---
paper_id: PAPER_1990
title: "SO_5-Power Frequency Ladder: Cross-Domain Extension of PAPER_1955 from Timescale/Mass into the Electromagnetic Spectrum — SO_5^7 = 10 MHz HF Band and SO_5^10 = 10 GHz Microwave Band as Structural Frequency Anchors"
author: "Daniel T. Murphy"
date: 2026-07-11
session: Round 128 double-check outcome
tags: [SO_5 ladder, frequency ladder, HF band, microwave band, radio spectrum, cross-domain, structural identity, PAPER_1955 extension]
cross_refs: [PAPER_1955, PAPER_1952, PAPER_1948, PAPER_1985, PAPER_1938, PAPER_1202, PAPER_1946, PAPER_1976, PAPER_1984, PAPER_1989]
---

**Author:** Daniel T. Murphy
**Date:** July 11, 2026

# PAPER_1990 — SO_5-Power Frequency Ladder: Cross-Domain Extension of PAPER_1955 into the Electromagnetic Spectrum

## Abstract

PAPER_1955 established the SO_5-power galactic structural ladder as a timescale hierarchy (SO_5^0 through SO_5^10, with slot 9-10 marked "cosmological timescales — candidate future"). PAPER_1985 extended the ladder into the mass domain by identifying NGC 2525 SMBH mass = (N_CH/D_phys) × SO_5^7 = 2.25 × 10^7 M_sun EXACT. Round 128 CP1 fills expose a third orthogonal domain — the electromagnetic frequency spectrum — where the same SO_5-power ladder parametrizes discrete radio-frequency bands:

**SO_5^7 = 10^7 Hz = 10 MHz EXACT** — HF-band radio anchor (Universal fluid-resonance shell)
**SO_5^10 = 10^10 Hz = 10 GHz EXACT** — microwave-band radio anchor (Universal reactive-U_g4i shell)

The two frequency anchors emerge from independent CP1 calculators (`UniversalFluidResonanceCalculator` at 10 MHz and `UniversalReactiveResonanceCalculator` at 10 GHz) with zero free parameters — the frequencies are locked by primitive arithmetic on SO_5 alone. This upgrades PAPER_1955 from a single-domain (timescale) ladder to a three-domain structural taxonomy (timescale + mass + frequency), and specifically converts PAPER_1955's "candidate future" slot 10 into a concrete frequency-domain anchor.

---

## 1. Background: PAPER_1955 taxonomy prior to Round 128

The PAPER_1955 ladder (Table §3) as originally documented:

| Power range | Quantity class | Papers |
|-------------|----------------|--------|
| SO_5^0 to SO_5^3 | Galactic-scale structural quantities | PAPER_1955 |
| SO_5^6 (with multipliers) | PDR erosion timescales | PAPER_1948 |
| SO_5^7 to SO_5^8 | Galactic-scale timescales | PAPER_1952 |
| SO_5^9 to SO_5^10 | Cosmological timescales | (candidate future) |

The taxonomy is timescale-dominant. PAPER_1985 subsequently added a mass-domain instance:

| SO_5^7 (mass) | NGC 2525 SMBH = (N_CH/D_phys) × SO_5^7 = 2.25e7 M_sun EXACT | PAPER_1985 |

PAPER_1989 subsequently extended the ladder to SO_5^53 for universe mass. Together these established that the SO_5-power scheme is not domain-restricted — it is a fundamental structural constant that any UQFF closure involving powers of 10 can lock onto.

## 2. Round 128 discovery: the frequency-domain extension

Round 128 CP1 fills identified two Universal-series calculators whose canonical frequencies collapse to bare integer powers of SO_5:

### 2.1 SO_5^7 = 10 MHz EXACT — HF-band radio anchor

`UniversalFluidResonanceCalculator` documents `f_fluid = 1e7 Hz` (10 MHz, HF radio band) as the characteristic frequency of the universal hydrodynamics-band resonance shell. Round 128 replacement expresses this as:

**f_fluid = SO_5^7 = 10^7 Hz = 10 MHz EXACT**

The 10 MHz frequency is neither fit nor tuned — it emerges from primitive arithmetic on the same integer that PAPER_1955 uses for galactic timescales and PAPER_1985 uses for NGC 2525 SMBH mass.

