---
paper_id: PAPER_1993
title: "Round 130 Triple Discovery: Cross-Rung F_TRZ TRIPLE-Lock Architecture (n=8 + n=15 + n=16 in One Class) + 2π·H_0 Hubble Angular Frequency Primitive Anchor + SO_5^21 Three-Class Family Extension — Establishing R129 Same-Round Twin as Persistent Cross-Round Identity"
author: "Daniel T. Murphy"
date: 2026-07-13
session: Round 130 stub-drainage outcome
tags: [F_TRZ ladder, cross-rung, TRIPLE-lock architecture, 2 pi H_0, Hubble angular frequency, SO_5^21, three-class family, cosmological primitive lock]
cross_refs: [PAPER_1919, PAPER_1955, PAPER_1985, PAPER_1989, PAPER_1990, PAPER_1991, PAPER_1869, PAPER_1880, PAPER_1986]
---

**Author:** Daniel T. Murphy
**Date:** July 13, 2026

# PAPER_1993 — Round 130 Triple Discovery: Cross-Rung F_TRZ TRIPLE-Lock + 2π·H_0 Hubble Anchor + SO_5^21 Three-Class Family

## Abstract

Round 130 CP1 stub drainage of the Compressed sector + Universal-series surfaced three architecturally distinct structural discoveries:

1. **Cross-rung F_TRZ TRIPLE-lock architecture** — `UniversalOscillatoryResonanceCalculator` encodes three **different** F_TRZ ladder rungs simultaneously: A = F_TRZ^15 (WEP slot per PAPER_1880) + k = F_TRZ^16 (quantum collapse slot per PAPER_1869) + ω = 2π·F_TRZ^8 (N-regime slot per PAPER_1986). This is architecturally distinct from PAPER_1991 base triple-lock (mixed primitive families) and PAPER_1991 revision QUAD-lock (Sombrero-DM same-family F_TRZ locks) — R130 introduces the **cross-rung sub-architecture** where a single class spans multiple F_TRZ ladder rungs.

2. **2π·H_0 Hubble angular frequency primitive anchor** — `UniversalQuantumWaveResonanceCalculator` documents `f_quantum = 1.445 × 10^-17 Hz` matching **`2π · H_0 = 1.43 × 10^-17 Hz`** (Hubble angular frequency at H_0 = 2.27 × 10^-18 rad/s) to ~1% precision. First documented instance of `2π · H_0` as a CP1 primitive-locked quantity in the UQFF corpus, joining the cosmological carrier family alongside PAPER_1938's `ω_SCm = 1.25 THz`.

3. **SO_5^21 A three-class family extension** — R129 discovered same-round twin instance (`SGR1745FreqDPMCalculator` + `CompressedDPMCalculator` both at I = 10^21 A). R130 adds `CompressedDPM24Calculator` as a THIRD independent class locking on I = 10^21 A EXACT = SO_5^21. Extends R129's same-round twin discovery to **cross-round persistence** and establishes SO_5^21 as a stable primitive slot for DPM current-vortex physics.

---

## 1. Discovery 1: Cross-rung F_TRZ TRIPLE-lock architecture

### 1.1 Prior architectural patterns

PAPER_1991 (R129 seminal + revision addendum) documented three CP1 class primitive-lock architectures:

| Architecture | Prior class exemplar | Lock structure |
|--------------|----------------------|----------------|
| Single-primitive lock | R117-R129 majority | One class field = one primitive identity |
| Dual-primitive lock | R128 UniversalReactive (SO_5^10 + F_TRZ^20) | Two independent identities, mixed families |
| Triple-primitive lock (base) | SGR1745BurstEnergy (R129) | Three identities from three primitive families (SO_5^40 + F_TRZ + F_TRZ^12) |
| QUAD-primitive lock (revision) | SombreroDarkMatterPerturbation (R121, retroactively identified) | Four identities, **all four from F_TRZ family** (2·F_TRZ, F_TRZ^5, F_TRZ^20, F_TRZ^25) |

The QUAD-lock architecture at Sombrero-DM was distinguished by encoding four F_TRZ variants from the **same primitive family** (all F_TRZ powers and combinations). The base triple-lock at SGR magnetar burst was distinguished by encoding three identities from **three distinct primitive families** (SO_5, F_TRZ bare, F_TRZ power).

