Cognitive Nexus Theory: Synthetic Field Laws v1.0 — Universal Drift Manifold and Nexus Coupling Sweet Spot

This dataset collects two synthetic “field laws” from Cognitive Nexus Theory (CNT), each expressed as a single clean curve with its underlying data:(1) a Universal Drift Manifold that collapses several distinct stochastic generators onto one rescaled drift curve, and(2) an SPJ Nexus Coupling Sweet Spot where CNT’s nexus richness peaks at intermediate coupling even as decoding accuracy monotonically approaches 100%.Together they form a compact, falsifiable testbed for CNT’s claims about structure in drift and coupling space. 1. Universal Drift Manifold (UDM)The UDM experiment compares three canonical synthetic processes: an Ornstein–Uhlenbeck process (SYN_OU), a random walk (SYN_RW), and a sinusoidal signal with noise (SYN_SIN). For each process we compute a scale-dependent drift measure D(τ)D(\tau)D(τ), normalize it by a characteristic scale D\*D^\*D\*, and express the results in collapsed coordinates u=τ/τ\*,d=D(τ)/D\*.u = \tau / \tau^\*, \qquad d = D(\tau)/D^\* .u=τ/τ\*,d=D(τ)/D\*. Despite their different raw behavior, the three generators fall onto a single power-law manifold with global fit d∝uαd \propto u^{\alpha}d∝uα, α≈0.57\alpha \approx 0.57α≈0.57, with a high goodness-of-fit over the central scaling range. Deviations at very small and very large uuu are visible and preserved rather than hidden.Within CNT, this is interpreted as a synthetic Universal Drift Manifold: once time and amplitude are renormalized, distinct stochastic fields share a common drift geometry. The accompanying JSON file exposes all key quantities (fit window, α, R2R^2R2, per-process local exponents, τ\*\tau^\*τ\*, D\*D^\*D\*) so that the manifold can be re-plotted, re-fit, or challenged with new processes. 2. SPJ v2 Nexus Coupling Sweet SpotThe second experiment uses a symbolic projection junction (SPJ) model in which multiple input channels are coupled through a shared “nexus” layer and decoded by a downstream classifier. We sweep the coupling strength ggg from 0 to 2 and measure: NEI_v2_mean — a CNT Nexus Enrichment Index quantifying richness and diversity of joint patterns at the nexus; Decode accuracy — the fraction of correct labels recovered by the decoder. As coupling increases, decoder accuracy rises smoothly and saturates at or near 100% for strong coupling. NEI_v2_mean, however, exhibits a clear inverted-U profile: it grows from weak coupling, peaks around intermediate ggg (the “Nexus Sweet Spot”), and then declines as coupling becomes too strong and the system locks into over-synchronized, less expressive joint states. This dissociation—maximum nexus richness at intermediate coupling, maximum accuracy at high coupling—supports a core CNT idea: the most informative, field-like regime is not where prediction is easiest, but where the nexus is dynamically rich yet still coherent. Contents and reuseThe deposit includes: cnt_udm_collapse.png — the Universal Drift Manifold collapse plot for SYN_OU, SYN_RW, and SYN_SIN. cnt_udm_summary.json — numerical summary of the UDM fits (global and per-process α, R2R^2R2, characteristic scales). spj_nei_v2_coupling_sweep.png — SPJ v2 Nexus Richness vs Coupling and Decoder Accuracy. spj_nei_v2_coupling_summary.csv — table of coupling values, NEI metrics, and decode performance used to generate the sweep. A short README.md describing how to re-plot both figures in Python. These files are intended as small, sharply defined test objects: anyone can re-plot the curves, re-fit the exponents, or plug the CSV/JSON into their own models. Both laws are stated as working hypotheses, not certainties, and are deliberately structured to be easy to falsify or extend with new generators, coupling schemes, or alternative richness metrics. Authorship and toolsAll simulations, analyses, and interpretations are authored by Caleb “Telos” Holmes. An AI research assistant (“Aetheron”) was used as a tool for code generation and documentation. Responsibility for the scientific claims and conclusions lies with the human author.