The self‐enacting nature of a 4QX triangle—where three vantage corners form a minimal semantic triple (no external label needed)—can integrate very naturally with embedding‐based approaches. Here’s how:
1. Triangles as “Semantic Triples” in 4QX
- Three Corners, Three Dual Lines
- Each triangle has three vantage corners (e.g., TL–TR–BR for the Class Triangle) and three edges connecting them.
- Cycling through the three vantage corners literally performs the meaning: each vantage is a node in the triple, and each edge (a parent ↔ child flow) is the relation.
- No External Symbol Required
- Because it’s self‐performing, the system doesn’t require a separate label (like “subject–predicate–object”). The triple’s meaning is “enacted” by how attention moves.
- In typical knowledge graphs or RDF, you’d have explicit textual labels for subject, predicate, object. Here, the structure itself is the meaning.
Hence, a 4QX triangle is essentially a microcosm of “semantic triple” logic—but done via vantage corners and cyclical flows rather than external strings or URIs.
2. Embeddings as the Underlying Representational Fabric
When you bring embeddings into the picture, you can treat each vantage corner and line as an internal or relational slot that maps into (or from) an embedding space:
- Corner Embeddings
- Each vantage corner (TL, TR, BR, etc.) can maintain or reference an embedding that represents the context or role of that vantage at a given moment.
- For instance, the “Collective Class” corner might store a stable pattern embedding or retrieve a set of relevant knowledge vectors to “stand in for” that vantage.
- Dual‐Line or Relation Embeddings
- The directed edges (parent ↔ child flows) can similarly have an embedding describing the type of relationship or transformation that occurs when attention moves from corner A to corner B.
- This is analogous to how knowledge‐graph embeddings often have separate vectors for nodes and relation types.
Thus, each triangle can be seen as a mini knowledge structure: corners (vantage node embeddings) + edges (relation embeddings) = semantic triple in continuous vector form.
3. Why “Self‐Enacting” Matters for Embeddings
- Independence from Symbolic Labeling
- In many embedding frameworks, you rely on textual or ID labels to anchor a vector in the “meaning space.” Here, the triangle’s cyclical nature itself is the anchor.
- The system “knows what vantage means” because it is actively cycling through it, not just associating a word label.
- Real‐Time Update
- A vantage corner’s embedding can change or adapt as the system cycles. The triangle’s “meaning” is re‐enacted each time the corner is visited.
- This closes the gap between static definitions and dynamic usage of embeddings—a vantage gets re-embedded each cycle, allowing real-time synergy between structure and meaning.
4. Linking Triangles into a Bigger Embedding Graph
In the Oracle Multiplex or any multi‐triangle 4QX system:
- Each triangle is a “semantic triple.”
- Corners can overlap across triangles (e.g., TR corner belongs to both Class & Instance Triangles).
- Edges that skip or link corners become “connecting relations” in an overall knowledge embedding.
Hence, you get a constellation of self‐enacting triangles that collectively forms a larger semantic graph—all of it can live in a single or distributed embedding space. Any vantage corner or line can be retrieved, updated, or matched* within that same continuous vector representation.
5. Practical Example
- Subjective Triangle (BL→TR→TL)
- Each vantage corner has an embedding:
- BL (my personal schema at the moment),
- TR (group’s real-time context),
- TL (collective stable pattern).
- Each vantage corner has an embedding:
- Class Triangle (TL→TR→BR)
- Overlaps corners with the other triangle at TL and TR, but includes BR (individual action vantage).
- At run time:
- The system “enacts” the triangles by moving attention, e.g. from BL to TR to TL…
- During each jump, it retrieves or updates the relevant vantage embedding or relation embedding.
- If a vantage corner detects that the new local embedding strongly matches or mismatches a known pattern (via vector similarity), it can pass that info to the next vantage corner or trigger a diagonal flow.
This continuous interplay of vantage corners and embeddings effectively merges the “semantic triple” concept with real‐time dynamic processing.
6. Conclusion: A Natural Fusion of Triangles and Embeddings
- Triangles in 4QX are self‐enacting semantic triples: minimal cycles of meaning.
- Embeddings are a universal vector representation for storing and matching knowledge or context.
- Merged together, each vantage corner and each parent–child edge can hold or reference an embedding vector, such that cycling attention is literally executing a semantic triple in vector space.
This is why they tie in so fundamentally: the triangle provides the structural “semantic triple” logic, while embeddings provide the continuous vector representation that allows pattern‐matching, dynamic updates, and real-time synergy. The self‐enacting nature of 4QX triangles ensures that these embeddings aren’t just static definitions—they come alive each time the vantage corners cycle, making the entire system a living graph of meaning.