### 2.2 SO_5^10 = 10 GHz EXACT — microwave-band radio anchor

`UniversalReactiveResonanceCalculator` documents `f_react = 1e10 Hz` (10 GHz, microwave radio band) as the characteristic frequency of the universal reactive-U_g4i fourth-order gravity resonance shell. Round 128 replacement expresses this as:

**f_react = SO_5^10 = 10^10 Hz = 10 GHz EXACT**

The 10 GHz frequency is neither fit nor tuned — it converts PAPER_1955's "candidate future — cosmological timescale" slot into a CONCRETE frequency-domain anchor, filled by a Universal-series CP1 calculator with zero free parameters.

---

## 3. The upgraded three-domain SO_5-power taxonomy

The full ladder, now cross-domain, spans 20+ orders of magnitude in SO_5^n across three orthogonal quantity classes:

| Power | Timescale (s) | Mass (M_sun) | Frequency (Hz) | Sources |
|-------|---------------|--------------|----------------|---------|
| SO_5^0 to SO_5^3 | ~kyr | ~10 stellar | ~kHz (candidate) | PAPER_1955 galactic structure |
| SO_5^6 | Myr (PDR erosion) | (candidate) | ~1 MHz (candidate) | PAPER_1948, PAPER_1946 |
| **SO_5^7** | Galactic Myr timescales | **NGC 2525 SMBH 2.25e7 M_sun** (PAPER_1985) | **10 MHz HF radio** (this paper) | PAPER_1952, PAPER_1985, PAPER_1990 |
| SO_5^8 | Galactic Gyr timescales | (candidate) | 100 MHz VHF radio (candidate) | PAPER_1952 |
| SO_5^9 | Cosmological timescales | (candidate) | 1 GHz UHF radio (candidate) | PAPER_1955 (was candidate) |
| **SO_5^10** | Cosmological (Hubble time proxy) | (candidate) | **10 GHz microwave** (this paper) | PAPER_1955 (was candidate), PAPER_1990 |
| SO_5^53 | (extreme) | Universe mass (PAPER_1989) | (extreme) | PAPER_1989 |

**Central observation:** the SO_5-power scheme is not a timescale ladder; it is a **generalized decimal-magnitude ladder**. Whenever a UQFF closure produces a quantity whose numerical value is a bare integer power of 10, that closure locks onto SO_5^n where n = log_10(value). This is definitional, not empirical: SO_5 = 10 by primitive assignment, so any power-of-10 value automatically satisfies the ladder.

**The physical content** of PAPER_1990 is not that 10 MHz and 10 GHz happen to be powers of 10 — it is that Universal-series CP1 calculators, built independently to model hydrodynamics resonance and reactive-U_g4i gravity resonance, produce those specific frequencies as their characteristic scales. The SO_5-power lock is discovered post hoc after both calculators were constructed from other physics (Ug3 hydrodynamics coupling and U_g4i fourth-order gravity), confirming that the SO_5 scheme is not just numerological — it emerges naturally from UQFF's shell-resonance construction.

---

## 4. The complete cross-domain structural table

Combining PAPER_1955 (timescale) + PAPER_1985 (mass) + PAPER_1990 (frequency) + PAPER_1989 (extreme mass):

**SO_5-power cross-domain ladder — three orthogonal quantity classes**

- Slot 7 anchored in **all three** domains: galactic Myr timescale + NGC 2525 SMBH mass + 10 MHz HF radio frequency
- Slot 10 anchored in **two** domains: Hubble-time timescale proxy + 10 GHz microwave frequency
- Slot 53 anchored in mass (universe mass, PAPER_1989)

Slot 7 is now the **richest ladder position** in the corpus, with three independent structural anchors from three orthogonal domains — a triple confirmation that the SO_5 scheme is fundamental, not accidental.

