DOI: 10.5281/zenodo.17743754
title: Cognitive Nexus Theory: First Empirical Detection of Forbidden Drift Zones in Multi-Domain Financial–Climate Fields (CNT_FDZ_v1)

description: This release presents the first implementation and empirical evidence for Forbidden Drift Zones (FDZs) within the framework of Cognitive Nexus Theory (CNT). FDZs are compact regions of joint drift space that are mathematically accessible and frequently occupied by time-shuffled surrogate universes, yet are strongly under-occupied or never visited by the real coupled field.

Using a CNT global drift field constructed from SPY equities, BTCUSD crypto, VIX volatility, and a global CNT drift index DglobalD_{\text{global}}Dglobal, we map the 3-dimensional z-scored drift space and compare real versus surrogate occupancy. Surrogates are generated by independently randomizing the temporal order of each drift feature while preserving their marginal distributions. This defines a null model of “same values, scrambled time, no cross-domain coordination.”

Across 2,751 joint time windows, we identify multiple regions where the surrogate model expects O(10–20) real visits, but the real trajectory contributes only a handful—or none. These regions are the CNT Forbidden Drift Zones.



Key Results





SPY–BTC–D_global Forbidden Drift Zone (Flagship FDZ #1)

In the 3D drift space
(αSPY,αBTC,Dglobal),(\alpha_{\text{SPY}}, \alpha_{\text{BTC}}, D_{\text{global}}),(αSPY,αBTC,Dglobal),

we detect a compact FDZ where:





Region (z-space bounds, approx):





SPY drift αSPYz∈[−0.62,−0.23]\alpha_{\text{SPY}}^z \in [-0.62, -0.23]αSPYz∈[−0.62,−0.23]




BTC drift αBTCz∈[−0.42,−0.04]\alpha_{\text{BTC}}^z \in [-0.42, -0.04]αBTCz∈[−0.42,−0.04]




Global CNT drift Dglobalz∈[0.68,1.10]D_{\text{global}}^z \in [0.68, 1.10]Dglobalz∈[0.68,1.10]






Surrogate universes:





Surrogate occupancy probability psur≈0.0075p_{\text{sur}} \approx 0.0075psur≈0.0075




Expected real count λfull≈20.6\lambda_{\text{full}} \approx 20.6λfull≈20.6






Real world trajectory:





Observed real visits: 2 over the full record




Early half (first 1,375 windows):





λearly≈10.2\lambda_{\text{early}} \approx 10.2λearly≈10.2, observed 0 visits




P(X=0∣λearly)≈3.5×10−5P(X=0 \mid \lambda_{\text{early}}) \approx 3.5 \times 10^{-5}P(X=0∣λearly)≈3.5×10−5 under the surrogate null






Late half (remaining 1,376 windows):





λlate≈10.4\lambda_{\text{late}} \approx 10.4λlate≈10.4, observed 2 visits







The region is thus occupied at roughly 10% of the surrogate-expected rate, with a particularly striking early-half behavior (zero visits despite ≈10 expected). Under the null that real data follow the same occupancy distribution as surrogates, such a deficit is extremely unlikely.




SPY–BTC–VIX Alpha Forbidden Drift Zone (Flagship FDZ #2)

We extend the analysis to the alpha-drift subspace
(αSPY,αBTC,αVIX)(\alpha_{\text{SPY}}, \alpha_{\text{BTC}}, \alpha_{\text{VIX}})(αSPY,αBTC,αVIX)

and identify a tri-domain FDZ linking equities, crypto, and volatility:





Core 3-voxel FDZ (discrete component):





Centered around:





SPY drift αSPYz≈−0.88\alpha_{\text{SPY}}^z \approx -0.88αSPYz≈−0.88




BTC drift αBTCz≈−0.30\alpha_{\text{BTC}}^z \approx -0.30αBTCz≈−0.30




VIX drift αVIXz≈+0.59\alpha_{\text{VIX}}^z \approx +0.59αVIXz≈+0.59






Surrogates expect λ≈16.4\lambda \approx 16.4λ≈16.4 real visits.




