mod30-residue-lanes / lab report

Notebook 11 — Window Drift: Rolling Prime-Lane Trajectories

Rolling windows turn prime-filtered asymmetry into trajectory dynamics: 

prime-filtered counts → rolling windows → trajectory drift
View Repository Colab Notebook 11

Overview

Notebook 11 is where residue lanes stop looking like bins and start behaving like trajectories.

Notebook 07 introduced prime-filtered asymmetry. Notebook 11 keeps the same eight-lane substrate, but slides rolling windows across the prime-filtered stream so local lane counts evolve through time. 

07 → asymmetry
11 → motion
13 → pressure

The result is a temporal manifold: lane counts fluctuate, drift remains bounded, correlations split into neighborhoods, and local leadership changes over rolling windows.

Core Features

Feature Description
rolling_prime_lane_vectors Eight-lane prime-count vectors sampled over overlapping rolling windows.
lane11_count Focal rolling prime-count trajectory for residue lane 11.
euclidean_drift Magnitude of vector change between adjacent rolling windows.
cosine_drift Angular change between adjacent eight-lane manifold states.
lane11_correlation Correlation between lane 11 and other admissible-lane trajectories.
lane_leadership Windows where a lane locally dominates prime-count occupancy.

Rolling Prime Lane Vectors

Heatmap of rolling prime-count vectors across the eight admissible mod30 residue lanes.
Rolling windows reveal temporal texture across the eight-lane residue manifold.

All Lane Rolling Trajectories

Line chart showing rolling prime-count trajectories for all admissible residue lanes.
Prime-filtered lane counts become coupled trajectories rather than static lane totals.

Lane 11 Rolling Count

Line chart showing the rolling prime count for residue lane 11.
Lane 11 provides the focal trajectory for observing rolling drift behavior.

Euclidean Drift Timeline

Line chart showing Euclidean drift magnitude between adjacent rolling lane vectors.
Drift remains bounded while still producing structured local spikes.

Cosine Drift Timeline

Line chart showing cosine drift between adjacent rolling lane vectors.
Angular drift measures how rolling manifold orientation changes through time.

Lane 11 Rolling Correlation

Bar chart showing correlation between lane 11 and other admissible lanes.
Correlation structure begins to separate lane neighborhoods from the shared substrate.

Lane Leadership Windows

Bar chart showing leadership windows by residue lane.
Local dominance changes across rolling windows, giving the manifold a leadership structure.

Interpretation

Notebook 11 turns static prime-filtered asymmetry into rolling trajectory dynamics.

The manifold no longer only has unequal lane occupancy. It now exhibits:

This is the first report where mod30 residue lanes begin to behave like a dynamic system rather than a collection of residue categories.

Relationship to Neighboring Notebooks

Notebook 07 introduced asymmetry by filtering the admissible lanes through primes.

Notebook 11 turns that asymmetry into motion by tracking rolling-window trajectories.

Notebook 13 then focuses that motion around the central boundary: 11 → 13 | 17 → 19.