PFT — φX174 Genomic Resonance

Abstract

We map the circular genome of φX174 onto the Allen Orbital Lattice (AOL) defined by ΛΦ Duplex geometry. Multiple independent visualizations (spiral lattice, phase rings, polar spokes, angular GC density, and periodograms) show k = 3 triplet dominance with secondary harmonics (2, 4, 10, 19), consistent with codon-scale resonance and Pattern Field Theory’s duplex hand‑off model.

All figures below are export‑quality PNG. Raw CSV and JSON are provided for replication.

Key Figures

Spiral AOL mapping of φX174, bases colored — Diagram 1 — Spiral AOL mapping (rings 0..42, ~5386 bp). Bases A/C/G/T colored. Visual clusters match duplex symmetries.

Phase ring colored by GC density — Diagram 2 — Phase ring colored by localized GC density (window=51). Angular order preserved.

Diagram 3 — Polar spokes of dominant GC periodicities (top FFT peaks → angles). k=3 dominant; harmonics labeled.

Spokes + number-theory ticks (BASE0123) — Diagram 4 — Spokes + number‑theory ticks (BASE0123). Major integer families align with duplex spokes.

GC spokes with number-theory ticks — Diagram 5 — GC spokes + ticks. Independent confirmation of the same angular families.

Angular GC density (polar histogram) — Diagram 6 — Angular GC density (360 bins). Peaks coincide with spokes found by FFT.

Diagram 7 — Circular periodogram of GC indicator (peaks = repeating periods). Triplet peak and higher harmonics visible.

Diagram 8 — Ring‑wise Z score for GC content across concentric rings; early rings deviate then stabilize around 0.

Methods (concise)

Mapping: sequence index n → polar angle θ = 2π n / N; rings follow AOL spiral indexing. No stochastic tuning.

Signals: BASE0123 indicator, GC indicator, KETO/PURINE masks. FFT on circular domain → dominant periods → spoke angles.

Reproducibility: scripts read FASTA, emit figures and CSV summaries; SHA256 of inputs recorded in JSON.

Datasets & Downloads

φX174 summary JSON FFT top periods (CSV) Angular barcode (PNG)

Place raw FASTA + SHA256 in this section for full lineage.

Interpretation

The φX174 genome exhibits a robust triplet resonance with matching secondary harmonics, aligning with ΛΦ duplex spokes predicted by Pattern Field Theory. The agreement across orthogonal analyses (spokes, histograms, periodograms) constitutes a structural convergence argument: independent measures → identical geometry.