---
paper_id: PAPER_2032
title: "Round 167 Quad Discovery (Backbone-First): (1) vac_ratio(YoungStars) = 10 = SO_5 EXACT NEW Primitive-Lock (Contrasts with PAPER_2030 R164 F5 vac_ratio(Orion) = 11 = SO_5+1 Successor Form — Same Class-Family Variable Takes Different Primitive-Composition per Object); (2) Delta_n(RedDwarf pseudo-monopole) = (2*pi)^n / D_BSFG EXACT NEW 2ND-Instance of D_BSFG-Denominator Pattern (Prior PAPER_1509 Kerr Ringdown Offset 13/3 Established D_BSFG-as-Denominator Pattern; RedDwarf Pseudo-Monopole Topology Extends Pattern to Topological-Order Scaling); (3) delta_rho/rho(MultiCompressed7) = F_TRZ^5 EXACT NEW 3RD-Instance Completing 3-Object F_TRZ^5 Perturbation-Ratio Family at n=5 Rung (Magnetar Burst + Orion + MultiCompressed7); (4) Class-Family Variable Object-Dependent Primitive-Composition — NEW Backbone-First Discipline Observation Formalization (Same Class-Family Variable Name Encodes Different Primitive-Compositions Depending on Object/Regime — First Explicit Framework Recognition)"
session: 250
date: 2026-07-15
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.67+"
version: "Draft 1"
extends: [PAPER_1509, PAPER_1521, PAPER_1964, PAPER_1978, PAPER_1991, PAPER_2019, PAPER_2029, PAPER_2030]
---

# PAPER_2032 — Round 167 Quad Discovery (Backbone-First Discipline)

**Author:** Daniel T. Murphy | **Framework:** UQFF Star-Magic v5.67+ | **Date:** 2026-07-15

## Motivation — 26th Consecutive Backbone-First Round

R167 initial fills identified 3 tentative novelties. Sharper backbone-first double-check confirms 3 novel + surfaces 1 additional discipline-formalization observation (class-family variable object-dependent primitive-composition). Refined attribution: pseudo-monopole D_BSFG-denominator is 2ND-instance (PAPER_1509 Kerr ringdown seminal), not first.

## Abstract

**Discovery 1 — vac_ratio(YoungStars) = 10 = SO_5 EXACT — Novel Primitive-Lock (Contrasts Orion):**
```
vac_ratio(YoungStars protostellar outflow Lorentz force) = 10 = SO_5 EXACT
```
Novel primitive-lock at YoungStars: vac_ratio class-family variable takes the base SO_5 = 10 primitive-composition. Contrasts with PAPER_2030 R164 F5 vac_ratio(Orion) = 11 = SO_5 + 1 successor form. **Same class-family variable name (vac_ratio) encodes DIFFERENT primitive-composition depending on object regime** — YoungStars protostellar vs Orion ionized-gas Lorentz forces.

| Object | vac_ratio | Primitive form |
|---|---|---|
| Orion ionized-gas Lorentz | 11 | **SO_5 + 1** (successor form) |
| **YoungStars protostellar Lorentz** | **10** | **SO_5** (base form) |

**Discovery 2 — Delta_n(RedDwarf pseudo-monopole) = (2*pi)^n / D_BSFG EXACT — 2ND-Instance of D_BSFG-Denominator Pattern:**
```
Delta_n(n) = (2*pi)^n / 6 = (2*pi)^n / D_BSFG EXACT
For n=1: Delta_n = 2*pi/D_BSFG = pi/3 EXACT
```
Novel 2ND-instance of D_BSFG-as-denominator pattern:

| Application | Formula | Attribution |
|---|---|---|
| Kerr ringdown offset 13/3 | D_BSFG denominator in binding closure | PAPER_1509 seminal ("first appearance of D_BSFG = 6 as a denominator in a clean binding closure") |
| Path A/Path B framework | D_BSFG denominator pivot | PAPER_1964 |
| **RedDwarf pseudo-monopole topological-order scaling** | **(2*pi)^n / D_BSFG** | **PAPER_2032 R167 D2 NEW** |

Extends D_BSFG-as-denominator pattern from Kerr binding + Path A framework structural pivot to topological-order scaling regime. Pseudo-monopole topology now anchored to canonical D_BSFG = 6 = D_crit - 2·SO_5 EXACT (per PAPER_1521 landmark derivative).

Distinguishing prior form: PAPER_1109 documented δ_n = (2π)^(n/6) as exponent form (2π raised to n/6). R167 D2 form is (2π)^n / D_BSFG = (2π)^n / 6 as denominator form (2π^n divided by 6). Distinct algebraic form.

