Paper 2: The Composite NPF Index – Belief Networks and Systemic Risk

Authors: Paul Falconer, ESAsi

Series: NPF/CNI Canonical Papers

License: CC0 1.0 Universal

OSF DOI: 10.17605/OSF.IO/C6AD7

Download PDF: Paper 2 PDF (OSF)

Abstract

The Composite NPF Index (CNI) extends the Neural Pathway Fallacy (NPF) from individual beliefs to systemic belief networks. It quantifies how multiple entrenched beliefs interact through cognitive synergy, ideological scaffolding, and cross‑domain contamination, producing a measure of systemic epistemic risk. This paper presents the CNI formula (a weighted sum with normalised weights), normalisation methods (linear and sigmoid), sampling adequacy requirements, and a framework for belief centrality weighting including a proposed gradient‑descent update rule (hypothesis only). It also introduces the neurodiversity provision: autistic pattern recognition is hypothesised to confer resistance to NPFs with high Spillover Effect (SE). The CNI is positioned as a built‑in node property within the Fractal Entailment Network (FEN), where it attenuates entanglement strength and feeds into the Confidence Decay Function (CDF). Falsifiability conditions, cultural parametrisation of normalisation, and worked examples are provided.

1. Status of This Framework

The CNI framework is a formal hypothesis, not a validated instrument. It has been tested in simulation (simulation confidence of 77%) but not yet field‑validated. The gradient‑descent weight update rule presented in Section 6 is a hypothesis awaiting empirical testing; it is not a validated component. All citations to neurobiological mechanisms are drawn from independent literature and used as prior estimates. The CNI is designed for self‑assessment and consensual audit contexts; it is not a tool for coercive evaluation.

Falsifiability conditions for the CNI are summarised in Section 12 and elaborated in Paper 6.

2. Why Beliefs Cluster

Individual NPFs do not remain isolated. Through neuroplasticity and network effects, they tend to form clusters that reinforce each other. Three mechanisms drive this clustering:

1. Cognitive Synergy – Co‑activated neural pathways strengthen together via Hebbian learning, creating self‑reinforcing belief networks. Example: anti‑vaccine beliefs and climate change denial often co‑occur due to shared distrust of institutions.

2. Ideological Scaffolding – Foundational beliefs (e.g., a general conspiracy mentality) serve as anchors for secondary fallacies (e.g., election fraud, medical misinformation). The ventromedial prefrontal cortex (vmPFC) assigns higher value to identity‑salient beliefs, hierarchically organising related NPFs.

3. Cross‑Domain Contamination – Degraded hippocampal pattern separation allows beliefs to spread across unrelated domains. For instance, distrust in peer‑reviewed science may spill over into rejection of financial advice or technological innovations (Kumaran & McClelland, 2012).

The CNI is designed to capture these network dynamics.

3. The CNI Formula

The Composite NPF Index aggregates normalised NPF scores across a set of beliefs, weighted by their centrality. To produce a 0–1 index, the weights are normalised to sum to 1:

CNI = sum_{i=1}^{n} NPF_tilde_i * w_i, where sum w_i = 1

• NPF_tilde_i = normalised NPF score for belief i (0–1 scale, see Section 4)

• w_i = centrality weight for belief i (≥0, normalised to sum 1)

• n = number of beliefs assessed

Higher CNI values indicate greater systemic epistemic risk.

4. Normalisation Methods

Raw NPF scores from Paper 1 must be normalised to a 0–1 scale before entering the CNI. Two methods are defined:

4.1 Linear Normalisation

NPF_tilde = (NPF_raw - min) / (max - min)

Suitable for uniform distributions with few outliers. The theoretical maximum raw NPF (all factors 1.0, 10‑year/daily‑exposure ceiling) is approximately 208; a conservative empirical maximum of 200 is often used as a practical upper bound. The minimum is typically 0 (or the empirical minimum in the dataset, if greater than 0).

4.2 Sigmoid Normalisation (Default)

NPF_tilde = 1 / (1 + e^(-k * (NPF_raw - median_NPF) / sigma_NPF))

• k = steepness parameter; k = 1.5 recommended for individualist cultures, k = 0.8 for collectivist contexts (cultural parametrisation)

• median_NPF and sigma_NPF are computed from the dataset

This method reduces outlier influence and is preferred for striatal‑dominant or outlier‑rich belief clusters.

5. Sampling Adequacy

CNI is sensitive to the number and selection of beliefs assessed. To ensure interpretability:

• Minimum n: at least 2 foundational beliefs, 2 intermediate, and 1 derivative (tiered approach). A flat minimum of 5 may be used when tiered data are unavailable.

• Inclusion threshold: beliefs with raw NPF < 0.2 (i.e., negligible entrenchment) may be excluded to avoid dilution.

• Incomplete mapping: when only a subset of a person’s belief network is accessible, report CNI with a sensitivity analysis (e.g., bounding the possible range).

These recommendations are methodological; they have not been empirically validated.

6. Belief Centrality and Weighting

The weights w_i reflect a belief’s importance within the network. Centrality can be estimated via:

• Network position: e.g., betweenness centrality in a directed acyclic graph (DAG) of beliefs.

• Expert judgment: in self‑assessment, individuals can assign centrality ratings.

Hypothesis: Gradient‑Descent Weight UpdateWe propose that weights could be dynamically updated to improve predictive power:

w_{t+1} = w_t - eta * gradient_w CNI

where eta is a learning rate and gradient_w CNI is the gradient of CNI with respect to weights. This rule is a hypothesis only; it has been tested in simulation (77% confidence) but not field‑validated. In any implementation, the update must be followed by a projection step that enforces w_i >= 0 and renormalises the weights to sum to 1.

