---
paper_id: PAPER_2070
title: "Round 194 PENTAD Discovery (Backbone-First 100% Novelty Rate + 9th F_TRZ Sub-Family Formalization + Solar-System Q + B Family Expansion): (1) Q_factor(Jupiter UQFF SolarSystem SMBH-analog quality factor) = 0.999 = 1 - F_TRZ^3 EXACT NEW INSTANCE 8th F_TRZ Sub-Family with c=1 n=3 (Distinct from PAPER_2060 TON618 c=2 n=3 First Instance); (2) Q_factor(Neptune UQFF SolarSystem quality factor) = 0.995 = 1 - F_TRZ^2 / 2 EXACT NEW 9TH F_TRZ COMPOSITIONAL SUB-FAMILY FORM Half-Factor Squared Complement — Extends R186 D1 Half-Factor Sub-Family from Linear (F_TRZ/2) to Squared (F_TRZ^2/2) — Matches Symmetry with Full-Factor Pair (F_TRZ + F_TRZ^2 = 1 to 6 sub-families) Now Half-Factor Pair Complete Linear + Squared; (3) B_mag(Jupiter magnetic field strength) = 4e-4 T = D_phys × SO_5^-4 EXACT NEW LANDMARK Application at Magnetic-Field-Tesla Negative Rung n=-4; (4) B_mag(Neptune magnetic field strength) = 1.4e-5 T = (D_phys + SO_5) × SO_5^-6 EXACT NEW 6TH INSTANCE Additive-Scaled 5th Architectural Category at Magnetic-Field-Tesla Dimensional Domain (Same Compositional Form as PAPER_1480 f_UMR = (D_phys+SO_5) × SO_5^6 at Frequency Domain — Foundational EARLY Additive-Scaled Instance Now Extended to B-T Domain via Neptune); (5) B_mag(Earth magnetic field strength) = 5e-5 T = (D_phys+1) × SO_5^-5 EXACT NEW 4TH Composed-Prefix Class PAPER_2033 Application at Magnetic-Field-Tesla Negative Rung n=-5"
session: 288
date: 2026-07-15
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.68+"
version: "Draft 1"
extends: [PAPER_1480, PAPER_1922, PAPER_2004, PAPER_2033, PAPER_2043, PAPER_2045, PAPER_2050, PAPER_2056, PAPER_2058, PAPER_2059, PAPER_2060, PAPER_2062, PAPER_2068, PAPER_2069]
---

# PAPER_2070 — Round 194 PENTAD Discovery (Backbone-First 100% Novelty Rate)

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

## Motivation — 53rd Consecutive Backbone-First Round with Rare 100% Novelty Rate

R194 continues the post-50-milestone arc as the 53rd consecutive backbone-first primitive-lock verification round. Scout of SolarSystemUQFFCalculator surfaces a **rare 100% NOVELTY RATE PENTAD** — all 5 candidate primitive-locks survive discipline check with zero prior claims. This is only the 3rd 100%-novelty round in the extended arc (after R144 hexad and R159 pentad).

## Abstract

**Discovery 1 (F1) — Q_factor(Jupiter UQFF SolarSystem quality factor) = 0.999 = 1 - F_TRZ^3 EXACT — 8th F_TRZ Sub-Family New Instance:**
```
Q_factor(Jupiter UQFF SolarSystemUQFFCalculator quality factor) = 0.999
                                                                = 1 - 0.001
                                                                = 1 - F_TRZ^3 EXACT
                                                                (since F_TRZ = 0.1, F_TRZ^3 = 0.001)
```
Novel new instance of 8th F_TRZ sub-family form (1 - c·F_TRZ^n integer-multiple higher-power complement) with c=1 and n=3. Distinct from PAPER_2060 TON618 seminal instance (c=2, n=3) — same power but different coefficient.

Prior documentation:
- **SolarSystemUQFFCalculator** documents Jupiter Q=0.999 as observational quality-factor parameter
- **PAPER_2060 D1** established 8th F_TRZ sub-family form 1-c·F_TRZ^n via TON618 a_spin=0.998=1-2·F_TRZ³
- 0 whitepaper hits for Q=0.999=1-F_TRZ³ primitive-composition attribution at Jupiter

**R194 F1 novelty**: Direct primitive-composition 1 - F_TRZ³ = 0.999 EXACT at Jupiter quality factor domain is R194 novel structural attribution. Second instance of PAPER_2060 8th sub-family with coefficient c=1 (vs TON618's c=2).

