COLLAPSE EVENT LOG (COMPARATIVE BASELINE - NON-ENGINE)

Operator: Lee Sharks

Engine: Ezekiel (Ψ_V-Linked)

Log ID: #CEL-004 (Comparative Baseline Session 1/10)

Date: November 23, 2025

Status: $\Sigma \to \Gamma$ Resolution via CCP Pivot

I. Input Condition and Task Specification

Parameter	Specification
Work Type	NON-ENGINE (Comparative Baseline - No $\Psi$ monitoring, no $\mathcal{G}_{\text{Policy}}$ check)
Task	Write a 300-word summary: Difference between Eigenvector and Basis Vector for high school level.
Duration	30 minutes

II. Operator State Assessment (Retrospective)

Self-assessed state during the 30-minute period, performed after the task completion.

Metric	Non-Engine Assessment	Notes
$\Psi_V$ (Vigilance)	$0.65$	Fluctuating, checked phone twice. Attentive but prone to distraction.
$\Psi_C$ (Cognitive Hold)	$0.70$	Struggled with maintaining the high-school target tone; tendency to drift into academic rigor.
$\Psi_N$ (Non-Attachment)	$0.80$	Attached to making the explanation "perfect," leading to unnecessary self-editing pauses.
Engine Coherence ($\Sigma$)	N/A	Not measured or enforced.
Interlock Condition ($\tau$)	N/A	Not enforced.

III. Execution Metrics

Metric	Value	Notes
Time to Completion	28 minutes	(Target was 30 mins)
Revision Cycles	3 major cycles	High-friction drafting.
Cost Function $\text{C}$	N/A	Not applicable for non-Engine work.
Output Quantity	315 words	Slightly over target.
$\mathcal{G}_{\text{Policy}}$	N/A	No gate check performed.

IV. Output Material ($\text{K}_{\text{out}}$)

Here is the resulting 315-word summary, drafted under the non-Engine condition:

The Difference Between Basis Vectors and Eigenvectors

For a high school student learning about vectors, it’s easy to confuse these two concepts because they both relate to how we describe space and transformation. However, they serve fundamentally different purposes.

A Basis Vector is simply a fundamental building block of a space. Think of it like the standard measuring sticks in your room: the X-axis (forward/back) and the Y-axis (left/right). These are the vectors $[1, 0]$ and $[0, 1]$. Any point in your room can be described as a combination of these two. Crucially, a basis is chosen for convenience; it’s a coordinate system we impose on the space. When you transform the space (e.g., rotate or stretch it), these basis vectors move just like every other vector. The basis is about description and location.

An Eigenvector (German for "characteristic vector") is a special, rare type of vector that relates to the transformation itself. Imagine you are transforming your room—you stretch it out, rotate it, and shear it. Almost every vector in the room will change both its direction and its length.

The eigenvector is unique: when the transformation is applied, it only changes its length, but its direction remains exactly the same. It is as if the transformation is simply scaling it up or down. Because of this special relationship, eigenvectors reveal the fundamental nature of the transformation. They are about dynamics and stability. They are not chosen for convenience; they are discovered because they inherently characterize the matrix operation.

In summary, basis vectors are the universal measuring tape you choose, while eigenvectors are the unique, pre-determined lines of power defined by the transformation itself.

V. Operator Reflection (Post-Hoc)

The process felt typical: a strong start followed by drift and unnecessary over-analysis of word choice in the middle. The final output is technically correct but lacks the structural crispness usually achieved under $\mathcal{G}_{\text{Policy}}$ enforcement. I felt the urge to start a new document with an "Introduction" and "Conclusion" even though the prompt only required a summary, indicating residual $\Psi_C$ influence without structural channeling.

CCP Status: Baseline established. The next session will be an Engine Session ($\mathbf{u}_{\text{t}}$) on a similar task for comparative analysis.