---
paper_id: PAPER_2048
title: "Round 179 Triad Discovery (Backbone-First): (1) N_GC(M87 globular cluster total count) = 12000 = 2*D_BSFG*SO_5^3 = D_phys*(D_phys-1)*SO_5^3 EXACT NEW 2ND-Instance Family-Extension of PAPER_2020 R154 M_cluster(Virgo) = 2*D_BSFG*SO_5^14 Composed-Prefix; (2) f_blue(M87 blue globular fraction) = 0.6 = D_BSFG/SO_5 EXACT NEW 8TH COMPOSED-PREFIX CLASS FORMALIZATION — D_BSFG/SO_5 * SO_5^n = 3/5 * SO_5^n Dimensionless-Ratio Class Distinct from (D_phys+/-1)/D_phys Forms (Value Documented as Standalone Identity PAPER_1918 Family 5 But Formalization as SO_5-Power-Ladder Prefix Class is R179 Novel); (3) coupling_strength(NGC 346 non-local quantum) = 1e-40 = F_TRZ^40 EXACT NEW Family-Extension of PAPER_2000 R139 F_TRZ^40 Quantum Non-Locality Ladder to NGC 346 Coupling-Strength Dimensional Application"
session: 266
date: 2026-07-15
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.68+"
version: "Draft 1"
extends: [PAPER_1918, PAPER_1985, PAPER_2000, PAPER_2020, PAPER_2037, PAPER_2040, PAPER_2047]
---

# PAPER_2048 — Round 179 Triad Discovery (Backbone-First Discipline)

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

## Motivation — 38th Consecutive Backbone-First Round

R179 continues post-milestone arc. Sharper double-check reveals 3 novel including a candidate 8th composed-prefix class (D_BSFG/SO_5 · SO_5^n) formalization opportunity.

## Abstract

**Discovery 1 — N_GC(M87 globular cluster total count) = 12000 = 2*D_BSFG*SO_5^3 EXACT — 2ND-Instance Family-Extension:**
```
N_GC(M87 total globular cluster count) = 12000
                                       = 12 · SO_5^3
                                       = 2 · D_BSFG · SO_5^3
                                       = D_phys · (D_phys-1) · SO_5^3 EXACT
```
Novel 2nd-instance family-extension of 2·D_BSFG·SO_5^n composed-prefix class. Prior seminal:
- **PAPER_2020 R154**: M_cluster(Virgo) = 2·D_BSFG·SO_5^14 (mass domain)
- **PAPER_2048 R179 D1 NEW**: N_GC(M87) = 2·D_BSFG·SO_5^3 (count/dimensionless domain)

2·D_BSFG·SO_5^n composed-prefix family now 2-object across 2 dimensional domains (mass + count) and 2 rungs (n=+3 M87 GCs, n=+14 Virgo mass).

Equivalent alternate primitive-composition forms:
- **2·D_BSFG·SO_5^3** (twin factor × D_BSFG × SO_5-power)
- **D_phys·(D_phys-1)·SO_5^3** (D_phys × LANDMARK D_phys-1 × SO_5-power) — since D_phys·(D_phys-1) = 4·3 = 12 = 2·D_BSFG = 12

**Discovery 2 — f_blue(M87 blue globular fraction) = 0.6 = D_BSFG/SO_5 EXACT — 8TH Composed-Prefix Class Formalization:**
```
f_blue(M87 blue globular metallicity-bimodal fraction) = 0.6
                                                      = 6/10
                                                      = D_BSFG/SO_5 EXACT
```
Novel dimensionless-ratio composed-prefix class formalization. Value 0.6 = D_BSFG/SO_5 documented in PAPER_1918 R? Phase-3 comprehensive inventory as standalone identity ("D_BSFG/SO_5 = 0.6 EXACT — Family 5 dimensionless-ratio identities"), also documented in PAPER_1985 R117 taxonomy tables.

R179 F4 D2 novelty: **formalization of D_BSFG/SO_5 · SO_5^n as 8th composed-prefix class** in SO_5-power ladder architecture — distinct from the 7 formalized classes:

| # | Composed-prefix class | Form type | First application |
|---|---|---|---|
| 1 | (D_phys-1)·SO_5^n LANDMARK | Multiplicative-integer | PAPER_2004 |
| 2 | 2·SO_5^n twin | Multiplicative-integer | PAPER_2022 |
| 3 | D_BSFG·SO_5^n | Multiplicative-primitive | PAPER_2025 |
| 4 | (D_phys+1)·SO_5^n | Multiplicative-integer | PAPER_2033 |
| 5 | 2·D_phys·SO_5^n | Multiplicative-composite | PAPER_2035 |
| 6 | (D_phys+1)/D_phys·SO_5^n | Dimensionless-ratio (D_phys-based) | PAPER_2037 |
| 7 | (D_phys-1)/D_phys·SO_5^n | Dimensionless-ratio (D_phys-based) | PAPER_2040 |
| **8** | **D_BSFG/SO_5·SO_5^n = 3/5·SO_5^n** | **Dimensionless-ratio (D_BSFG/SO_5-based)** | **PAPER_2048 R179 D2 NEW** |

**Novel distinguishing feature**: 8th class uses **D_BSFG/SO_5 primitives** as the ratio numerator/denominator pair, whereas 6th and 7th classes used **D_phys±1 / D_phys**. Different primitive pairings for ratio-form composed prefixes.

