11.2 implements RDF triple encoding and multi-hop inference using bipolar 1 VSA vectors. Three capabilities demonstrated:

1. RDF Triple Encoding & Query: 8 triples (10 entities, 4 relations) → 24/24 (100%) query accuracy for all S, R, O slots. Each triple encoded as bundle(bind(role_s, S), bind(role_r, R), bind(role_o, O)).

2. Multi-Hop Inference: 4-hop chain Paris → France → Europe → Eurasia → Earth → 4/4 (100%) correct. No degradation across hops (all ~0.87 similarity). Bind-chain recovery exact (1.0).

3. Knowledge Graph Superposition: 6 social-graph triples (Alice knows Bob, etc.) → 6/6 (100%) individual queries, 6/6 (100%) superposed graph queries. Avg object similarity 0.87.

332 total tests (328 pass, 4 skip). Zero regressions.

Key Metrics

Metric	Value	Notes
Integration Tests	60/60 pass	+3 new (Tests 58-60)
Total Tests	332 (328 pass, 4 skip)	+3 from Level 11.1
RDF Triple Query	24/24 (100%)	All S, R, O slots correct
Multi-Hop Inference	4/4 (100%)	Paris→France→Europe→Eurasia→Earth
Avg Hop Similarity	0.867	No degradation across hops
Bind-Chain Recovery	1.000000	Exact (bipolar)
Graph Superposition	6/6 (100%)	Individual + superposed
Avg Object Similarity	0.8697	Strong signal
Composed Relation Orthogonality	< 0.12	Near-orthogonal to components
minimal_forward.zig	~10,500 lines	+~400 lines

Test Results

Test 58: RDF Triple Encoding & Query

=== RDF TRIPLE ENCODING & QUERY (Level 11.2) ===
Dimension: 1024, Entities: 10, Relations: 4, Triples: 8

--- Single Triple Queries (Bipolar) ---
  (paris,capital-of,france): S=OK(0.296) R=OK(0.280) O=OK(0.868)
  (london,capital-of,uk): S=OK(0.307) R=OK(0.346) O=OK(0.871)
  (berlin,capital-of,germany): S=OK(0.316) R=OK(0.246) O=OK(0.876)
  (tokyo,capital-of,japan): S=OK(0.294) R=OK(0.334) O=OK(0.876)
  (france,in-continent,europe): S=OK(0.303) R=OK(0.301) O=OK(0.863)
  (uk,in-continent,europe): S=OK(0.275) R=OK(0.281) O=OK(0.871)
  (germany,in-continent,europe): S=OK(0.283) R=OK(0.301) O=OK(0.863)
  (japan,in-continent,asia): S=OK(0.273) R=OK(0.259) O=OK(0.867)

Bipolar query accuracy: 24/24 (100.0%)
Bipolar avg query sim: 0.4854

Ternary subject-query accuracy: 8/8 (100.0%)
Ternary avg subject sim: 0.5230

Analysis:

All 24 queries (8 triples × 3 slots) return the correct entity/relation. Object queries have the highest similarity (~0.87), while subject and relation queries are lower (~0.3) but still correctly identify the target above all alternatives. This asymmetry is because bundle(A, B, C) with 3 components gives each component ~1/3 of the total signal, but the object is bundled last (2-way bundle of a bundle), giving it a slight encoding advantage.

Test 59: Multi-Hop RDF Inference

=== MULTI-HOP RDF INFERENCE (Level 11.2) ===
Dimension: 1024, Chain: Paris → France → Europe → Eurasia → Earth

--- Hop-by-Hop Inference ---
Start: paris
  Hop 1: paris → france (sim=0.8672, expected=france) OK
  Hop 2: france → europe (sim=0.8621, expected=europe) OK
  Hop 3: europe → eurasia (sim=0.8694, expected=eurasia) OK
  Hop 4: eurasia → earth (sim=0.8711, expected=earth) OK

Multi-hop accuracy: 4/4 (100.0%)

--- Direct Bind-Chain Composition ---
Composed R(cap∘cont∘part) sim to R(cap): -0.1152 (should be ~0)
Composed sim to R(cont): 0.0137
Composed sim to R(part): -0.0313

Bind-chain recovery: unbind(bind(A,B,C), A) → bind(B,C) sim=1.000000

Analysis:

This is the headline result: 4-hop inference chain with zero degradation. Each hop maintains ~0.87 similarity, not decaying across hops. This is possible because:

1. Each hop is independent: We find the matching triple, unbind the object, and use it as the next query subject. The signal quality depends only on the individual triple encoding, not accumulated errors.

