Cognitive Nexus Theory: CNT Hazard-Memory Entropy Collapse v1 (powergrid)

This dataset documents the first empirical test of the CNT Hazard-Memory Entropy Collapse hypothesis within Cognitive Nexus Theory (CNT).

CNT models unstable systems in terms of drift geometry and hazard memory: how often a system revisits certain “safe” or “dangerous” configurations as it moves toward collapse. In this release, we define a new quantity, CNT hazard-memory entropy, and apply it to the power grid domain.

For each (system, observable) pair in the CNT Drift Memory Atlas, we build a discrete state space of “safe shells” identified by tuples

s=(window_min,Hmin⁡\*,auc_threshold)s = (\text{window\_min}, H^\*_{\min}, \text{auc\_threshold})s=(window_min,Hmin\*,auc_threshold)

We then estimate a probability distribution over these shells and compute the Shannon entropy

HCNT(system,observable)=−∑spslog⁡ps,H_{\text{CNT}}(\text{system}, \text{observable}) = - \sum_s p_s \log p_s,HCNT(system,observable)=−s∑pslogps,

which we interpret as the entropy of reachable safe drift states for that observable.

In the powergrid system, we compare:

• a baseline driver observable: frequency

• a collapse-like observable: outage

using derived hazard-memory shells from the CNT Drift Memory Atlas. In natural units (nats), we obtain:

• HCNT(powergrid,frequency)=2.840994H_{\text{CNT}}(\text{powergrid}, \text{frequency}) = 2.840994HCNT(powergrid,frequency)=2.840994

• HCNT(powergrid,outage)=2.079442H_{\text{CNT}}(\text{powergrid}, \text{outage}) = 2.079442HCNT(powergrid,outage)=2.079442

• ΔH=Hbaseline−Hcollapse≈0.761553>0\Delta H = H_\text{baseline} - H_\text{collapse} \approx 0.761553 > 0ΔH=Hbaseline−Hcollapse≈0.761553>0

Thus, the collapse / outage channel occupies a strictly lower-entropy hazard-memory shell than the underlying frequency channel. In CNT language, the menu of reachable safe drift states is narrower in the collapse observable than in the baseline driver. This is consistent with the CNT Hazard-Memory Entropy Collapse hypothesis: as real collapse becomes relevant, the system’s accessible “safe” drift configurations contract.

This v1 release focuses on a single domain (powergrid) where both a continuous driver observable and a discrete collapse proxy are available in the current drift-memory atlas. Cross-domain tests (finance, crypto, seismic, climate, spaceweather) are left explicitly as future work and are not claimed here.

The dataset is part of the broader Cognitive Nexus Theory research program, which studies universal drift and collapse patterns across heterogeneous systems (markets, geophysics, space weather, climate, and more).

Files included

• evidence/CNT_ENTROPY_HAZARD_MEMORY_SUMMARY_v1.csv

  • Per-(system, observable) hazard-memory entropy summary: number of atlas rows, number of distinct safe shells, entropy value HCNTH_{\text{CNT}}HCNT, and a heuristic flag for collapse-like observables.

• evidence/CNT_ENTROPY_DELTA_H_BY_SYSTEM_v1.csv

  • System-level ΔH summaries across observables, including (where applicable) collapse vs baseline contrasts.

• evidence/CNT_ENTROPY_CLAIM_EVIDENCE_v1.csv

  • Focused claim table for systems that have both collapse-like and baseline observables. For this v1, it contains the powergrid row that underpins the claim above.

• plots/CNT_ENTROPY_by_observable_powergrid.png

  • Bar plot of hazard-memory entropy HCNTH_{\text{CNT}}HCNT for the powergrid system, showing the entropy difference between frequency and outage. Collapse-like observables are visually marked.

Data provenance

All derived tables and plots are computed from CNT_DRIFT_MEMORY_ATLAS_v1.csv produced by the cnt_drift_memory_atlas_v1 project in the CNT lab. The atlas itself is published in its own Zenodo record and should be cited together with this release.

Citation (suggested)

Holmes, Caleb (2025). Cognitive Nexus Theory: CNT Hazard-Memory Entropy Collapse v1 (powergrid). CNT Entropy Toolkit dataset. Zenodo. DOI: [to be assigned].