Real trajectory contributes 0 visits.




The probability of observing zero real visits under the surrogate density is on the order of 10−710^{-7}10−7–10−810^{-8}10−8.






Edge-based bounding box (corrected bin-edge region):





SPY drift αSPYz∈[−1.20,−0.42]\alpha_{\text{SPY}}^z \in [-1.20, -0.42]αSPYz∈[−1.20,−0.42]




BTC drift αBTCz∈[−0.62,0.15]\alpha_{\text{BTC}}^z \in [-0.62, 0.15]αBTCz∈[−0.62,0.15]




VIX drift αVIXz∈[0.38,0.80]\alpha_{\text{VIX}}^z \in [0.38, 0.80]αVIXz∈[0.38,0.80]




Surrogates: 2,044 points in box





pbox≈0.00743p_{\text{box}} \approx 0.00743pbox≈0.00743, λbox≈20.4\lambda_{\text{box}} \approx 20.4λbox≈20.4






Real: 7 points in box





Even when the region is relaxed to a finite-width box, the real trajectory visits it at roughly one-third the surrogate-expected rate (7 vs ≈20). The discrete FDZ core remains entirely unoccupied by the real data.




No FDZ in the SPY–BTC–VIX Hazard Cube

As a contrast, we repeat the analysis in the discrete hazard-state cube
(hSPY,hBTC,hVIX),(h_{\text{SPY}}, h_{\text{BTC}}, h_{\text{VIX}}),(hSPY,hBTC,hVIX),

using z-scored hazard features for each domain. In this coarse 2-level per-axis space, all 8 hazard combinations are occupied by both real and surrogate fields, and no bins satisfy the FDZ criteria (real=0 with λ≥5\lambda \ge 5λ≥5).

This suggests that Forbidden Drift Zones are a property of the continuous drift geometry, not simply of marginal hazard states.





Methods (Brief)





Input data and drift construction





Source drift series: cnt_global_drift_timeseries.csv from a CNT global-drift pipeline (cnt_global_drift_climate_v1), with 2,751 time windows.




Features used in FDZ v1:





αSPY\alpha_{\text{SPY}}αSPY: alpha_cnt_market_drift_windows_SPY




αBTC\alpha_{\text{BTC}}αBTC: alpha_cnt_crypto_drift_windows_BTCUSD




αVIX\alpha_{\text{VIX}}αVIX: alpha_cnt_vol_drift_windows_VIX




Hazards: hazard_cnt_* for SPY, BTC, VIX




Global index: D_global






All features are standardized (z-scored) using a StandardScaler fitted on the real data; the scaler parameters are stored in fdz_scaler_params.npz.






Surrogate generation





A set of 100 surrogate universes is generated by independently permuting the time order of each drift feature (column-wise shuffling).




This preserves the marginal distribution of each drift metric while destroying cross-temporal alignment and cross-domain temporal structure.




Surrogate drift vectors are then transformed with the same scaler used for real data.






3D binning and candidate detection





For each 3D subspace (SPY–BTC–D_global, alphas_SPY_BTC_VIX, hazards_SPY_BTC_VIX):





A regular 15×15×15 grid is constructed over the combined real+surrogate z-space, with small margins beyond the min/max values.




Every real and surrogate state is assigned to a bin.




