Applied Resonance Architecture

Allen Orbital Lattice™ — the prime‑seeded lattice derived from Pattern Field Theory™. All implementations and applications are protected intellectual property of James Johan Sebastian Allen.

Intellectual Property Statement ↓

What is the Framework?

The Pattern Field Framework™ is the official implementation and licensing platform for the Allen Orbital Lattice™ (AOL) — a resonance lattice using primes, φ, π, and perfect numbers to organize stable structure across physics, biology, and information systems.

Looking for the science behind the framework? Read the theory at PatternFieldTheory.com — origin from the Metacontinuum, Differentiats, and the derivation of π, primes, φ, and perfect-number shells.

Ownership

Intellectual Property Statement

All methods, algorithms, systems, designs, data formats, and products based on the Allen Orbital Lattice™ are proprietary intellectual property of James Johan Sebastian Allen. No reproduction, modification, distribution, or commercialization is permitted without prior written authorization.

Licensing & Inquiries

Email: contact@patternfieldframework.com · Alt: contact@patternfieldtheory.com

Empirical Evidence — Cross‑Domain

Top‑6 Target Alignment Grid

Remainder‑token → triadic (n,k) mapping of planetary mean motions and φ constant on AOL.

Explain

Here is an example of a deterministic tokenization rule locating independent quantities on the same annulus. As you can see, the data shows clear convergence to the outer ring with small |Δ|, supporting discretization at π shells.

First π Anchors & Special Numbers

Nested resonance shells at π, 6 (perfect), 7 (prime), 9 (~π×3), and 28 (perfect).

Explain

This illustrates the baseline lattice radii used across analyses. The perfect-number radii (6, 28) act as closure points; in multiple datasets, alignments concentrate near these shells more than expected by chance.

Angular Two‑Point Correlation

Landy–Szalay w(θ) showing excess correlation at the lattice spacing.

Explain

We compare the observed pair counts to randomized catalogs. A statistically significant excess appears exactly at the predicted spacing, then decays to ≈0—signature of structure, not Poisson noise.

GOODS‑S on AOL hex lattice

17 GOODS‑S galaxies mapped on AOL hex grid; numbered for clarity.

Explain

Each source is snapped to the nearest lattice node (no model fitting). Short connectors show residuals; clustered short connectors imply a preferred spacing consistent with the φ‑scaled hex step.

Pair Separation Histogram

Sample shows peaks near lattice‑predicted spacings.

Explain

A simple histogram of pairwise separations reveals modes at 1× and 2× the lattice constant. Under a uniform sky model the distribution is smooth; these peaks are unlikely without an underlying lattice.

Digit χ² by Quintuplet Position (√2 example)

Quintuplet position biases suggest a phase structure across digits.

Explain

We partition digits into 5‑tuples and compute χ² vs a flat distribution. Position‑dependent trends across N show non‑random phase memory compatible with a prime‑seeded generator rather than iid digits.

Ring‑1 Synchronization Locking

Phase convergence in a 6‑node ring (Kuramoto‑style) with small coupling.

Explain

Independent oscillators with random initial phases converge onto a locked phase over time on the hex ring, demonstrating that the AOL geometry supports stable phase locking with minimal assumptions.

DNA Evidence — Resonance & Information

φX174 Ringwise Shannon Entropy

Mean entropy per ring shows structured dissipation.

Explain

Here is an example of a biological string mapped to lattice rings. As you can see, entropy is not flat; specific rings exhibit lower variability, consistent with resonance‑locked coding segments.

Consensus vs Reference — Overlay (clear)

Consensus (filled) vs reference (outline) mapped on AOL with S=1.

Explain

Overlap concentrates within the same radial band; the small radial offset is consistent with expected coverage gaps at low depth and does not erase the shared ring signature.

Consensus vs Reference — Overlay (alt color)

Alternate visualization emphasizing filled consensus area.

Explain

Same geometry as prior panel; provides a high‑contrast look to inspect where consensus extends or shrinks along the band.

Reference Lattice (S=3 codons)

Reference genome projected with 3‑base step.

Explain

A codon‑scale step emphasizes periodic structures. Notably, band edges persist after the stride change, indicating the feature is geometric rather than an artifact of step size.

Rings Overlay Footprint

Aggregate coverage vs ring index for the same sample.

Explain

This summarizes radial occupancy. A sharp shoulder and plateau imply preferred rings (resonance locking) rather than uniform filling.