UGFM

What UGFM is

UGFM stands for Unified Generative Field Model. SEIS is the theory; UGFM is its mathematics. Together they are the SEIS-UGFM framework.

UGFM studies harmonic relationships, phase and coherence. Its subject is how frequencies sit against one another over time.

The 700/N cascade

The cascade is the set of frequencies f_N = 700 / N. The members most used in the work are the prime-indexed ones:

Three points define it:

• It is a coupled system. The framework is about the relationships between members: cross-frequency coupling, harmonic locking and mutual phase structure. It is not about any one frequency.
• Prime N selects the stable modes. This is a statement about stability and persistence over time, not about loudness.
• 41.176 Hz is one member. 700 / 17 = 41.17647… Hz. Its significance is its place in the cascade.

Relationship, not a single note

Coherence in this work is a relationship: phase and tempo between oscillators. A single steady tone is only a frequency. Order is built, and unhealthy order is broken, by how a signal sits against what is already there.

The Klein Spiral

The Klein Spiral is the geometry of the model: a three-dimensional projection of a four-dimensional non-orientable manifold. A helix has an inside and an outside, and so it leaks information. The Klein Spiral has neither. It holds phase-lock through topological closure.

The anchor frequency f* = 700 / 17 is not fitted to data. It comes from the requirement for topological closure, rooted in the GF(17) algebraic kernel.

Where it is used

The cascade is the subject of U.S. Non-Provisional Patent Application 19/862,334, coherence detection via the 700/N harmonic cascade (filed November 2026, pending). Each application of it keeps its own measurements and its own tests.

Read more

• The Klein Spiral: Framing Parity as a Testable Constraint on Resonant Coherence (PDF)
• From Empirical to Derived: The 110 Hz Convergence
• The live Klein Spiral instrument