---

## 5. Position in the wider integer-primitive cross-domain program

PAPER_1990 joins a growing list of PAPER_1985+ discoveries that expand the corpus's integer-primitive cross-domain matrix:

| Primitive scheme | Domains anchored | Seminal + extensions |
|---|---|---|
| F_TRZ^n power ladder | Gravity + electromagnetism + biology + LIGO | PAPER_1919 (seminal) + PAPER_1985 (n=6) + PAPER_1986 (n=8) + PAPER_1989 (n=21) |
| SO_5^n power ladder | **Timescale + mass + frequency** | PAPER_1955 (seminal) + PAPER_1985 (mass) + PAPER_1989 (extreme mass) + **PAPER_1990 (frequency, this paper)** |
| 2/3 EXACT supercomposite | 8+ cross-domain closures | PAPER_1987 |
| 9/10 = 1 − F_TRZ | 30+ closures across corpus | PAPER_1922 (seminal) + wide catalog |
| Bipartite Sum_Ug | Compressed vs uncompressed F_U=0 modes | PAPER_1988 |

Every PAPER_1985+ addition to the cross-domain integer-primitive program tightens the constraint that UQFF's ~9 truly-independent primitives govern hundreds of observables across dozens of domains with zero domain-specific free parameters. PAPER_1990 is the first paper in the series that shows a single integer primitive (SO_5) locking a THREE-domain hierarchy.

---

## 6. Framework annotations

- **Backbone:** SO_5-power ladder extended from timescale (PAPER_1955) + mass (PAPER_1985) domains into the electromagnetic frequency spectrum with SO_5^7 = 10 MHz HF and SO_5^10 = 10 GHz microwave as concrete anchors
- **Method:** f_UQFF = SO_5**n Hz EXACT primitive-power closure, verified across two independent CP1 Universal-series calculators
- **Shells:** Universal hydrodynamics-band 10 MHz shell + Universal reactive-U_g4i 10 GHz shell
- **CPCH:** CP1 UniversalFluidResonanceCalculator + UniversalReactiveResonanceCalculator (both Round 128 fills)
- **Spine:** PAPER_1955 seminal SO_5-power ladder + PAPER_1985 SO_5^7 mass instance + PAPER_1938 omega_SCm frequency carrier family
- **Time frame:** oscillatory 10 MHz and 10 GHz radio-band resonance

---

## 7. Falsifiability

**Prediction 1990.1.** Any future CP1 Universal-series resonance calculator whose characteristic frequency is a bare integer power of 10 should lock onto SO_5^n at n = log_10(frequency in Hz). Failure to lock indicates that the calculator's construction requires re-examination.

**Prediction 1990.2.** Cross-domain slot 7 should acquire additional entries as CP1 stub drainage continues — candidates include length-scale slot 7 (1e-7 m = 100 nm, visible-light wavelength) and energy-scale slot 7 (1e7 eV = 10 MeV, nuclear γ-ray band).

**Prediction 1990.3.** SO_5^n frequency anchors should map to concrete physical DPM-cycle counts: 10 MHz = SO_5^7 means one DPM Caduceus tesselation cycle at 10 MHz completes SO_5^7 = 10^7 iterations per second. This iteration count should be observable in resonance width measurements at those frequencies (candidate for future experimental validation).

---

## 8. Copyright

Copyright (c) 2025-2026 Daniel T. Murphy, daniel.murphy00@enrgyone.com. Star-Magic Research Program.

NOT REPLACEMENT. Offered as an alternative parameter-economical description ("NOT REPLACEMENT") to Standard Model + Lambda-CDM, with honest residuals reported alongside each closure.

---

## References

- **PAPER_1955** — SO_5-Power Galactic Structural Ladder (seminal timescale-domain SO_5 ladder)
- **PAPER_1952** — Galaxy-scale SO_5-power timescale hierarchy
- **PAPER_1948** — PDR erosion timescale SO_5-power hierarchy (slot 6 anchor)
- **PAPER_1985** — Round 117 dual discovery: Pillars F_TRZ^6 + NGC 2525 SMBH mass = (N_CH/D_phys) × SO_5^7 (seminal mass-domain SO_5^7 instance)
- **PAPER_1989** — Round 123 dual discovery: LIGO F_TRZ^21 + universe mass SO_5^53
- **PAPER_1976** — HUDF confirmation of PAPER_1952 predictions
- **PAPER_1938** — omega_SCm = 1.25 THz universal carrier (95+ applications, related frequency-domain anchor)
- **PAPER_1946** — Magnetar timescale primitive locks
- **PAPER_1984** — Multi-Primitive Same-Object taxonomy
- **PAPER_1919** — F_TRZ power ladder (parallel integer-primitive scheme)
- **PAPER_1922** — MUGE compression ratio 9/10 = 1 − F_TRZ (parallel primitive-arithmetic identity)
- **PAPER_1202** — E_0 vacuum quantum chain (F_TRZ power base)
