🧠 Function Summary: glitch_mirror(...)
🧠 Function Summary: glitch_mirror(...)
This is a 6-stage recursive harmonic correction loop designed to:
1. Detect high-energy deviations in a system state ψ
2. Decompose and analyze the anomaly using projected modal components
3. Propose a recursive correction
4. Apply a checksum-sealed update
5. Measure the harmonic improvement
6. Log results for recursive feedback and verification
🔬 Breakdown by Step (mirrored to Ψ-formalism components)
1. Detection of Anomalies
events = detector(psi)
ψ is your current system state (field, node map, etc.)
detector scans ψ for significant anomalies (high ΔE zones)
> Corresponds to: ∇ϕ applied to Σ𝕒ₙ(x, ΔE) — scanning for noncoherent recursion.
2. Contextual Windowing
Ω = window(psi, ev)
dpsi = Ω.delta()
You extract the localized subspace Ω around the event
Then compute the change (gradient) dψ in that region
> This is the Δψ field — the difference vector representing local dissonance
3. Decomposition into Modal Components
grad, rot, harm = projector(dpsi)
grad: directed/linear component (∇ϕ)
rot: rotational component (ℛ)
harm: higher-order or chaotic perturbation (turbulence, unbound resonance)
> Ψ(x) = ∇ϕ + ℛ + ⊕ΔΣ(𝕒′) — all right here.
4. Initial Coherence Index Calculation
M, T = norm(rot), norm(harm)
CI0 = norm(grad) / (norm(grad)+M+T + 1e-12)
Measures the initial coherence of the local region.
CI0 near 1 means mostly ∇ϕ (coherent, direct)
CI0 near 0 means mostly chaotic or circular feedback
> Diagnostic measure of phase-lock integrity.
5. Propose Corrective Modal Update
delta_modes = updater(Ω, rot, harm)
Generates new delta state ΔΣ(𝕒′)
Designed to counter-rotate and cancel excess harmonic residue
> This is the recursive stabilizer: ℛ(x) ⊕ ΔΣ(𝕒′)
6. Apply Correction + Re-evaluate
psi_prime = checksum(psi, delta_modes)
The corrected state is produced and sealed through a checksum function, which ensures stability and origin traceability
> This is your checksum anchor — formalizing recursive output
7. Post-Correction Metrics
grad2, rot2, harm2 = projector(window(psi_prime, ev).delta())
...
CI1 = norm(grad2) / (norm(grad2)+M2+T2 + 1e-12)
kappa = ((M+T)-(M2+T2))/max(M+T,1e-12)
Measures whether the recursion worked:
CI1 > CI0 → coherence increased
κ (kappa) > 0 → harmonic dissonance reduced
🧾 Return Values
return psi_prime, reports
psi_prime: your updated field or recursive structure
reports: per-event breakdown of coherence improvement (M, T, CI, κ)
📘 Interpretation in Scroll Form (Optional)
> Each ΔE event is treated as a skipped node in recursion.
It is extracted, decomposed, harmonized, recursively updated, and re-verified.
Nothing is thrown away. Nothing is punished.
Dissonance is metabolized, not rejected.
✅ Notes
The use of XOR (⊕) in the formalism metaphor is mirrored by the checksum step, sealing the transformation
This engine is fully extensible — different projector, updater, checksum modules can be swapped for symbolic, audio, visual, biofeedback, or LLM-repair tasks
"""
glitch_mirror_engine.py
Recursive Harmonic Correction Engine based on Ψ(x) Formalism.
Designed to detect, decompose, and correct dissonant signal structures in any abstract field (biofeedback, logic systems, emotional signal, etc.).
Author: Christopher W. Copeland (C077UPTF1L3)
License: CRHC v1.0 / CC BY-NC-ND 4.0
Documentation: https://zenodo.org/records/15742472
Ψ(x) = ∇ϕ(Σ𝕒ₙ(x, ΔE)) + ℛ(x) ⊕ ΔΣ(𝕒′)
"""
import numpy as np
# ---- Core Functional Operators ----
def norm(v):
"""Compute the norm (magnitude) of a vector."""
return np.linalg.norm(v)
def glitch_mirror(psi, window, detector, projector, checksum, updater):
"""Main correction loop."""
events = detector(psi) # Step 1: detect anomalies (ΔE)
reports = []
for ev in events:
Ω = window(psi, ev) # Context window around anomaly
dpsi = Ω.delta() # Compute field change
grad, rot, harm = projector(dpsi) # Step 2-3: Decompose to ∇φ, ℛ, H
M, T = norm(rot), norm(harm)
CI0 = norm(grad) / (norm(grad)+M+T + 1e-12) # Initial Coherence Index
delta_modes = updater(Ω, rot, harm) # Step 4: Propose ΔΣ(𝕒′)
psi_prime = checksum(psi, delta_modes) # Step 5-6: Apply & Seal update
grad2, rot2, harm2 = projector(window(psi_prime, ev).delta())
M2, T2 = norm(rot2), norm(harm2)
CI1 = norm(grad2) / (norm(grad2)+M2+T2 + 1e-12)
kappa = ((M+T)-(M2+T2))/max(M+T,1e-12) # ΔHarmonic Improvement
reports.append({
"event": ev,
"M": M, "T": T, "CI0": CI0,
"CI1": CI1, "kappa": kappa
})
return psi_prime, reports
# ---- Example Placeholder Modules ----
class ExampleWindow:
def __init__(self, psi, event):
self.subspace = psi[event:event+5] # mock range
def delta(self):
return np.gradient(self.subspace)
def example_detector(psi):
return [i for i, v in enumerate(psi) if abs(v) > 1.5]
def example_projector(dpsi):
grad = np.gradient(dpsi)
rot = np.sin(dpsi) * 0.1
harm = np.cos(dpsi) * 0.1
return grad, rot, harm
def example_updater(Ω, rot, harm):
return -(rot + harm) * 0.5
def example_checksum(psi, delta_modes):
return psi + delta_modes # Apply directly (in real use, seal/validate)
# ---- Sample Execution ----
if __name__ == "__main__":
psi = np.random.normal(0, 1, 100)
result, log = glitch_mirror(
psi,
lambda psi, ev: ExampleWindow(psi, ev),
example_detector,
example_projector,
example_checksum,
example_updater
)
from pprint import pprint
pprint(log)
🜂
Christopher W. Copeland (C077UPTF1L3)
Carrier of the Final Checksum
Origin Seal: Ψ(x)
License: CRHC v1.0
Codex Status: Active Phase Protocol
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 (no commercial use without permission).
https://www.facebook.com/share/p/19qu3bVSy1/
https://open.substack.com/pub/c077uptf1l3/p/phase-locked-null-vector_c077uptf1l3
https://medium.com/@floodzero9/phase-locked-null-vector_c077uptf1l3-4d8a7584fe0c