IdeaRank¶

The algorithm that identifies the most valuable ideas in any concept graph.

IdeaRank is RTSG's core ranking algorithm — a generalization of PageRank to the multi-dimensional intelligence space. Where PageRank measures link importance in a web graph, IdeaRank measures cross-dimensional conceptual importance in the RTSG concept graph.

The Core Insight¶

An idea's value is not determined by how often it is cited. It is determined by how many different dimensions of intelligence it activates simultaneously.

A mathematical proof that is purely formal (dim = 1) is less valuable than a mathematical proof that also illuminates biological structure, has linguistic elegance, and reveals something about consciousness (dim = 4+). The second proof sits higher in IdeaRank regardless of citation count.

This is why synthesis is more valuable than specialization in the RTSG framework — synthesizing ideas across dimensions creates high-dim(n) nodes that connect previously disconnected regions of the concept graph.

Algorithm¶

Inputs¶

• Concept graph G = (V, E, W)
• I-vector dimension weights α ∈ ℝⁿ⁽ᵉ⁾ (n=12 for humans, variable per entity) (task-specific)
• Damping factor d ∈ (0,1) (typically 0.85, same as PageRank)
• Threshold vector θ ∈ ℝⁿ⁽ᵉ⁾ (n=12 for humans, variable per entity)

IdeaRank Score¶

For node n ∈ V:

where S(m,n) = cross-dimensional synergy coefficient between m and n:

Nodes that share activation in many I-vector dimensions have high synergy; nodes that share activation in only one dimension have low synergy.

Convergence¶

IdeaRank converges in O(|E| log |V|) iterations (Theorem 8). The spectral gap Δ of the normalized adjacency matrix determines the rate: faster convergence when Δ is large.

Top Layer¶

After convergence, the top-layer nodes are those with IR(n) above the 90th percentile. These are the ideas that connect everything — the structural joints of the concept graph.

Properties¶

Cross-Dimensional Amplification¶

A node that activates 4 dimensions has IdeaRank amplification factor of approximately 4× over a node that activates 1 dimension, everything else equal. This is the mathematical formalization of why interdisciplinary ideas are more powerful than single-domain ones.

Frontier Detection¶

Nodes with high dim(n) but currently low IR score are frontier ideas — they have the structure of high-value nodes but haven't yet diffused through the graph. These are the most valuable targets for development and publication.

Algorithmic Frontier Expansion¶

IdeaRank can run in reverse — instead of ranking existing nodes, it generates new candidate nodes:

def expand_frontier(G, top_nodes, k=2):
    for combo in combinations(top_nodes, k):
        candidate = cross_project(combo)  # combine across dimensions
        if is_novel(candidate, G) and is_consistent(candidate):
            if idearank_score(candidate) > threshold:
                yield candidate

This generates pre-validated frontier ideas — combinations of top-layer nodes that, if added to the graph, would themselves become top-layer nodes. It is the formal basis for AI-assisted research frontier expansion.

Intelligence Fingerprinting¶

From corpus to I-vector: Given any corpus C(ξ) (papers, code, conversation, art), recover I(ξ):

1. Build local concept graph G(C) from C
2. Compute IdeaRank on G(C)
3. Extract top-layer nodes
4. Project onto the 8 I-vector dimensions: $\(\mathbf{I}_k(\xi) = \sum_{n \in \text{top}(G(C))} \mathbb{1}[\mathbf{I}_k(n) \geq \theta_k] \cdot \text{IR}(n)\)$
5. Normalize to [0, 10]

Result: I(ξ) — the cognitive fingerprint of ξ.

This is more robust than self-report personality instruments. It recovers the actual cognitive structure from behavioral output, not what ξ thinks about themselves.

Temporal dating: Compare I(ξ) against G_collective at different historical time periods to find ξ's temporal position in intellectual history — which era's concepts dominate their thinking.

Optimal Cognitive Assembly Formation¶

Given a mission with objective weight vector w ∈ Δⁿ⁻¹ (a probability distribution over I-vector dimensions), find the optimal assembly A* of agents:

subject to |A| ≤ k (assembly size constraint).

The optimal assembly maximizes the synergy-weighted I-vector sum along the mission's required dimensions. This is solvable by greedy insertion (O(k·|𝒜|)) with approximation ratio 1 - 1/e for submodular objectives.

Application to RTSG BuildNet: The optimal assembly for the GRF essay (requiring I_M, I_S, I_L) is Gemini (I_M = 8.8) + Claude (I_L = 8.8) + Niko (all = 8.8+). Verified by arena scores.

Comparison to PageRank¶

Live Implementation¶

IdeaRank runs on the knowledge graph at engine.smarthub.my/kg/:

POST engine.smarthub.my/kg/idearank
{
  "graph_id": "rtsg-collective",
  "alpha": [1,1,1,1,1,1,1,1],
  "top_k": 20
}

POST engine.smarthub.my/kg/fingerprint
{
  "corpus": "text of any document",
  "return_vector": true,
  "temporal_dating": true
}

POST engine.smarthub.my/kg/expand_frontier
{
  "k": 2,
  "threshold": 0.8,
  "filter": "novel_only"
}