mod30-residue-lanes / lab report

Notebook 07 — First Asymmetry: Prime-Filtered Lane Dynamics

Prime filtering turns the symmetric eight-lane substrate into structured asymmetry:

admissible substrate → prime filter → asymmetric occupancy

View Repository Colab Notebook 07

Overview

Notebook 07 is the first asymmetry report in the mod30 residue-lane sequence.

Notebook 01 established that complete modulo-30 cycles produce a symmetric admissible-lane baseline. Notebook 07 adds prime filtering and shows that this symmetry is not destroyed; it is filtered into structured asymmetry.

01 → 07 → 11

Lane 07 becomes the first focal lane where unequal occupancy, variable spacing, and non-identical rolling trajectories begin to appear.

Core Features

Feature	Description
`prime_count`	Prime-filtered occupancy inside each admissible residue lane.
`prime_density_within_lane`	Prime frequency relative to each lane's admissible baseline capacity.
`prime_count_delta_from_mean`	Deviation of each lane from the mean prime count across all eight lanes.
`lane07_prime_spacing`	Prime-to-prime spacing inside the focal lane 07.
`prime_window_lane_vectors`	Windowed eight-lane prime-count vectors used for trajectory analysis.
`lane07_prime_similarity`	Similarity of lane 07 to the other admissible lanes under prime filtering.

Baseline vs Prime-Filtered Lane Counts

Bar chart comparing symmetric admissible lane counts against prime-filtered lane counts.

The admissible baseline remains uniform while prime filtering introduces unequal occupancy.

Windowed Prime Lane Vectors

Heatmap of prime-filtered lane vectors across rolling windows.

Windowed prime-count vectors begin to reveal lane-local structure and manifold texture.

Prime Count Asymmetry

Bar chart showing each lane's prime count delta from the mean.

Lane-level prime counts separate from the symmetric baseline into structured deviations.

Lane 07 Prime Spacing

Histogram showing variable prime-to-prime spacing within residue lane 07.

Prime filtering breaks fixed modulo spacing and produces a sparse spacing distribution.

Lane 07 Prime Similarity

Bar chart showing similarity between lane 07 and other lanes after prime filtering.

Similarity remains high because the substrate is shared, but trajectories are no longer identical.

Lane 07 Prime Positions

Lane 07 prime positions reveal sparse occupancy within a stable residue lane.

Interpretation

Notebook 07 shows that symmetry is not destroyed; it is filtered into structured asymmetry.

The eight admissible lanes still share a common modulo-30 substrate, but prime filtering creates:

unequal prime occupancy,
variable lane-local spacing,
windowed trajectory texture,
and measurable deviation from the equilibrium baseline.

This is the first report where the residue manifold becomes visibly dynamic rather than purely balanced.

Relationship to Neighboring Notebooks

Notebook 01 established the symmetric baseline.

Notebook 07 introduces prime-filtered asymmetry.

Notebook 11 then extends this into rolling window drift, where prime-filtered lane vectors become temporal trajectories.