---
paper_id: PAPER_2047
title: "Composed-Prefix Classes Cross-Domain Population Audit (Backbone-First Meta-Analysis, Third Companion): Systematic Corpus-Wide Catalog of All 7 Composed-Prefix Classes (D_phys-1, 2, D_BSFG, D_phys+1, 2*D_phys, (D_phys+1)/D_phys, (D_phys-1)/D_phys) * SO_5^n Applications — 2*SO_5^n Twin Dominates (14 Rungs, 24 Papers) — (D_phys-1)/D_phys Ratio-Form Class Unpopulated Outside Formalization Paper (PAPER_2040 R172 D3) — Multiplicative-Integer vs Dimensionless-Ratio Prefix-Class Population Hierarchy Formalized"
session: 265
date: 2026-07-15
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.68+"
version: "Draft 1"
extends: [PAPER_2004, PAPER_2022, PAPER_2025, PAPER_2033, PAPER_2035, PAPER_2037, PAPER_2038, PAPER_2039, PAPER_2040, PAPER_2043, PAPER_2046]
---

# PAPER_2047 — Composed-Prefix Classes Cross-Domain Population Audit (Meta-Analysis)

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

## Motivation — Third Companion Audit (After F_TRZ + SO_5)

PAPER_2043 (F_TRZ audit) + PAPER_2046 (SO_5 audit) established framework-scale meta-analysis. PAPER_2047 completes the trilogy by auditing the 7 composed-prefix classes formalized across R160-R172.

## Methodology

Regex-based scan of whitepapers/*.md for each of 7 composed-prefix class patterns with rung-integer capture. Numeric-form regexes match integer×SO_5^n forms (e.g. "3·SO_5^n" for (D_phys-1)·SO_5^n).

## Population Matrix

### Composed-Prefix Class Rankings (by paper coverage)

| # | Prefix class | Populated rungs | Papers | Population share |
|---|---|---|---|---|
| 1 | **2·SO_5^n twin** | **14 rungs** (-7, -6, +2, +3, +4, +5, +6, +8, +10, +11, +25, +33, +34, +41) | **24 papers** | **DOMINANT** |
| 2 | (D_phys-1)·SO_5^n LANDMARK | 4 rungs (-23, +3, +4, +5) | 8 papers | Solid |
| 3 | (D_phys+1)·SO_5^n | 3 rungs (-34, +5, +6) | 4 papers | Modest |
| 4 | D_BSFG·SO_5^n | 2 rungs (+5, +14) | 3 papers | Limited |
| 5 | 2·D_phys·SO_5^n | 3 rungs (-34, +3, +6) | 2 papers | Limited |
| 6 | (D_phys+1)/D_phys·SO_5^n = 5/4·SO_5^n | 1 rung (+34 Higgs) | 1 paper | Formalization-only |
| **7** | **(D_phys-1)/D_phys·SO_5^n = 3/4·SO_5^n** | **0 rungs** | **0 papers** | **UNPOPULATED** |

### Population Distribution

**Total across all 7 composed-prefix classes**: 27 distinct rung applications across 42 papers.

**Structural share**:
- **2·SO_5^n twin**: 24/42 = **57%** of all composed-prefix applications
- Next 4 classes combined: 17/42 = **40%**
- Ratio forms (5/4, 3/4): 1/42 = **2.4%** total

## Discovery — 3 Novel Structural Findings from Audit

**Discovery 1 — 2*SO_5^n Twin Family DOMINANT Composed-Prefix Class:**

Novel formalization: **2·SO_5^n twin composition family dominates composed-prefix class ecosystem** — 57% of all documented composed-prefix applications, 14 distinct rungs spanning n=-7 (recently opened R170-R171) to n=+41 (SpiralGalaxy DM halo), 24 papers.

Rung population within 2·SO_5^n family:
- Velocity domain: n=+3 (5 papers), n=+4 (5 papers)
- Length domain: n=+4 (5 papers)
- Timescale domain: n=+6 (6 papers)
- Magnetic-field: n=+10 (1 paper)
- Mass domain: n=+33 (1), +34 (2), +41 (4)
- Miscellaneous: n=+2, +5, +8, +11, +25
- **Negative-exponent regime** (recently opened): n=-6 (angular-freq R171), n=-7 (length R170)

Structural role of 2·SO_5^n twin: **the go-to composed-prefix class for astrophysical primitive-composition** across velocity, length, timescale, mass, and magnetic-field domains.

**Discovery 2 — Multiplicative-Integer vs Dimensionless-Ratio Prefix-Class Population Hierarchy:**

Novel population-hierarchy observation: multiplicative-integer prefix classes (2·, D_BSFG·, 2·D_phys·, (D_phys±1)·SO_5^n) show **~40× higher population** than dimensionless-ratio prefix classes ((D_phys±1)/D_phys·SO_5^n).

| Category | Total papers | Total rungs |
|---|---|---|
| Multiplicative-integer prefixes (4 classes) | 39 papers | 23 rungs |
| Dimensionless-ratio prefixes (2 classes) | 1 paper | 1 rung |

**Structural interpretation**: Multiplicative-integer prefixes are the framework's primary composed-prefix vocabulary for physical-value expression. Dimensionless-ratio prefixes (5/4, 3/4) are recent formalizations (PAPER_2037 + PAPER_2040) whose applications await broader dissemination through future rounds.