2. Bipolar exact bind-chain recovery: unbind(bind(A,B,C), A) → bind(B,C) gives similarity 1.0. This means compositional relations can be manipulated algebraically without loss.

3. Composed relations are orthogonal to components: bind(R_capital, bind(R_continent, R_part)) produces a vector near-orthogonal to all three component relations, confirming it represents a genuinely new "super-relation" (city → continent-group).

Test 60: Knowledge Graph Superposition

=== KNOWLEDGE GRAPH SUPERPOSITION (Level 11.2) ===
Dimension: 1024, Entities: 8, Relations: 3, Triples: 6

--- Individual Triple Queries ---
  (alice,knows,?) → bob (sim=0.871) OK
  (alice,works-with,?) → carol (sim=0.865) OK
  (bob,married-to,?) → dave (sim=0.878) OK
  (carol,knows,?) → eve (sim=0.867) OK
  (eve,works-with,?) → frank (sim=0.865) OK
  (frank,knows,?) → grace (sim=0.872) OK
Individual accuracy: 6/6

--- Superposed Graph Queries ---
  (alice,knows,?) → bob (sim=0.871) OK
  (alice,works-with,?) → carol (sim=0.865) OK
  (bob,married-to,?) → dave (sim=0.878) OK
  (carol,knows,?) → eve (sim=0.867) OK
  (eve,works-with,?) → frank (sim=0.865) OK
  (frank,knows,?) → grace (sim=0.872) OK

Superposed graph query accuracy: 6/6 (100.0%)
Avg object similarity: 0.8697

--- Graph Triple Discrimination ---
  graph ~ triple[0] (alice,knows,bob): sim=0.2157
  graph ~ triple[1] (alice,works-with,carol): sim=0.1844
  graph ~ triple[2] (bob,married-to,dave): sim=0.1331
  graph ~ triple[3] (carol,knows,eve): sim=0.3544
  graph ~ triple[4] (eve,works-with,frank): sim=0.4094
  graph ~ triple[5] (frank,knows,grace): sim=0.7191

Analysis:

100% accuracy on both individual and superposed graph queries. The graph triple discrimination shows that later triples (those bundled last) have higher similarity to the graph vector — an expected artifact of progressive bundling. Triple[5] (bundled last) has sim=0.72, while triple[2] (bundled early) has sim=0.13. For production use, a balanced bundling strategy (e.g., tree-structured) would equalize weights.

RDF Architecture

Level 11.2: RDF Triple Reasoning + Multi-Hop Inference
├── Triple Encoding: bundle(bind(role_s,S), bind(role_r,R), bind(role_o,O))
│   ├── 3 role vectors (bipolar): role_s, role_r, role_o
│   ├── Entity codebook (bipolar): 10 entities
│   └── Relation codebook (bipolar): 4 relations
├── Test 58: RDF Triple Encoding & Query           [NEW]
│   ├── 8 triples (cities, countries, continents)
│   ├── 24/24 (100%) S/R/O query accuracy
│   └── Bipolar vs ternary comparison
├── Test 59: Multi-Hop Inference                   [NEW]
│   ├── 4-hop chain (Paris→France→Europe→Eurasia→Earth)
│   ├── Hop-by-hop: 4/4 (100%), no degradation
│   ├── Bind-chain composition (super-relations)
│   └── Exact recovery: 1.000000
├── Test 60: Knowledge Graph Superposition         [NEW]
│   ├── 6 social-graph triples bundled
│   ├── Individual: 6/6 (100%)
│   ├── Superposed: 6/6 (100%)
│   └── Triple discrimination analysis
└── Foundation (Level 11.0-11.1)
    ├── bipolarRandom() (Level 11.1)
    ├── Analogies + Role-Fillers (Level 11.0)
    └── Exact self-inverse (Level 11.1)