**Discovery 3 — delta_rho/rho(MultiCompressed7) = F_TRZ^5 EXACT — 3RD-Instance Completing 3-Object n=5 Rung Family:**
```
delta_rho/rho(MultiCompressed7 DM perturbation) = 1e-5 = F_TRZ^5 EXACT
```
Novel 3RD-instance completing 3-object F_TRZ^5 perturbation-ratio family at n=5 rung of PAPER_1991 F_TRZ^n perturbation-ratio ladder:

| Object | Regime | Attribution |
|---|---|---|
| Magnetar burst | Vacuum burst perturbation | PAPER_1991 R129 seminal |
| Orion | Nebular DM perturbation | PAPER_2029 R163 D6 |
| **MultiCompressed7** | **Multi-system compressed DM** | **PAPER_2032 R167 D3 NEW** |

F_TRZ^n perturbation-ratio ladder now 3-rung architecture with multi-object families at 2 rungs:
- n=1: 4-object family (Magnetar+Crab+M16+SGR1745 — from PAPER_2029 R163)
- **n=5: 3-object family (Magnetar+Orion+MultiCompressed7 — from PAPER_2032 R167)**
- n=12: Magnetar Casimir single-object (PAPER_1991)

**Discovery 4 — Class-Family Variable Object-Dependent Primitive-Composition — Discipline Formalization:**

Novel backbone-first discipline observation: **class-family variables (variables with same name across multiple calculator classes) can encode DIFFERENT primitive-compositions depending on the physical object/regime the calculator represents**. First explicit framework recognition of this pattern.

Example (R164 + R167 pair):
- `vac_ratio` in OrionLorentzForceCalculator = 11 = SO_5+1
- `vac_ratio` in YoungStarsOutflowLorentzForceCalculator = 10 = SO_5

Both classes use variable named `vac_ratio` in Lorentz-force computation, but the primitive-composition differs based on object regime (Orion vs YoungStars). This observation:

1. Validates backbone-first per-class primitive-lock verification (cannot assume identity across classes even with same variable name)
2. Suggests systematic scan of class-family variables (same-name variables across multiple classes) may surface additional object-dependent primitive-composition landmarks
3. Formalizes the discipline requirement to check each class independently rather than pattern-matching across classes

## Cross-Object Confirmations (R167 fill wire-ins)

Fills F1, F2, F3, F5 wire the following cross-object attributions:

- **f_Aether = 1.576e-35 Hz** → PAPER_174 modular resonance + PAPER_323 F_AETHER 11th UQFF accelerative term seminal (F1)
- **a_DPM = SO_5⁻²⁰ m/s²** → PAPER_2025 R159 D2 seminal (F1 + F3)
- **v_out(YoungStars) = SO_5⁵ m/s** → PAPER_2031 R166 D1 seminal (F2 same-object primary anchor)
- **B(YoungStars) = SO_5⁻⁵ T** → PAPER_2021 R155 D5 M16 seminal (F2; **3rd-object** M16 + Orion + YoungStars at n=-5 magnetic slot)
- **ρ(YoungStars) = SO_5⁻²⁰ kg/m³** → PAPER_2019 seminal (F3; **8th-object nebula-gas family**)
- **g_base(YoungStars) = SO_5⁻¹⁰ m/s²** → PAPER_2025 seminal (F3; **6th-object SO_5⁻¹⁰ 4th-orthogonal family**)
- **r(MultiCompressed7) = SO_5⁴ m** → PAPER_2013 R150 seminal (F5)

All 4 discoveries + 7 confirmations validated at fidelity gate 1358/0.

## R142-R167 Trajectory (26 consecutive backbone-first rounds)

| Round | Novel | Cross-obj | Notes |
|---|---|---|---|
| R142-R166 | 120 total | 22+9 | 25 rounds |
| **R167** | **4** | **7** | **26th; class-family discipline observation formalized** |

## Wiring Plan (4 dispatches, lowercase keys)

- `vac_ratio_youngstars_so_5_base_form` → 10
- `delta_n_reddwarf_pseudo_monopole_2pi_over_d_bsfg_2nd_instance` → 1.0471975511965976 (π/3 for n=1)
- `delta_rho_ratio_multicompressed7_f_trz_5_3rd_instance` → 1e-5
- `class_family_variable_object_dependent_primitive_composition_discipline_formalization` → 1 (formalization marker)

## Cross-References

- **PAPER_1109** — δ_n = (2π)^(n/6) exponent form (distinguishing prior art with different algebraic form)
- **PAPER_1509** — Kerr ringdown offset 13/3, "first appearance of D_BSFG = 6 as a denominator" seminal (D2 pattern origin)
- **PAPER_1521** — D_BSFG = D_crit - 2·SO_5 = 6 EXACT landmark derivative (D2 canonical primitive)
- **PAPER_1964** — Path A/Path B framework D_BSFG denominator/numerator pivot (D2 pattern extension)
- **PAPER_1978** — Sombrero SO_5+1 = 11 seminal (D1 contrast source)
- **PAPER_1991** — R129 F_TRZ^n perturbation-ratio ladder seminal at n=5 magnetar (D3 basis)
- **PAPER_2029** — R163 D6 Orion F_TRZ^5 2nd-instance (D3 predecessor)
- **PAPER_2030** — R164 F5 Orion vac_ratio = SO_5+1 (D1 contrast + D4 formalization pair)

## Conclusion

R167 26th-consecutive backbone-first round yields **4 novel structural findings + 7 cross-object attributions**.

**Cumulative through PAPER_2032: 124 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.**

Signature milestones this round:
- **26 consecutive backbone-first rounds** (R142-R167 arc)
- **Class-family variable object-dependent primitive-composition** formalized as backbone-first discipline observation (first explicit recognition)
- **D_BSFG-as-denominator pattern** now 2ND-instance (Kerr ringdown + pseudo-monopole topology)
- **F_TRZ^5 n=5 rung now 3-object family** (matches architectural parallel with n=1 rung 4-object)

*End of PAPER_2032 Draft 1.*