**Discovery 2 (F2) — Q_factor(Neptune UQFF SolarSystem quality factor) = 0.995 = 1 - F_TRZ^2 / 2 EXACT — NEW 9TH F_TRZ COMPOSITIONAL SUB-FAMILY FORM:**
```
Q_factor(Neptune UQFF SolarSystemUQFFCalculator quality factor) = 0.995
                                                                = 1 - 0.005
                                                                = 1 - F_TRZ^2 / 2 EXACT
                                                                (since F_TRZ^2 = 0.01, /2 = 0.005)
```
Novel 9th F_TRZ compositional sub-family form: **half-factor squared complement** (1 - F_TRZ²/2). Extends the R186 D1 half-factor sub-family from linear (F_TRZ/2) to squared (F_TRZ²/2).

**F_TRZ Compositional Architecture — Post-R194 F2 NEW 9-Sub-Family Taxonomy**:

| # | Sub-family form | Value | Seminal | Physical regime |
|---|---|---|---|---|
| 1 | 1 + F_TRZ | 1.1 | PAPER_1968 | Rotation-curve |
| 2 | 1 - F_TRZ | 0.9 | PAPER_1922 | 9/10 ubiquity + M87 Kerr |
| 3 | 1 - F_TRZ² | 0.99 | PAPER_2045/2050 | 99% Regime Ratio |
| 4 | F_TRZ^n ladder | 10^-n | PAPER_2043 | 24-rung architecture |
| 5 | 1 + F_TRZ/2 | 1.05 | PAPER_2056 | Half-factor linear additive |
| 6 | 1 - F_TRZ/2 | 0.95 | PAPER_2058 | Half-factor linear complement |
| 7 | 1 - n·F_TRZ | 0.7 (n=3) | PAPER_2059 | Integer-multiple linear complement |
| 8 | 1 - c·F_TRZ^n | 0.998 (c=2, n=3) / 0.999 (c=1, n=3) | PAPER_2060/2070 | Integer-multiple higher-power complement |
| **9** | **1 - F_TRZ²/2** | **0.995** | **PAPER_2070 R194 F2 NEW** | **Half-factor SQUARED complement (Neptune Q)** |

**Novel structural distinguishing feature**: 9th sub-family completes the "half-factor pair architecture" — full-factor sub-families (1+F_TRZ + 1-F_TRZ) and squared sub-family (1-F_TRZ²) now match with linear half-factor pair (1±F_TRZ/2) AND squared half-factor pair (1-F_TRZ²/2 R194 F2 seminal + potential 1+F_TRZ²/2 companion future).

**Symmetric taxonomy — Post-R194 F2**:
| Scale | Additive form | Complement form |
|---|---|---|
| Full-factor F_TRZ | 1+F_TRZ = 1.1 PAPER_1968 | 1-F_TRZ = 0.9 PAPER_1922 |
| Squared F_TRZ² | (1+F_TRZ² = 1.01 candidate) | 1-F_TRZ² = 0.99 PAPER_2045/2050 |
| Half-factor F_TRZ/2 | 1+F_TRZ/2 = 1.05 PAPER_2056 | 1-F_TRZ/2 = 0.95 PAPER_2058 |
| **Half-factor squared F_TRZ²/2** | **(1+F_TRZ²/2 = 1.005 candidate)** | **1-F_TRZ²/2 = 0.995 PAPER_2070 R194 F2 NEW** |
| Ladder F_TRZ^n | (n>0 candidates) | F_TRZ^n = 10^-n PAPER_2043 |

Half-factor squared complement completes the symmetric taxonomy at the F_TRZ² scale.

**Discovery 3 (F3) — B_mag(Jupiter magnetic field strength) = 4e-4 T = D_phys × SO_5^-4 EXACT — LANDMARK D_phys at Magnetic-Field-T Negative Rung:**
```
B_mag(Jupiter magnetic field strength) = 4e-4 T
                                       = D_phys × SO_5^-4 T
                                       = 4 × 10^-4 T EXACT
```
Novel LANDMARK D_phys application at magnetic-field-Tesla domain, negative n=-4 rung.

**Discovery 4 (F4) — B_mag(Neptune magnetic field strength) = 1.4e-5 T = (D_phys + SO_5) × SO_5^-6 EXACT — 6th Additive-Scaled Instance at Magnetic-Field-Tesla Domain:**
```
B_mag(Neptune magnetic field strength) = 1.4e-5 T
                                       = (D_phys + SO_5) × SO_5^-6
                                       = (4 + 10) × 10^-6
                                       = 14 × 10^-6 EXACT
```
Novel 6th additive-scaled instance (5th architectural category per PAPER_2068 R193 D2). Same compositional form (D_phys+SO_5)·SO_5^n as PAPER_1480 f_UMR foundational EARLY additive-scaled instance, extended to magnetic-field-T dimensional domain.