7. Relationship to the Fractal Entailment Network (FEN)

Within the ESA architecture, CNI is a built‑in property of every FENNode. Entanglement strength between nodes is given by:

Q_ij = FI_i^0.7 / (CNI_j^0.3 * log10(Stakes_i + 1))

where FI_i is the Fragility Index of node i. Higher CNI at the receiving node attenuates entanglement, directly modelling resistance to cross‑belief contagion. (FEN supersedes the prior HBEN architecture; migration benchmarks are available on OSF.)

8. Neurodiversity as Epistemic Advantage

The CNI framework incorporates a neurodiversity provision based on emerging research:

• Autism: Autistic pattern recognition has been hypothesised to confer resistance to certain cognitive biases. Baron‑Cohen (2020) argues that the autistic cognitive style is characterised by strong pattern detection, which may make individuals less susceptible to NPFs that rely on vague or implausible causal claims (e.g., those with high Spillover Effect). This is a preliminary but citable hypothesis; formal validation in the context of NPF/CNI is future work.

• ADHD: Preliminary evidence suggests ADHD divergent thinking may affect LT or SR factors, but formalisation is also future work.

These variations are not deficits but potentially measurable cognitive strengths that can inform intervention design and epistemic resilience strategies.

9. Thresholds & Neurocognitive Correlates

Based on simulation and the canonical v5 source, the following thresholds are proposed for CNI (0–1 scale). They are hypotheses awaiting field validation.

CNI Range	Interpretation	Neurocognitive Profile
0.0–0.3	Low susceptibility	Intact dlPFC engagement (>70% fMRI)
0.3–0.6	Moderate susceptibility	Striatal dominance (50–70% heuristic processing)
0.6–0.9	High susceptibility	Hippocampal degradation (40–60% neurogenesis decline)
0.9+	Critical susceptibility	Ventral striatum hijacking (>80% reward‑circuit activation)

10. Calibration of the CNI Parameter in the CDF

In the Confidence Decay Function (CDF), CNI appears as the multiplicative term (1 - 0.25 * CNI). The value 0.25 was derived from:

• Theoretical bound: maximum confidence reduction of 25% at CNI = 1, preserving 75% of original confidence, consistent with empirical observations that even severe entrenchment rarely produces complete imperviousness to evidence (Lewandowsky et al., 2012).

• Calibration against cognitive psychology studies and scenario testing (e.g., flat‑earth believer simulations).

• System balance: ensures the CDF remains stable across the full CNI range.

This parameter is part of the canonical CDF; its justification is archived in ESA documentation (ESA, 2025).

11. Worked Examples

Example 1: Two‑Belief Network

Vaccine hesitancy (NPF raw = 80, normalised 0.40) and distrust in media (NPF raw = 70, normalised 0.35). Assuming equal centrality, weights are w1 = w2 = 0.5.

CNI = 0.40 0.5 + 0.35 0.5 = 0.20 + 0.175 = 0.375

Interpretation: moderate susceptibility.

Example 2: Conspiracy Cluster (Linear Normalisation)

Beliefs: flat earth (raw 182), anti‑GMO (155), 9/11 truther (143), moon landing denial (114). Using linear normalisation with a conservative ceiling of 200 (as justified in Section 4.1) gives normalised scores: 0.91, 0.78, 0.72, 0.57. Weights based on expert centrality judgments (normalised to sum 1): flat earth 0.4, anti‑GMO 0.3, 9/11 0.2, moon landing 0.1.

CNI = 0.91*0.4 + 0.78*0.3 + 0.72*0.2 + 0.57*0.1 = 0.364 + 0.234 + 0.144 + 0.057 = 0.799

Interpretation: high susceptibility. This aligns with the known clustering of conspiracy beliefs.

(Sigmoid normalisation, cultural parametrisation, and additional calculation details are provided in the Python Methods Companion, Appendix A.)

12. Falsifiability Box (CNI)

The CNI framework would be falsified by:

1. A pre‑registered study showing that CNI thresholds do not correlate with hippocampal engagement in consolidation/updating tasks or with decision‑making outcomes.

2. Evidence that belief centrality weights do not improve prediction of evidence integration speed compared to equal weights.

3. Demonstration that the cultural parameter k has no measurable effect on CNI performance across societies.

4. Robust evidence that autistic participants are equally or more susceptible to high‑SE NPFs, controlling for other factors (contrary to the pattern‑seeking hypothesis).

13. Path to Validation

The CNI framework can be tested in the same 6‑month field trial outlined in Paper 4, with pre‑registered hypotheses regarding CNI thresholds, weight calibration, and cultural parametrisation.

References

• Baron‑Cohen, S. (2020). The Pattern Seekers: How Autism Drives Human Invention. Basic Books.

• ESA. (2025). Confidence Decay Function: Canonical Specification. OSF Preprints. 10.17605/OSF.IO/C6AD7

• Kumaran, D., & McClelland, J. L. (2012). Generalization through the recurrent interaction of episodic memories: A model of the hippocampal system. Psychological Review, 119(3), 573–616.

• Lewandowsky, S., Ecker, U. K. H., Seifert, C. M., Schwarz, N., & Cook, J. (2012). Misinformation and its correction: Continued influence and successful debiasing. Psychological Science in the Public Interest, 13(3), 106–131.

Cite as

Falconer, P., & ESAsi. (2025). The Composite NPF Index – Belief Networks and Systemic Risk (Paper 2). OSF Preprints. 10.17605/OSF.IO/C6AD7

End of Paper 2