mod30-residue-lanes / lab report

Notebook 01 — Symmetric Equilibrium in Residue Space

Foundational baseline analysis for the eight admissible modulo-30 residue lanes:

01 → 07 → 11 → 13 → 17 → 19 → 23 → 29

View Repository Colab Notebook 01

Overview

Notebook 01 establishes the symmetric baseline for the mod30 residue-lane manifold.

Before adding prime filtering, rolling drift, boundary pressure, graph embeddings, or sparse reset events, the repo first verifies that the eight admissible residue lanes form a balanced substrate.

01, 07, 11, 13, 17, 19, 23, 29

This notebook demonstrates that complete modulo-30 cycles produce equal admissible-lane counts. That equilibrium result becomes the reference state for every later notebook.

Core Features

Feature	Description
`lane_01`	Anchor residue lane used to establish the first baseline comparison.
`admissible_lane_counts`	Counts across the eight residue lanes coprime to 30.
`lane01_spacing`	Spacing between repeated lane-01 occurrences in complete modulo cycles.
`window_lane_vectors`	Eight-lane count vectors used as reusable manifold-state representations.
`lane01_similarity`	Cosine similarity between lane 01 and all other admissible lanes.

Admissible Lane Counts

Bar chart showing equal counts across the eight admissible modulo-30 residue lanes.

Complete modulo-30 cycles produce balanced counts across all admissible lanes.

Lane 01 Positions Across Cycles

Scatter plot showing lane 01 positions across repeated modulo-30 cycles.

Lane 01 repeats regularly as the anchor lane across modulo-30 cycles.

Lane 01 Spacing Distribution

Histogram showing fixed spacing of lane 01 occurrences across complete modulo-30 cycles.

The lane-01 spacing baseline remains fixed before prime filtering introduces sparse variation.

Window Lane Vectors

Heatmap of windowed lane-count vectors showing uniform eight-lane structure.

Window vectors provide the reusable eight-lane state representation used by later notebooks.

Lane 01 Similarity

Bar chart showing cosine similarity between lane 01 and all admissible residue lanes.

Under complete-cycle sampling, all admissible lanes remain structurally equivalent.

Interpretation

Notebook 01 is intentionally calm.

The point is not to find instability immediately. The point is to establish an equilibrium state: a balanced eight-lane residue manifold before additional constraints are introduced.

Lane counts remain uniform.
Lane 01 spacing remains fixed.
Window vectors remain stable.
Cosine similarity remains maximal under symmetric sampling.

Later notebooks become meaningful because Notebook 01 defines the baseline that they break, bend, rotate, or sparsify.

Relationship to Later Notebooks

Notebook 01 establishes:

the admissible lane substrate,
the symmetric count baseline,
the first lane-vector representation,
and the anchor state for later comparisons.

Notebook 07 then introduces the first major departure from this equilibrium by adding prime filtering. Later notebooks extend the sequence into rolling drift, boundary pressure, spectral decomposition, graph embeddings, and sparse reset-boundary emergence.