mod30-residue-lanes / lab report

Notebook 13 — Boundary Effects: Pre-15 Prime-Lane Pressure

Rolling drift becomes measurable boundary pressure at the central split: 

11 → 13 | 17 → 19
View Repository Colab Notebook 13

Overview

Notebook 13 is where rolling motion becomes boundary pressure.

Notebook 11 introduced rolling prime-lane trajectories. Notebook 13 focuses that motion around the central mod30 split between lane 13 and lane 17. 

rolling drift → central split → boundary pressure

This report measures reflected-pair behavior, pre/post imbalance, local pressure, boundary drift, and leadership changes around the transition: 11 → 13 | 17 → 19.

Core Features

Feature Description
lane13_count Rolling prime count for the pre-15 boundary lane.
lane17_count Rolling prime count for the reflected post-15 partner lane.
reflection_gap_13_17 Difference between lane 13 and lane 17 rolling counts.
boundary_imbalance Pre-boundary lane occupancy minus post-boundary lane occupancy.
boundary_pressure Normalized magnitude of pre/post boundary imbalance.
reflection_pressure Normalized pressure between reflected lanes 13 and 17.

Boundary Rolling Prime Lane Vectors

Heatmap of rolling prime-count vectors across residue lanes, focused on boundary behavior.
Rolling vectors show coherent lane structure around the central boundary.

Lane 13 vs Lane 17

Line chart comparing rolling prime counts for residue lanes 13 and 17.
Lane 13 and lane 17 behave as reflected partners: coupled but not identical.

Reflection Gap 13 − 17

Line chart showing the rolling reflection gap between lane 13 and lane 17.
The reflection gap oscillates around zero, exposing bounded reflected-pair pressure.

Pre/Post Boundary Imbalance

Line chart showing pre-boundary minus post-boundary rolling prime occupancy.
Pre-boundary and post-boundary lane groups exchange local dominance over time.

Boundary and Reflection Pressure

Line chart showing boundary pressure and reflection pressure across rolling windows.
Pressure metrics transform rolling lane imbalance into measurable state variables.

Boundary Vector Drift

Line chart showing boundary vector drift across rolling windows.
Drift remains bounded while the boundary continues to oscillate and reorganize.

Boundary Leadership Windows

Bar chart showing leadership windows by residue lane near the boundary.
Local lane leadership helps identify which residue lanes dominate boundary windows.

Interpretation

Notebook 13 turns rolling drift into measurable boundary pressure.

The central split between lanes 13 and 17 lets the manifold express:

This is the first report where the residue manifold has explicit pressure variables rather than only counts, similarities, or drift magnitudes.

Relationship to Neighboring Notebooks

Notebook 11 introduced rolling drift trajectories across the eight admissible lanes.

Notebook 13 focuses those trajectories around the central boundary: 11 → 13 | 17 → 19.

Notebook 17 then turns the reflected side of this boundary into a spectral decomposition problem, using lane 17 as the post-15 anchor.