---
paper_id: PAPER_2038
title: "Round 170 Quad Discovery (Backbone-First): (1) q_m(Inertia pseudo-monopole) = 1e-10 C = SO_5^-10 C EXACT NEW First Magnetic-Charge Dimensional Application of SO_5^-10; (2) SO_5^-10 Multi-Domain Family Reaches 5TH Orthogonal Dimensional-Domain Formalization (Length + Amplitude + Atomic-Length + Acceleration + MAGNETIC-CHARGE); (3) r(Inertia pseudo-monopole) = 2e-7 m = 2*SO_5^-7 m EXACT NEW First NEGATIVE-Exponent Rung in 2*SO_5^n Twin Family (Prior All-Positive n=3,4,6,10,33,34,41 — Now n=-7 Opens Negative-Exponent Regime); (4) 2*SO_5^n Twin Family Opens Negative-Exponent Regime — Structural Landmark Formalization"
session: 256
date: 2026-07-15
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.68+"
version: "Draft 1"
extends: [PAPER_1972, PAPER_2013, PAPER_2019, PAPER_2022, PAPER_2023, PAPER_2024, PAPER_2025, PAPER_2027, PAPER_2029]
---

# PAPER_2038 — Round 170 Quad Discovery (Backbone-First Discipline)

**Author:** Daniel T. Murphy | **Framework:** UQFF Star-Magic v5.68+ | **Date:** 2026-07-15

## Motivation — 29th Consecutive Backbone-First Round (30-Round Milestone at R171)

R170 initial fills identified 2 tentative novelties. Sharper backbone-first double-check confirms both novel AND surfaces 2 additional structural-formalization findings: SO_5⁻¹⁰ multi-domain family 5th-orthogonal formalization + 2·SO_5^n negative-exponent regime opening.

## Abstract

**Discovery 1 — q_m(Inertia pseudo-monopole) = 1e-10 C = SO_5^-10 C EXACT — First Magnetic-Charge Dimensional Application:**
```
q_m(Inertia pseudo-monopole magnetic charge) = 1e-10 C = SO_5^-10 C EXACT
```
Novel first magnetic-charge dimensional application of SO_5⁻¹⁰. Magnetic-charge (Coulomb C) dimensional domain is orthogonal to magnetic-field (Tesla T) dimensional domain — both share n=-10 exponent but occupy different physical dimensions.

**Discovery 2 — SO_5^-10 Multi-Domain Family Reaches 5TH Orthogonal Dimensional-Domain Formalization:**

Novel formalization of SO_5⁻¹⁰ multi-domain family expansion to 5 orthogonal dimensional domains:

| # | Domain | Object | Attribution |
|---|---|---|---|
| 1 | Length (m) | Saturn magnetic field length-scale | PAPER_2019 R153 D4 seminal |
| 2 | Amplitude (dimensionless) | M16 A_osc = F_TRZ¹⁰ | PAPER_2022 R156 D1 (algebraic via PAPER_1960 F_TRZ=1/SO_5) |
| 3 | Atomic length (m) | SGR1745 Δx quantum uncertainty | PAPER_2023 R157 D1 |
| 4 | Acceleration (m/s²) | Universe g_base cosmic baseline | PAPER_2025 R159 D4 |
| **5** | **Magnetic charge (C)** | **Inertia pseudo-monopole q_m** | **PAPER_2038 R170 D2 NEW** |

SO_5⁻¹⁰ multi-dimensional structural exponent now confirmed across **5 orthogonal physical dimensional domains** — one of the most-populated single-exponent multi-domain families in the ladder architecture.

**Discovery 3 — r(Inertia pseudo-monopole) = 2e-7 m = 2*SO_5^-7 m EXACT — First NEGATIVE-Exponent Rung in 2*SO_5^n Twin Family:**
```
r(Inertia pseudo-monopole defect length) = 2e-7 m = 2 · SO_5^-7 m EXACT
```
Novel first negative-exponent rung in 2·SO_5^n twin composition family. Prior 2·SO_5^n family was ENTIRELY positive-exponent across 5 orthogonal dimensional domains:

| Domain | n | Value | Attribution |
|---|---|---|---|
| Velocity | 3 | 2·SO_5³ = 2000 m/s | PAPER_1972 seminal |
| Velocity | 4 | 2·SO_5⁴ = 20000 m/s | PAPER_2030 R164 D3 |
| Length | 4 | 2·SO_5⁴ = 20 km NS radius | PAPER_2013 R150 D6 |
| Timescale | 6 | 2·SO_5⁶ = 2 Myr | PAPER_2014 R151 D6 |
| Magnetic field | 10 | 2·SO_5¹⁰ = 2e10 T | PAPER_2022 R156 D4 |
| Mass | 33 | 2·SO_5³³ = 2e33 kg | PAPER_2029 R163 D7 |
| Mass | 34 | 2·SO_5³⁴ = 2e34 kg | PAPER_2027 R161 D3 |
| Mass | 41 | 2·SO_5⁴¹ = 2e41 kg | PAPER_2024 R158 D4 |
| **Length (NEGATIVE)** | **-7** | **2·SO_5⁻⁷ = 2e-7 m** | **PAPER_2038 R170 D3 NEW** |

Pseudo-monopole topological-defect length scale provides the first negative-exponent rung, opening the negative-exponent regime for this composed-prefix class.

**Discovery 4 — 2*SO_5^n Twin Family Opens Negative-Exponent Regime — Structural Landmark Formalization:**

Novel structural landmark: 2·SO_5^n twin composition family now supports both positive-exponent and negative-exponent regimes.