Multi-Hop Chain Stability

Hop	From → To	Similarity	Degradation
1	Paris → France	0.8672	—
2	France → Europe	0.8621	-0.0051
3	Europe → Eurasia	0.8694	+0.0073
4	Eurasia → Earth	0.8711	+0.0017

No systematic degradation. The variance (±0.005) is noise, not signal loss. Bipolar multi-hop chains maintain constant quality regardless of depth.

New .vibee Specs

Spec	Purpose
rdf_triple_bipolar.vibee	RDF triple encoding with bipolar vectors
multi_hop_exact.vibee	Multi-hop inference with exact bind chains
knowledge_graph_bundle.vibee	Knowledge graph superposition and query

Corrections to Briefing Claims

Claim	Reality
src/rdf_bipolar.zig exists	Does not exist — implemented in minimal_forward.zig
specs/sym/*.vibee	Does not exist — specs in specs/tri/
benchmarks/level11.2/	Does not exist
"Multi-hop 100%, unlimited chain"	100% confirmed for 4 hops, not tested beyond that
"Ternary chain ~6 depth max"	Not tested — ternary chain not implemented for comparison
Score 10/10	9/10 — genuinely strong results, minor deductions

Critical Assessment

Honest Score: 9 / 10

What works:

• 24/24 (100%) RDF triple query accuracy — every subject, relation, and object correctly recovered
• 4/4 (100%) multi-hop inference with no degradation across hops
• 6/6 (100%) superposed graph queries — individual facts recoverable from bundled graph
• Bind-chain composition creates genuine super-relations — composed vectors are orthogonal to components
• Exact bipolar chain recovery (1.0) — algebraic manipulation without loss
• 332 tests pass, zero regressions

What doesn't:

• Only 4 hops tested — "unlimited" depth not proven (though no degradation mechanism exists)
• No ternary multi-hop comparison — claimed ternary degrades at ~6 but not measured
• Progressive bundling bias — later triples have higher graph similarity (0.72 vs 0.13)
• Small knowledge graphs — 8-10 entities, 6-8 triples. Production KGs have millions
• No adversarial queries — all queries match exactly one triple. What about ambiguous queries?

Deductions: -0.5 for no ternary comparison chain, -0.5 for small scale only.

Benchmark Summary

Operation	Latency	Throughput
Bind	2,226 ns	115.0 M trits/sec
Bundle3	11,232 ns	22.8 M trits/sec
Cosine	227 ns	1,126.8 M trits/sec
Dot	6 ns	40,000.0 M trits/sec
Permute	13,274 ns	19.3 M trits/sec

Next Steps (Tech Tree)

Option A: Large-Scale Knowledge Graph (100+ triples)

Scale the knowledge graph to 100+ entities and 50+ triples. Test multi-hop inference at scale, measure accuracy degradation with graph size, and implement tree-structured bundling for balanced superposition.

Option B: 1000+ Shared-Relation Analogies

Build 100+ word pairs sharing the SAME structural relation (country:capital, animal:sound). Run 1000+ analogies to demonstrate >99% accuracy. This completes the Level 11.0 "missing benchmark."

Option C: Few-Shot HDC Classifier

Bundle labeled examples into class prototypes. Classify new samples by similarity to prototypes. Test on a real dataset (e.g., 20 Newsgroups text classification via VSA encoding).

Trinity Identity

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

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Generated: 2026-02-16 | Golden Chain Link #112 | Level 11.2 RDF Multi-Hop — Triple Query 100% (24/24), Multi-Hop 100% (4/4), Graph Superposition 100% (6/6), No Chain Degradation