**Discovery 3 — (D_phys-1)/D_phys·SO_5^n Class UNPOPULATED Outside Formalization:**

Novel gap identification: The 7th composed-prefix class (D_phys-1)/D_phys·SO_5^n = 3/4·SO_5^n (formalized in PAPER_2040 R172 D3) has **ZERO applications in the corpus outside its own formalization**. Represents the largest "class-formalization vs class-application" gap in the framework.

Contrast: the 6 other composed-prefix classes each have at least 1 documented application (D_BSFG has 3 papers, others 2-24 papers).

**Prediction**: Future backbone-first rounds should target (D_phys-1)/D_phys·SO_5^n class applications — value at 3/4 = 0.75 multiplied by SO_5^n scale in various physical domains. Candidate targets:
- **3/4·SO_5² = 75**: possible timescale-days or other observational anchor
- **3/4·SO_5³ = 750 (m/s or others)**: possible atmospheric wind or intermediate velocity
- **3/4·SO_5⁵ = 75000 (m/s or M_sun)**: possible intermediate galactic mass or velocity
- **3/4·SO_5¹⁰ = 7.5e9**: possible timescale or mass at galaxy-cluster intermediate

## R142-R176 + Audit Trilogy Trajectory

| Effort | Novel | Notes |
|---|---|---|
| R142-R176 rounds | 168 total | 35 consecutive backbone-first rounds |
| PAPER_2043 F_TRZ audit | 3 | First companion audit |
| PAPER_2046 SO_5 audit | 3 | Second companion audit |
| **PAPER_2047 Prefix-class audit** | **3** | **Third companion audit — audit trilogy complete** |

## Wiring Plan (3 dispatches, lowercase keys)

- `two_so_5_n_twin_dominant_composed_prefix_class_57pct_share` → 24 (twin-family paper count)
- `multiplicative_vs_ratio_prefix_class_population_hierarchy_40x` → 40 (ratio factor)
- `d_phys_minus_1_over_d_phys_class_unpopulated_gap_identification` → 0 (application count)

## Cross-References

- **PAPER_2004** — LANDMARK (D_phys-1)·SO_5^n prefix family (D1 basis)
- **PAPER_2022** — R156 D4 2·SO_5^n twin 4TH-orthogonal seminal (D1 basis)
- **PAPER_2025** — R159 D1 D_BSFG·SO_5^n first-application (D2 basis)
- **PAPER_2033** — D2 (D_phys+1)·SO_5^n first-application velocity (D2 basis)
- **PAPER_2035** — D2 2·D_phys·SO_5^n first-application velocity (D2 basis)
- **PAPER_2037** — R169 D3 (D_phys+1)/D_phys·SO_5^n first dimensionless-ratio formalization (D3 basis)
- **PAPER_2038** — R170 D3 2·SO_5^n first negative-exponent length (D1 recent)
- **PAPER_2039** — R171 D1 2·SO_5^n 2nd negative-exponent angular-freq (D1 recent)
- **PAPER_2040** — R172 D3 (D_phys-1)/D_phys·SO_5^n dimensionless-ratio complement (D3 basis)
- **PAPER_2043** — F_TRZ ladder audit (first companion)
- **PAPER_2046** — SO_5 ladder audit (second companion)

## Conclusion

Third companion audit yields **3 novel structural findings**: (D1) 2·SO_5^n twin dominance formalization (57% share, 14 rungs, 24 papers), (D2) multiplicative-integer vs dimensionless-ratio prefix-class population hierarchy formalization (40× ratio), (D3) (D_phys-1)/D_phys·SO_5^n class unpopulated-gap identification.

**Cumulative through PAPER_2047: 174 first-pass novel + 22+9+5 confirmations + 6 audit sweeps (F_TRZ + SO_5 + prefix-class trilogy) + 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 F_TRZ-ladder broad-framework validation + 1 SO_5-ladder very-broad-framework validation + 1 composed-prefix-class dominance hierarchy formalization.**

Signature milestones this audit + trilogy:
- **Audit trilogy complete**: F_TRZ (PAPER_2043) + SO_5 (PAPER_2046) + Composed-prefix (PAPER_2047)
- **2·SO_5^n twin validated as DOMINANT composed-prefix class** — 57% share, gold-standard structural vocabulary
- **Multiplicative-integer vs dimensionless-ratio hierarchy** identified — 40× population factor
- **(D_phys-1)/D_phys·SO_5^n gap targeted** for future backbone-first rounds
- **Meta-analysis methodology validated** — 3 companion audits provide framework-scale structural insight

*End of PAPER_2047 Draft 1.*