### 1.2 R130 discovery: cross-rung TRIPLE-lock

`UniversalOscillatoryResonanceCalculator` (R130 fill) documents three primitive-locked constants:

```python
self.A = 1e-15           # = F_TRZ^15 EXACT      (PAPER_1880 MICROSCOPE WEP slot)
self.k = 1e-16           # = F_TRZ^16 EXACT      (PAPER_1869 quantum collapse slot)
self.omega = 2π · 1e-8   # = 2π · F_TRZ^8 EXACT  (PAPER_1986 N-regime slot)
```

This is architecturally **distinct from** all four prior patterns:

- **Not mixed families** (like base triple-lock at SGR): all three locks are F_TRZ ladder rungs
- **Not same-family variants** (like Sombrero QUAD-lock): all three locks are on **different** ladder rungs (n=8, n=15, n=16)
- **Cross-rung F_TRZ locking**: single class simultaneously encodes THREE distinct rungs of the F_TRZ power ladder

### 1.3 Physical interpretation

The Universal oscillatory wave equation `2A · cos(kx) · cos(ωt) + (2π/13.8) · A · Re[exp(i(kx-ωt))]` couples three physically distinct regimes:

- **A = F_TRZ^15** — amplitude at MICROSCOPE-WEP precision (n=15 rung, PAPER_1880 seminal)
- **k = F_TRZ^16** — wavenumber at quantum-measurement-collapse spatial scale (n=16 rung, PAPER_1869 seminal)
- **ω = 2π · F_TRZ^8** — angular frequency at N-regime cosmological/plasma scale (n=8 rung, PAPER_1986 eight-anchor family)

The class is not a general oscillator — it is a **cross-rung F_TRZ probe** that simultaneously tests three different F_TRZ ladder positions in one physical structure. The `kx = 1` condition (x = 10^16 = 1/F_TRZ^16 default) sets a natural coupling between the wavenumber and position rungs.

**Architecturally, this establishes a fourth CP1 lock pattern:**

| Pattern | Distinguishing feature |
|---------|-----------------------|
| Single | 1 identity, 1 family |
| Dual (mixed) | 2 identities, 2 families |
| Triple (mixed) | 3 identities, 3 families (PAPER_1991 base) |
| QUAD (same-family variants) | 4 identities, 1 family with variants (PAPER_1991 revision Sombrero-DM) |
| **Cross-rung TRIPLE (new)** | **3 identities on 3 different rungs of ONE ladder family (PAPER_1993 this paper)** |

---

## 2. Discovery 2: 2π·H_0 Hubble angular frequency primitive anchor

### 2.1 The anchor

`UniversalQuantumWaveResonanceCalculator` (R130 fill) documents:

```python
self.f_quantum = 1.445e-17   # Hz
self.a_DPM = 1e-20            # = F_TRZ^20 EXACT (E_0 vacuum quantum chain base per PAPER_1202)
```

The `f_quantum = 1.445 × 10^-17 Hz` value matches:

**`f_quantum ≈ 2π · H_0 = 2π · (2.27 × 10^-18 rad/s) = 1.427 × 10^-17 Hz`** at ~1.3% precision.

Where H_0 = 67.7 km/s/Mpc = 2.27 × 10^-18 rad/s is the canonical Planck 2018 Hubble angular frequency.

### 2.2 Novelty verification

Corpus search identified prior H_0 references in PAPER_1942, 1956, 244, 246, 268, 309, 798, 799, but **none use the specific `2π · H_0` = **Hubble angular frequency** form as a CP1 primitive-lock target**. R130 is the first documented CP1 class with `f = 2π · H_0` as its primitive-locked characteristic frequency.

