CNT Memory Law Note v1: Two Universality Classes of Predictive-Memory Decay

This release documents an empirical result emerging from the CNT (Cognitive Nexus Theory) lab pipeline: predictive advantage decays approximately exponentially with forecast horizon, and the decay exhibits two robust universality classes. What is being measured We define predictive advantage using ROC-AUC: ΔAUC(h) = AUC(h) − 0.5 and model decay with horizon hhh as: ΔAUC(h) ≈ Δ0 · exp(−h/τ) From this, we derive a dimensionless predictive-memory half-life in steps: N½ = τ ln(2) / base_step where base_step is the smallest horizon step present in the sweep. We also compute a normalized constant tying decay time to input mixing time: τ_steps = N½ / ln(2) IAT(input) = integrated autocorrelation time of the run’s input signal (from run manifests) κ_input = τ_steps / IAT(input) Dataset summarized in this note 27 horizon-sweep curves (derived from 9 unique runs) Each curve corresponds to a model/variant evaluated across multiple horizons. Core finding: two universality classes Both N½ and κ_input separate into two distinct regimes (fast vs slow memory), behaving like phase-like universality classes rather than a single universal constant. 1) Half-life in steps (N½) Two regimes are present and strongly separated: fast class (n=5) centered near ~3 steps slow class (n=22) centered near ~24 steps slow/fast ratio ≈ ~8× (robust) This separation is supported by: model selection via mixture modeling (two-class structure), permutation testing on log-median separation, stratified bootstrap confidence intervals on the slow/fast ratio. 2) Normalized constant (κ_input) After repairing run manifests to ensure each run declares a valid input signal and mixing-time estimate, κ_input is computed for all 27 curves (full coverage), and it does not collapse the two regimes—it sharpens them. Cluster summaries (from this release artifacts): κ_input (fast class, n=5): mean ≈ 0.00258, median ≈ 0.002589 range ≈ 0.002019 → 0.003109 (tight) κ_input (slow class, n=22): mean ≈ 0.02236, median ≈ 0.020436 range ≈ 0.007033 → 0.042891 The slow/fast separation persists under statistical testing: Observed median ratio (slow/fast): ~7.894× Permutation test (log median separation): p ≈ 0.00085 Bootstrap ratio 95% CI: [6.14×, 11.73×] (median ~7.923×) Interpretation The world does not hand us one constant; it hands us regime constants. The shared “law-form” (exponential advantage decay) appears broadly, while the characteristic constants differ by regime—consistent with universality-class behavior seen in complex systems. In other words: the same kind of forgetting occurs, but on different clocks. Reproducibility and artifacts This upload includes: CNT_Memory_Law_Note.md (full note) CNT_Memory_Law_Note.pdf (print-ready) plots/ (histograms + boxplots for half-life steps and κ_input) tables/ (summary CSVs and κ_input tables) CITATION.cff + README.md Additionally, κ_input is computed from run_manifest.json files (inputs[0]) stored in the corresponding run directories under E:\CNT\artifacts\.... These manifests were repaired to include inputs[0].mix_iat (IAT of the input signal). Limitations The note summarizes curves from a limited set of projects; while the separation is statistically strong, broader domain coverage is an explicit next step. Input provenance was repaired retroactively; future runs should write manifests at run time to avoid inference and ensure clean lineage. Next steps Expand the curve set (especially the fast class) to tighten class estimates. Test whether the slow class contains stable sub-classes (e.g., grid-like vs hazard-memory). Replicate across additional domains with standardized sweep schemas and automatic manifest writing. Acknowledgments This work was developed in collaboration with an AI assistant (ChatGPT) as a tool for analysis, automation, and drafting. All empirical results reported here are derived from the user’s local CNT Lab artifacts and statistical procedures documented in the included release files.