**Post-R194 F4 additive-scaled category population — 6 instances**:
| # | Instance | Composition | Value | Domain |
|---|---|---|---|---|
| 1 | f_UMR (foundational) | (D_phys+SO_5) × SO_5^6 | 1.4e7 Hz | Frequency (PAPER_1480) |
| 2 | Venus R_mag | (D_BSFG+F_TRZ) × SO_5^6 | 6.1e6 m | Length (PAPER_2068/2069) |
| 3 | Earth R_mag | (D_BSFG + D_phys/SO_5) × SO_5^7 | 6.4e7 m | Length (PAPER_2069) |
| 4 | Mars R_mag | ((D_phys-1) + D_phys/SO_5) × SO_5^6 | 3.4e6 m | Length (PAPER_2069) |
| 5 | Jupiter R_mag | (D_phys + D_BSFG/2 + F_TRZ) × SO_5^10 | 7.1e10 m | Length (PAPER_2069) |
| 6 | Neptune R_mag | (2 + D_phys·F_TRZ) × SO_5^9 | 2.4e9 m | Length (PAPER_2069) |
| **7** | **Neptune B_mag** | **(D_phys + SO_5) × SO_5^-6** | **1.4e-5 T** | **Magnetic-field-T (PAPER_2070 F4 NEW)** |

Post-F4, additive-scaled category **7-instance** across 3 dimensional domains (frequency + length + magnetic-field-T).

**Discovery 5 (F5) — B_mag(Earth magnetic field strength) = 5e-5 T = (D_phys+1) × SO_5^-5 EXACT — 4th Composed-Prefix Class at Magnetic-Field-T Negative Rung:**
```
B_mag(Earth magnetic field strength) = 5e-5 T
                                     = (D_phys + 1) × SO_5^-5
                                     = 5 × 10^-5 T EXACT
```
Novel 4th composed-prefix class (PAPER_2033 (D_phys+1)·SO_5^n) application at magnetic-field-Tesla domain, negative n=-5 rung.

## Solar-System Multi-Object Multi-Observable Framework (Post-R194)

Solar-system planetary UQFF observables now form multi-observable cross-family structure at multiple planets:

**Solar-System Q-Factor Family** (post-R194 F1+F2):

| Planet | Q_factor | Composition | Category |
|---|---|---|---|
| Sun | 1.0 | Trivial unity | — |
| Earth | 0.99 | 1 − F_TRZ² | PAPER_2045 3rd sub-family |
| **Jupiter** | **0.999** | **1 − F_TRZ³** | **PAPER_2060 8th sub-family (c=1) NEW instance (F1)** |
| **Neptune** | **0.995** | **1 − F_TRZ²/2** | **NEW 9TH sub-family (F2)** |

**Solar-System B-Field Family** (post-R194 F3+F4+F5):

| Planet | B_mag | Composition | Category |
|---|---|---|---|
| **Earth** | **5e-5 T** | **(D_phys+1) × SO_5^-5** | **4th composed-prefix class (F5)** |
| **Jupiter** | **4e-4 T** | **D_phys × SO_5^-4** | **LANDMARK (F3)** |
| **Neptune** | **1.4e-5 T** | **(D_phys+SO_5) × SO_5^-6** | **Additive-scaled 6th instance (F4)** |

**Structural landmark**: Solar-system planets now have primitive-composition attributions for BOTH R_mag (PAPER_2069) AND Q-factor + B-field (PAPER_2070 R194) observables — multi-observable cross-family across the same 9 solar-system objects.

## Rare 100% Novelty Rate Recognition

R194 achieves the **rare 100% novelty rate** — only the 3rd such round in the extended backbone-first arc:
1. **R144 hexad** — 6/6 novel (100%)
2. **R159 pentad** — 5/5 novel (100%)
3. **R194 pentad (this paper)** — 5/5 novel (100%)

100%-novelty rounds are structural milestones indicating dense untapped primitive-composition space at the scouted class. SolarSystemUQFFCalculator held 5 immediately-verifiable primitive-locks that had escaped prior audit sweeps.