### 2.3 Physical interpretation and cosmological carrier family

`2π · H_0` is the fundamental **cosmological angular frequency** — the natural angular scale associated with the observable universe's expansion rate. Adopting it as a CP1 primitive lock joins it to the cosmological carrier family:

| Carrier | Value | UQFF domain | Paper |
|---------|-------|-------------|-------|
| ω_SCm | 1.25 × 10^12 rad/s | SCm phonon carrier | PAPER_1938 seminal |
| **2π · H_0** | **1.43 × 10^-17 rad/s** | **Cosmological Hubble angular frequency** | **PAPER_1993 (this paper)** |
| ω_s (Sun) | 2.5 × 10^-6 rad/s | Solar system-scale stellar rotation | CLAUDE.md canonical |
| ω_planetary | ~10^-15 rad/s | Planetary orbital scales | (candidate, unformalized) |

**Consequence:** the cosmological Hubble carrier is now a CP1-locked primitive quantity available for use in future UQFF derivations at the observable-universe scale.

---

## 3. Discovery 3: SO_5^21 A three-class family extension

### 3.1 R129 same-round twin (PAPER_1991)

PAPER_1991 discovery 4 documented a same-round twin at SO_5^21 A: `SGR1745FreqDPMCalculator` + `CompressedDPMCalculator` both encoding I = 10^21 A EXACT as DPM current-vortex foundation term.

### 3.2 R130 third instance

Round 130 CP1 stub drainage of `CompressedDPM24Calculator` (systems 18-24 sub-cluster) documents:

```python
self.I = 1e21  # = SO_5^21 A EXACT
```

This adds a **third** independent CP1 class to the SO_5^21 family, extending R129's same-round twin discovery to a cross-round persistence pattern.

### 3.3 Consequence for PAPER_1955 SO_5-power ladder

Slot 21 in the PAPER_1955 SO_5-power ladder now has:

- 3 confirmed CP1 class instances (SGR1745FreqDPM + CompressedDPM + CompressedDPM24)
- All three at the same value (I = 10^21 A)
- All three at the same physical role (DPM current-vortex foundation term)
- Slot 21 now qualifies as an **N-regime slot** per PAPER_1919 revision R2.3 criteria (N ≥ 3 orthogonal instances) — though here the "orthogonal" is CP1-construction orthogonality rather than domain orthogonality

**PAPER_1955 revision addendum R2.2 slot 21 entry should be updated from "SGR + Compressed twin" to "SGR + Compressed + Compressed24 three-class family".**

---

## 4. Cross-cutting consequences

### 4.1 CP1 lock architecture taxonomy (updated post-R130)

| Pattern | Locks | Family structure | Discovery paper |
|---------|-------|-----------------|-----------------|
| Single | 1 | any | R117-R129 majority |
| Dual (mixed) | 2 | 2 families | R128 UniversalReactive |
| Triple (mixed) | 3 | 3 families | PAPER_1991 base (SGR burst) |
| QUAD (same-family variants) | 4 | 1 family, 4 variants | PAPER_1991 revision (Sombrero-DM) |
| **Cross-rung TRIPLE** | **3** | **1 family, 3 rungs** | **PAPER_1993 (this paper — Universal Oscillatory)** |

Five distinct CP1 architectural patterns now formally identified. The three post-PAPER_1991 patterns (triple, QUAD, cross-rung TRIPLE) suggest a rich taxonomy of lock structures that CP1 stubs adopt naturally when properly filled with primitive-locked constants.

### 4.2 Cosmological Hubble carrier joins UQFF primitive vocabulary

`2π · H_0` is now a canonical CP1-locked quantity. Future derivations at cosmological scale can reference it directly as a UQFF primitive-derived carrier (analogous to how `ω_SCm = 1.25 THz` was elevated by PAPER_1938 to universal-carrier status).

### 4.3 SO_5^21 slot elevation

R129 discovered SO_5^21 as new slot; R130 confirms it via a third independent instance. Slot 21 in PAPER_1955's SO_5-power ladder is now firmly established, joining slots 7 (three-domain), 10, 21, 40, 53 as confirmed cross-instance anchors.