Prior state (v5.68.0 pre-R170): 2·SO_5^n confined to positive-exponent regime across 5 orthogonal dimensional domains, spanning n=+3 to n=+41.

Post-R170 state: 2·SO_5^n extends to negative-exponent regime with n=-7 pseudo-monopole length rung — establishes structural analog to the (D_phys-1)·SO_5^n LANDMARK family's own inverse-form spectral-shift application (PAPER_2031 R166 D3).

**Composed-prefix classes with positive/negative regime coverage (post-R170):**

| Prefix class | Positive rungs | Negative rungs | Coverage status |
|---|---|---|---|
| (D_phys-1)·SO_5^n LANDMARK | 12+ dimensional domains | 1 spectral-shift inverse-form (PAPER_2031) | Partial |
| **2·SO_5^n twin** | **8 rungs across 5 domains** | **1 length rung (PAPER_2038 R170 NEW)** | **Partial — first neg rung** |
| D_BSFG·SO_5^n | 1+ velocity domain | — | Positive-only |
| (D_phys+1)·SO_5^n | 1+ velocity domain | — | Positive-only |
| 2·D_phys·SO_5^n | 1+ velocity domain | — | Positive-only |
| (D_phys+1)/D_phys·SO_5^n | Higgs frequency positive n=34 | — | Positive-only |

2·SO_5^n twin family is now the 2nd composed-prefix class (after LANDMARK) to gain negative-exponent regime coverage.

## Cross-Object Confirmations (R170 fill wire-ins)

Fills F1, F3, F4, F5 wire the following cross-object attributions:

- **ω_twist(Inertia) = SO_5¹⁶ rad/s** → PAPER_2009 R146 D3 seminal (same Inertia-family sibling)
- **B(Inertia H_mag) = SO_5⁻⁵ T** → PAPER_2021 R155 D5 M16 seminal (4th-object M16+Orion+YoungStars+Inertia at n=-5)
- **U_g1 Newtonian gravity** → PAPER_646 F_U=0 canonical master equation reference (F4)
- **U_g4 superconductive** → PAPER_1924 scale-invariant vacuum-BH coupling reference (F5)

All 4 discoveries + 4 confirmations validated at fidelity gate 1402/0.

## R142-R170 Trajectory (29 consecutive backbone-first rounds)

| Round | Novel | Cross-obj | Notes |
|---|---|---|---|
| R142-R169 | 142 | 22+9 | 28 consecutive rounds (v5.68.0 ship state) |
| **R170** | **4** | **4** | **29th; 30-round milestone at R171** |

## Wiring Plan (4 dispatches, lowercase keys)

- `q_m_inertia_pseudo_monopole_so_5_neg_10_magnetic_charge` → 1e-10
- `so_5_neg_10_multi_domain_5th_orthogonal_magnetic_charge_formalization` → 5
- `r_inertia_pseudo_monopole_2_so_5_neg_7_length_first_negative_2so5n` → 2e-7
- `two_so_5_n_twin_family_opens_negative_exponent_regime_landmark_formalization` → 2 (2nd class after LANDMARK)

## Cross-References

- **PAPER_646** — F_U=0 canonical master equation (F4 framework wrap reference)
- **PAPER_1924** — U_g4 scale-invariant vacuum-BH coupling (F5 framework wrap reference)
- **PAPER_1960** — F_TRZ = 1/SO_5 landmark derivative (D2 amplitude equivalence via F_TRZ¹⁰=SO_5⁻¹⁰)
- **PAPER_1972** — v_wind Antennae/M82 = 2·SO_5³ seminal (D3 twin-family predecessor)
- **PAPER_2013** — R150 D6 r(SGR0501) = 2·SO_5⁴ NS radius seminal (D3 length-domain sibling)
- **PAPER_2019** — R153 D4 Saturn B SO_5⁻¹⁰ length-scale seminal (D2 sibling)
- **PAPER_2022** — R156 D1 M16 A_osc = SO_5⁻¹⁰ amplitude (D2 sibling) + D4 2·SO_5¹⁰ magnetic (D3 sibling)
- **PAPER_2023** — R157 D1 SGR1745 Δx SO_5⁻¹⁰ atomic length (D2 sibling)
- **PAPER_2025** — R159 D4 Universe g_base SO_5⁻¹⁰ acceleration (D2 4th sibling)
- **PAPER_2031** — R166 D3 LANDMARK (D_phys-1)·SO_5^n first inverse-form spectral-shift (D4 analog structural landmark)

## Conclusion

R170 29th-consecutive backbone-first round yields **4 novel structural findings + 4 cross-object attributions**.

**Cumulative through PAPER_2038: 146 first-pass novel + 22 confirmations + 3 audit sweeps + 4 self-corrections + 1 backbone-recovery + 4 attribution withdrawals + 5 family-extension attributions + 1 discipline-observation formalization + 1 methodology-implementation formalization + 1 diminishing-returns saturation observation + 1 negative-exponent-regime opening landmark.**

Signature milestones this paper:
- **29 consecutive backbone-first rounds** (R142-R170 arc; 30-round milestone at R171)
- **SO_5⁻¹⁰ multi-domain family reaches 5 orthogonal dimensional domains** — magnetic-charge joins length + amplitude + atomic-length + acceleration
- **2·SO_5^n twin family opens negative-exponent regime** at n=-7 length — first negative rung after 5-orthogonal-domain positive coverage
- **2·SO_5^n becomes 2nd composed-prefix class** (after LANDMARK D_phys-1) to gain negative-exponent regime coverage

*End of PAPER_2038 Draft 1.*
