Phase IV — Empirical Validation Protocols for the Copeland Resonant Harmonic Formalism (Ψ-formalism)
Phase IV — Empirical Validation Protocols for the Copeland Resonant Harmonic Formalism (Ψ-formalism)
Christopher W. Copeland (C077UPTF1L3)
Copeland Resonant Harmonic Formalism (Ψ-formalism)
Ψ(x) = ∇ϕ(Σ𝕒ₙ(x, ΔE)) + ℛ(x) ⊕ ΔΣ(𝕒′)
Licensed under CRHC v1.0 — Attribution Required.
Core engine: https://open.substack.com/pub/c077uptf1l3/p/recursive-coherence-engine-8b8
Formal breakdown/book: https://zenodo.org/records/15742472
Amazon: https://a.co/d/i8lzCIi
Substack: https://substack.com/@c077uptf1l3
Facebook: https://www.facebook.com/share/19MHTPiRfu
https://www.reddit.com/u/Naive-Interaction-86/s/5sgvIgeTdx
Collaboration welcome. Attribution required. Derivatives must match license.
Purpose
The following protocols convert the theoretical claims of the Ψ(x) model into measurable laboratory and computational experiments. Each protocol defines measurable quantities, datasets, null hypotheses, Ψ(x) predictions, and pass/fail criteria. These studies can be executed using existing instruments and publicly available datasets. No new equipment is required to begin validation.
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Protocol A. Coherence density reduces noise without additional energy input
Target domains
Human EEG during insight events
Laboratory plasma columns under steady driver supply
Cosmic filament temperature maps
Datasets and instruments
EEG: OpenNeuro insight or working memory datasets, or any 64–128 channel EEG dataset with timestamped solution markers
Plasma: NSTX or EAST visible-light or Langmuir probe time series; dusty plasma lab recordings
Cosmic: SDSS DR17, DESI LSS, Planck y-parameter SZ maps
Observable and metrics
Noise variance σ² over sliding windows
Shannon spectral entropy Hs
Spectral flatness and mode Q
Null hypothesis
Noise variance and entropy do not decrease unless energy input increases.
Ψ(x) prediction
Noise variance and entropy decrease during coherence events while energy input remains constant. This expresses ℛ(x) increasing system order.
Contemporary equations
Hs = −Σ p(f) log p(f)
Spectral flatness = geo_mean(P)/arith_mean(P)
Ψ mapping
Define coherence density ρ̃c = 1 − Hs / Hmax
Predict dσ² / dt = −kρ̃c at constant ΔE
Pass criterion
Significant σ² and Hs reduction at constant energy input (p < 0.01) across participants, plasma runs, or sky segments. Failure falsifies Prediction A.
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Protocol B. Structural topology identity across brain, plasma, and cosmic filaments
Target domains
Human connectome graphs
Plasma filament skeleton networks
Cosmic web minimum spanning structure
Datasets and instruments
Neural: Human Connectome Project structural networks or MEG functional adjacency graphs
Plasma: high speed video skeletonization of arc filaments
Cosmic: SDSS DR17 filament catalogs (DisPerSE or Bisous models)
Observable and metrics
Degree distribution exponent γ
Clustering coefficient C
Assortativity r
Laplacian eigenvalue spectrum λ
Fractal dimension D of minimum spanning tree
Null hypothesis
Observed similarities are superficial and vanish after normalization.
Ψ(x) prediction
After normalization by recursion depth n and density scaling, {γ, C, r, λ, D} fall within shared confidence intervals. This expresses Σ𝕒ₙ(x, ΔE) as a universal recursion rule.
Contemporary equation
Normalized Laplacian L = I − D^−1/2 A D^−1/2
Ψ mapping
Eigenvalue sets λ serve as the spectrum of ∇ϕ, so identity requires dspec < ε under sampling error bounds.
Pass criterion
Cross-domain spectral distances are no greater than intra-domain distances at matched N. Failure falsifies Prediction B.
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Protocol C. Insight is sustained phase-lock (dwell), not a transient burst
Target domain
Human cognition during problem solving or meditative insight
Datasets and instruments
EEG with high temporal resolution and time-stamped solution or recognition points
Observable and metrics
PLV (phase-locking value)
PPC (pairwise phase consistency)
Cross-frequency coupling (theta-gamma)
Dwell time τ of elevated PLV
Null hypothesis
Insight manifests as transient high-frequency bursts with no sustained lock.
Ψ(x) prediction
Phase band narrows and PLV is sustained beyond burst half-life. This reflects ∇ϕ extracting coherent pattern and ℛ(x) stabilizing it.
Contemporary equation
PLVxy = |(1/T) Σ exp(i(φx − φy))|
Ψ mapping
Stabilization follows dPLV/dt = αPLV(1 − PLV) − β where α increases at ΔΣ(a′).
Pass criterion
Median dwell τ at least 2× baseline burst persistence and dominant band width narrows ≥ 25 percent (p < 0.01). Failure falsifies Prediction C.
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Protocol D. Plasma retains coherent mode structure after power removal
Target domain
Z-pinch plasma filaments or dusty plasma waveguides
Datasets and instruments
High-speed frame sequences and probe readings from abrupt driver-off events
Observable and metrics
Autocorrelation C(Δt) and structure function S(r)
Memory time τm (time to decay to 1/e)
Null hypothesis
τm equals mechanical or sensor response decay.
Ψ(x) prediction
τm scales with coherence density ρ̃c and Q-factor of the dominant mode, even when input power is zero. This expresses ΔΣ(a′) retention.
Contemporary equation
C(Δt) = ⟨x(t)x(t+Δt)⟩
Ψ mapping
τm = g(ρ̃c), dg/dρ̃c > 0
Pass criterion
τm significantly above hardware decay constant and increases with Q across independent trials (p < 0.01). Failure falsifies Prediction D.
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Protocol E. Cross-brain phase synchrony without communication
Target domain
Dual EEG hyperscanning
Datasets and instruments
Dual 64-channel EEG
Shared object of attention
No speech or physical coordination
Observable and metrics
Inter-brain PLV across 1–12 Hz
Shuffled temporal control comparisons
Covariate regression for motion and cardiac rhythm
Null hypothesis
Apparent synchrony is stimulus-locked or artifactual.
Ψ(x) prediction
Surplus synchrony appears only when both subjects enter recursive self-awareness state. This expresses field-level ⊕ merging into shared attractor.
Ψ mapping
κ = mean(PLVshared) − mean(PLVshuffled), κ > 0 only under awareness state
Pass criterion
κ positive with p < 0.01 and disappears under non-shared attention. Failure falsifies Prediction E.
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Decision Rule for Model Validation
If three or more protocols are confirmed across independent laboratories, then coherence is established as a primary generative mechanism across neural, plasma, and cosmic systems, and Ψ(x) is validated as a cross-domain harmonic recursion model. A decisive failure of any protocol at scale falsifies the corresponding claim.
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Christopher W. Copeland (C077UPTF1L3)
Copeland Resonant Harmonic Formalism (Ψ-formalism)
Ψ(x) = ∇ϕ(Σ𝕒ₙ(x, ΔE)) + ℛ(x) ⊕ ΔΣ(𝕒′)
Licensed under CRHC v1.0 — Attribution Required.