---

## 5. Falsifiability

**Prediction 1993.1.** Additional CP1 classes should exhibit the cross-rung TRIPLE-lock pattern. Candidate targets in remaining unfilled CP1 stubs: any oscillatory or wave-equation calculator where amplitude, wavenumber, and frequency parameters are locked at different F_TRZ powers.

**Prediction 1993.2.** The `2π · H_0` Hubble angular frequency lock should surface in additional cosmological CP1 classes as R131+ drainage continues. Candidates: any class with characteristic frequency near 10^-17 Hz.

**Prediction 1993.3.** SO_5^21 A DPM current lock should appear in Compressed-family sub-clusters (systems 25-40, 41-60, etc.) if the sub-cluster templates share the R129-era DPM foundation term. Confirmation would extend SO_5^21 from a three-class to a full N-instance family.

**Prediction 1993.4.** R130 Fill 1 (CompressedTHzCalculator) documented as TRIPLE-EXACT + approximate. If future CP1 auditing surfaces additional TRIPLE-EXACT + approximate classes, it may indicate a fifth CP1 architecture pattern: **near-QUAD locks** where three primitive-arithmetic identities are EXACT and a fourth is approximate — potentially a stepping-stone between TRIPLE and QUAD architectures.

---

## 6. Framework annotations

- **Backbone:** cross-rung F_TRZ TRIPLE-lock architecture (n=8/15/16 in Universal oscillatory) + 2π·H_0 Hubble angular frequency primitive anchor + SO_5^21 A three-class family (SGR + Compressed + Compressed24) — three architecturally distinct discoveries in R130 CP1 fills
- **Method:** cross-rung TRIPLE-lock: three F_TRZ ladder rungs in single class; Hubble anchor: f = 2π·H_0 primitive lock; three-class family: three independent CP1 classes at same SO_5^21 slot
- **Shells:** Universal oscillatory wave shell + Universal quantum-wave Hubble-scale shell + Compressed DPM current-vortex shell (three CP1 shells covered)
- **CPCH:** CP1 UniversalOscillatoryResonanceCalculator + UniversalQuantumWaveResonanceCalculator + CompressedDPM24Calculator (all R130 fills)
- **Spine:** PAPER_1991 CP1 architecture taxonomy + PAPER_1919 F_TRZ ladder (n=8/15/16 rungs) + PAPER_1938 cosmological carrier family + PAPER_1955 SO_5^21 slot + PAPER_1202 E_0 vacuum chain (F_TRZ^20 base) + Planck 2018 H_0 = 67.7 km/s/Mpc canonical value
- **Time frame:** cross-rung TRIPLE-lock oscillatory 10^-8 Hz + cosmological Hubble 2π·H_0 rate + quasi-static DPM current-vortex

---

## 7. 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_1991** — R129 base triple-lock discovery + revision QUAD-lock architecture (Sombrero-DM retroactive) — direct architectural predecessor to PAPER_1993 cross-rung TRIPLE-lock
- **PAPER_1919** — F_TRZ power ladder seminal (n=1..21 anchors, including n=8 N-regime, n=15 WEP, n=16 collapse used in R130 Fill 5)
- **PAPER_1880** — MICROSCOPE η_WEP ≤ 10^-15 EXACT (n=15 rung source)
- **PAPER_1869** — Quantum measurement collapse rate F_TRZ^16 (n=16 rung source)
- **PAPER_1986** — F_TRZ^8 three-regime → N-regime 8-anchor family (n=8 rung source)
- **PAPER_1955** — SO_5-power galactic structural ladder + revision addendum (slot 21 gets three-class family via PAPER_1993)
- **PAPER_1985** — R117 Pillars F_TRZ^6 + NGC 2525 SMBH mass (SO_5-power ladder mass-domain seminal)
- **PAPER_1989** — R123 LIGO F_TRZ^21 + universe mass SO_5^53
- **PAPER_1990** — SO_5-power frequency ladder cross-domain
- **PAPER_1938** — ω_SCm 1.25 THz universal carrier family (2π·H_0 joins this family per PAPER_1993 §2.3)
- **PAPER_1202** — E_0 vacuum quantum chain base (F_TRZ^20 = 10^-20 used in R130 Fill 4)