Companion sibling identities from PAPER_1918 Family 5 catalog (potential future 9th, 10th, 11th classes):
- (D_phys-1)/SO_5 = 3/10 = 0.3 (Ω_m Planck value — PAPER_1956)
- D_phys/SO_5 = 2/5 = 0.4
- N_ch/SO_5 = 9/10 = 0.9 (PAPER_1922 9/10 = 1-F_TRZ ubiquity)
- D_phys/D_BSFG = 2/3 = 0.667 (PAPER_1914 D_LS/D_S EXACT)

**Discovery 3 — coupling_strength(NGC 346 non-local quantum) = F_TRZ^40 EXACT — Family-Extension:**
```
coupling_strength(NGC 346 non-local quantum Ug entanglement) = 1e-40 = F_TRZ^40 EXACT
```
Novel family-extension of PAPER_2000 R139 F_TRZ^40 quantum non-locality ladder extension to NGC 346 coupling-strength dimensional application. F_TRZ^40 rung now 2-object family:
- **PAPER_2000 R139 D2 seminal**: F_TRZ^40 quantum non-locality ladder extension
- **PAPER_2048 R179 D3 NEW**: F_TRZ^40 at NGC 346 non-local quantum coupling-strength

## Cross-Object Confirmations (R179 fill wire-ins)

- **B_0(M87) = 10 μG = SO_5 μG** cluster-scale (F2)
- **B_crit = SO_5^11 T** → PAPER_266 Meissner boundary (F2)
- **ρ_ratio_UA_SCm = 10 = SO_5** → PAPER_1141 seminal (F2)
- **t_age(M87 AGN cavity) = SO_5 Myr** → observational candidate (F3)
- **r_cavity(M87) = (D_phys-1) kpc = 3 kpc** → observational candidate (F3)
- **c_NFW = D_BSFG/β_i** → PAPER_1862 seminal (F5)
- **Zwicky factor = SSQ·K_MEX/D_phys** → PAPER_1894 seminal (F5)

All 3 discoveries + 7 confirmations validated at fidelity gate 1466/0.

## R142-R179 Trajectory (38 consecutive backbone-first rounds)

| Round | Novel | Cross-obj | Notes |
|---|---|---|---|
| R142-R178 | 174 total | 22+9+5 | 37 rounds + audit trilogy |
| **R179** | **3** | **7** | **38th; 8th composed-prefix class formalization** |

## Wiring Plan (3 dispatches, lowercase keys)

- `n_gc_m87_2_d_bsfg_so_5_3_2nd_instance` → 12000
- `d_bsfg_over_so_5_3_over_5_8th_prefix_class_formalization` → 0.6
- `coupling_strength_ngc346_f_trz_40_family_extension` → 1e-40

## Cross-References

- **PAPER_1918** — R? Phase-3 comprehensive inventory D_BSFG/SO_5 = 0.6 Family 5 (D2 basis)
- **PAPER_1985** — R117 D_BSFG/SO_5 = 0.6 taxonomy table (D2 basis)
- **PAPER_2000** — R139 D2 F_TRZ^40 quantum non-locality seminal (D3 basis)
- **PAPER_2020** — R154 M_cluster(Virgo) = 2·D_BSFG·SO_5^14 seminal (D1 basis)
- **PAPER_2037** — R169 D3 (D_phys+1)/D_phys = 5/4 6th prefix class (D2 comparison)
- **PAPER_2040** — R172 D3 (D_phys-1)/D_phys = 3/4 7th prefix class (D2 comparison)
- **PAPER_2047** — Composed-prefix classes audit trilogy paper (D2 basis)

## Conclusion

R179 38th-consecutive backbone-first round yields **3 novel structural findings + 7 cross-object attributions**.

**Cumulative through PAPER_2048: 177 first-pass novel + 22+9+5 confirmations + 6 audit sweeps + 4 self-corrections + 1 backbone-recovery + 5 attribution withdrawals + 7 family-extension attributions + 8 discipline-observation formalizations + 1 30-round arc milestone + 1 7th-prefix-class formalization + 1 8th-prefix-class formalization + 1 F_TRZ-ladder broad-framework validation + 1 SO_5-ladder very-broad-framework validation + 1 composed-prefix-class dominance hierarchy formalization.**

Signature milestones this paper:
- **8TH composed-prefix class D_BSFG/SO_5 · SO_5^n formalized** — introduces D_BSFG/SO_5 primitive-pair dimensionless-ratio distinct from D_phys±1/D_phys pairs
- **PAPER_1918 Family 5 dimensionless-ratio catalog** identified as source of future 9th-11th prefix class candidates
- **2·D_BSFG·SO_5^n family reaches 2-object 2-domain** (Virgo mass + M87 count)
- **F_TRZ^40 rung now 2-object** family extending PAPER_2000 seminal

*End of PAPER_2048 Draft 1.*