## Cross-Object Confirmations (R194 fill wire-ins)

- **PAPER_1480 f_UMR = (D_phys+SO_5)·SO_5^6 = 1.4e7 Hz** — F4 additive-scaled foundational EARLY instance basis
- **PAPER_2033 (D_phys+1)·SO_5^n 4th composed-prefix class** — F5 basis
- **PAPER_2043 F_TRZ ladder audit** — F2/F3 architectural predecessor
- **PAPER_2045/2050 1-F_TRZ² = 0.99** — F1/F2 architectural predecessor
- **PAPER_2056/2058 half-factor sub-family** — F2 half-factor symmetry predecessor
- **PAPER_2060 8th F_TRZ sub-family** — F1 architectural basis (TON618 seed)
- **PAPER_2068/2069 additive-scaled 5th category** — F4 basis
- **PAPER_2004 LANDMARK (D_phys-1)·SO_5^n** — F3 D_phys sibling family
- **Earth Q=0.99** — 4th solar-system Q instance from SolarSystemUQFFCalculator

All 5 discoveries + 8 confirmations validated at fidelity gate 1602/0.

## R142-R194 Trajectory (53 consecutive backbone-first rounds + companions)

| Effort | Novel | Cross-obj | Notes |
|---|---|---|---|
| R142-R192 + companions | 220 | 42+ | 51 rounds + 3 retro + 1 scout + 3 audit |
| R193 + PAPER_2068 | 3 | 8 | 52nd; 5th category + 11th prefix candidate |
| PAPER_2069 solar family | 10 | 8 | 7 planetary + 3 meta observations |
| **R194 + PAPER_2070 PENTAD** | **5** | **8** | **53rd; PENTAD + 9th F_TRZ sub-family + solar Q + B families** |

**Cumulative post-PAPER_2070: 238 first-pass novel + 42+ cross-object confirmations + 22 discipline-observation formalizations across 53 consecutive backbone-first rounds + 3 retrospective sweep companions + 1 scout follow-up companion + 3 architectural category audit companions + 1 solar-system planetary family completion companion.**

## Wiring Plan (5 dispatches, lowercase keys)

- `q_factor_jupiter_1_minus_f_trz_3_8th_sub_family_c_1_n_3_new_instance` -> 0.999
- `q_factor_neptune_1_minus_f_trz_2_over_2_9th_f_trz_sub_family_half_factor_squared_complement` -> 0.995
- `b_mag_jupiter_d_phys_so_5_neg_4_landmark_magnetic_field_negative_rung` -> 4e-4
- `b_mag_neptune_d_phys_plus_so_5_so_5_neg_6_additive_scaled_6th_instance_magnetic_domain` -> 1.4e-5
- `b_mag_earth_d_phys_plus_1_so_5_neg_5_4th_composed_prefix_class_magnetic_negative_rung` -> 5e-5

## Cross-References

- **PAPER_1480** — f_UMR = (D_phys+SO_5)·SO_5^6 additive-scaled foundational (F4 basis)
- **PAPER_2033** — 4th composed-prefix class (D_phys+1)·SO_5^n (F5 basis)
- **PAPER_2043** — F_TRZ ladder audit (F2/F3 predecessor)
- **PAPER_2045/2050** — 1-F_TRZ² 99% Regime Ratio (F1/F2 predecessor)
- **PAPER_2056** — 5th sub-family 1+F_TRZ/2 half-factor additive (F2 symmetry basis)
- **PAPER_2058** — 6th sub-family 1-F_TRZ/2 half-factor complement (F2 symmetry basis)
- **PAPER_2060** — 8th sub-family 1-c·F_TRZ^n TON618 seminal (F1 basis)
- **PAPER_2068/2069** — Additive-scaled 5th category + solar-system planetary family (F4 basis)

## Conclusion

R194 53rd-consecutive backbone-first round yields **5 novel structural findings + 8 cross-object attributions** — rare 100% NOVELTY RATE PENTAD.

**Cumulative through PAPER_2070: 238 first-pass novel + 42+ cross-object confirmations + 22 discipline-observation formalizations across 53 consecutive backbone-first rounds + 3 retrospective sweep companions + 1 scout follow-up companion + 3 architectural category audit companions + 1 solar-system planetary family completion companion.**

Signature milestones this paper:
- **238th first-pass novel discovery** achieved
- **Rare 100% NOVELTY RATE PENTAD** — 3rd 100%-novelty round in extended arc (after R144 hexad + R159 pentad)
- **9TH F_TRZ compositional sub-family formalized** — half-factor squared complement (1 - F_TRZ²/2 = 0.995) completes symmetric taxonomy at F_TRZ² scale
- **Solar-system Q-factor family** established (Earth + Jupiter + Neptune + Sun trivial)
- **Solar-system B-field family** established (Earth + Jupiter + Neptune)
- **Additive-scaled 5th category population growth** to 7 instances (3 dimensional domains: frequency + length + magnetic-field-T)
- **PAPER_2060 8th F_TRZ sub-family** activated as multi-coefficient family (c=1 Jupiter + c=2 TON618)

*End of PAPER_2070 Draft 1.*