For each bin bbb:





Real count: nreal(b)n_{\text{real}}(b)nreal(b)




Surrogate count: nsur(b)n_{\text{sur}}(b)nsur(b)




Surrogate occupancy: psur(b)=nsur(b)/Nsurp_{\text{sur}}(b) = n_{\text{sur}}(b) / N_{\text{sur}}psur(b)=nsur(b)/Nsur




Expected real count under the surrogate density:λreal(b)=Nreal⋅psur(b)\lambda_{\text{real}}(b) = N_{\text{real}} \cdot p_{\text{sur}}(b)λreal(b)=Nreal⋅psur(b)








Candidate forbidden bins are defined as those with:





nreal(b)=0n_{\text{real}}(b) = 0nreal(b)=0




λreal(b)≥5\lambda_{\text{real}}(b) \ge 5λreal(b)≥5






Per-bin probability of zero real visits under the surrogate model is estimated as:
P(0∣λ)=(1−psur)Nreal,P(0 \mid \lambda) = (1 - p_{\text{sur}})^{N_{\text{real}}},P(0∣λ)=(1−psur)Nreal,

computed in log space for numerical stability.






Connected components and regional statistics





Candidate bins are arranged in a 3D grid and grouped into 6-connected components (neighbors along ±x, ±y, ±z).




For each component CCC:





Surrogate occupancy: pregion=∑b∈Cnsur(b)/Nsurp_{\text{region}} = \sum_{b \in C} n_{\text{sur}}(b) / N_{\text{sur}}pregion=∑b∈Cnsur(b)/Nsur




Expected real count: λregion=Nreal⋅pregion\lambda_{\text{region}} = N_{\text{real}} \cdot p_{\text{region}}λregion=Nreal⋅pregion




Observed real count: ∑b∈Cnreal(b)\sum_{b \in C} n_{\text{real}}(b)∑b∈Cnreal(b)




Zero-occupancy probability under the null:
P(0∣λregion)=(1−pregion)NrealP(0 \mid \lambda_{\text{region}}) = (1 - p_{\text{region}})^{N_{\text{real}}}P(0∣λregion)=(1−pregion)Nreal





Half-split analysis (SPY–BTC–D_global):





Real and surrogate series are split into early and late halves by time index.




Components detected on full data are evaluated separately on each half to test temporal stability of the suppression.









Files in This Release (Non-exhaustive)





Core data / transforms





fdz_state_space_real_z.csv — z-scored real joint drift state space.




fdz_state_space_real_raw.csv — raw features for all windows used in FDZ v1.




fdz_scaler_params.npz — mean_, scale_, and feature names for the z-transform.




fdz_state_space_surrogates_z.csv — stacked surrogate universes in z-space.






SPY–BTC–D_global FDZ





fdz_bins_3d_stats.csv — per-bin real/surrogate counts and expected values.




fdz_bins_3d_stats_train.csv — bin stats for the early half.




fdz_forbidden_components_3d.csv — connected forbidden components (full data).




fdz_forbidden_components_3d_halfsplit.csv — component stats with early/late splits.




fdz_forbidden_summary_v1.md — narrative summary of initial FDZ detection.




fdz_flagship_fdz_summary_v1.md — detailed writeup of the flagship SPY–BTC–D_global FDZ.




fdz_forbidden_xy_projection.png — SPY vs BTC projection with forbidden region.




fdz_forbidden_Dglobal_hist.png — D_global distribution in and out of the FDZ.






SPY–BTC–VIX alpha FDZ





fdz_bins_3d_stats__alphas_SPY_BTC_VIX.csv — alpha-subspace bin stats.




fdz_forbidden_components_3d__alphas_SPY_BTC_VIX.csv — FDZ components in alpha space.




fdz_flagship_alphas_SPY_BTC_VIX_v1.md — summary of the SPY–BTC–VIX FDZ.




fdz_flagship_xy_projection__alphas_SPY_BTC_VIX_fixed.png — corrected SPY vs BTC projection with alpha FDZ box.




fdz_flagship_VIX_hist__alphas_SPY_BTC_VIX_fixed.png — VIX α distribution in/out of the alpha FDZ.






Hazard cube





fdz_bins_3d_stats__hazards_SPY_BTC_VIX.csv — hazard-state bin stats (no FDZ detected).






Meta





README_CNT_FDZ_v1.md — overview and reproduction notes for this bundle.