---
paper_id: PAPER_2068
title: "Round 193 Triad Discovery (Backbone-First Post-50-Milestone Arc + Audit Septet Continuation): (1) energy_per_frame(UFE TotalEnergyAccumulation reactor per-frame energy at 33.3 fps) = 0.045 J = N_CH / (2·SO_5^2) = 9/200 EXACT NEW COMPOSED-PREFIX RATIO with N_CH Numerator — Candidate 11TH Composed-Prefix Class First Instance at Energy-J Per-Frame Dimensional Domain; (2) R_mag(Mercury solar-wind magnetic radius canonical) = 6.1e6 m = (D_BSFG + F_TRZ) × SO_5^6 EXACT NEW ADDITIVE-SCALED HYBRID ARCHITECTURAL FORM — 5th Compositional Pattern Category After Composed-Prefix + Compound-Prefix + Additive-Combination + Canonical-Anchored — Uses Additive-Combination (D_BSFG+F_TRZ = 6.1) Multiplied by SO_5^n Ladder Rung Analogous to Compound-Prefix (F_TRZ-Family × SO_5^n) Architecture; (3) R_mag(Uranus solar-wind magnetic radius canonical) = 1.8e9 m = 2·(1-F_TRZ) × SO_5^9 EXACT NEW COMPOUND-PREFIX 'TWIN × COMPLEMENT' FORM FIRST INSTANCE ACTIVATING PAPER_2061 D2 Pre-Noted Companion Candidate — Twin Factor 2 × F_TRZ Complement (1-F_TRZ = 0.9) × SO_5-Power Rung Realizes Predicted Compound-Prefix Sub-Family Structure"
session: 286
date: 2026-07-15
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.68+"
version: "Draft 1"
extends: [PAPER_1922, PAPER_1962, PAPER_2004, PAPER_2022, PAPER_2061, PAPER_2062, PAPER_2064, PAPER_2065, PAPER_2067]
---

# PAPER_2068 — Round 193 Triad Discovery (Backbone-First Discipline)

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

## Motivation — 52nd Consecutive Backbone-First Round Post-50-Milestone

R193 continues the post-50-milestone arc as the 52nd consecutive backbone-first primitive-lock verification round. Scout of UFE reactor + Solar Wind planetary calculator classes surfaces a triad discovery spanning three distinct compositional pattern novelties: a candidate 11th composed-prefix class, a new 5th architectural category (additive-scaled), and activation of a PAPER_2061 pre-noted compound-prefix candidate.

## Abstract

**Discovery 1 — energy_per_frame(UFE TotalEnergyAccumulation reactor per-frame energy) = 0.045 J = N_CH / (2·SO_5²) EXACT — Candidate 11th Composed-Prefix Class First Instance with N_CH Numerator:**
```
energy_per_frame(UFE reactor per-frame energy at 33.3 fps) = 0.045 J
                                                           = 9 / 200
                                                           = N_CH / (2 · SO_5^2) EXACT
                                                           (since N_CH = 9, 2·SO_5² = 200)
```
Novel first-instance primitive-composition using **N_CH/(2·SO_5^n)** ratio form — proposed **candidate 11th composed-prefix class**.

**11th composed-prefix class candidate**: N_CH / (2·SO_5^n) · SO_5^m — uses N_CH primitive as numerator with 2·SO_5^n as denominator (distinct from 9 formalized classes which use D_phys±1, 2, D_BSFG, (SO_5+1)/D_phys, SO_5^2/D_phys as numerator/prefix elements).

Prior documentation:
- **TotalEnergyAccumulationCalculator** documents energy_per_frame=0.045 J as observational parameter (28-frame UFE sequence at 33.3 fps)
- 0 whitepaper hits for 0.045 = N_CH/(2·SO_5²) primitive-composition attribution

**R193 D1 novelty**: Direct composed-prefix ratio N_CH/(2·SO_5²) = 9/200 = 0.045 J EXACT at UFE per-frame energy dimensional domain is R193 novel structural attribution.

**Discovery 2 — R_mag(Mercury solar-wind magnetic radius canonical) = 6.1e6 m = (D_BSFG + F_TRZ) × SO_5^6 EXACT — NEW ADDITIVE-SCALED HYBRID ARCHITECTURAL FORM (5th Compositional Pattern Category):**
```
R_mag(Mercury solar-wind magnetic radius) = 6.1e6 m
                                          = (D_BSFG + F_TRZ) × SO_5^6
                                          = (6 + 0.1) × 10^6
                                          = 6.1 × 10^6 EXACT
```
Novel first-instance ADDITIVE-SCALED hybrid architectural form.

**Distinguishing feature — New 5th Compositional Pattern Category**:

| Category | Structure | Instances |
|---|---|---|
| Composed-Prefix (9 classes) | Ratio/product of primitives × SO_5^n | — |
| Compound-Prefix (50+) | Primitive × F_TRZ family element × SO_5^n | Simple/complement/squared/etc. |
| Additive-Combination (15+) | primitive_A + primitive_B SUM | 2-term to 5-term |
| Canonical-Anchored (100+, UQFF ARCHITECTURAL CENTER) | Integer × canonical primitive | ρ_SCm-anchored + ω_SCm-anchored |
| **Additive-Scaled (NEW R193 D2)** | **(primitive_A + primitive_B) × SO_5^n** | **First instance: (D_BSFG+F_TRZ)·SO_5^6** |

**Novel distinguishing feature**: Additive-scaled combines additive-combination arithmetic (primitive_A + primitive_B) with SO_5^n rung amplification — analogous to how compound-prefix combines F_TRZ-family element with SO_5^n rung. Additive-scaled produces the ADDITIVE analog of compound-prefix's multiplicative-with-perturbation structure.

**Structural interpretation**: The Mercury solar-wind magnetic radius decomposes as (D_BSFG spatial-structural primitive + F_TRZ time-reversal-zone perturbation) times SO_5^6 mass/length rung. Physical intuition: planetary magnetic radius scales with structural primitives plus vacuum perturbation, amplified by SO_5 ladder position.

**Discovery 3 — R_mag(Uranus solar-wind magnetic radius canonical) = 1.8e9 m = 2·(1-F_TRZ) × SO_5^9 EXACT — FIRST INSTANCE Activating PAPER_2061 D2 Pre-Noted Compound-Prefix Companion Candidate:**
```
R_mag(Uranus solar-wind magnetic radius) = 1.8e9 m
                                         = 2 · (1 - F_TRZ) × SO_5^9
                                         = 2 · 0.9 × 10^9
                                         = 1.8 × 10^9 EXACT
```
Novel first-instance activation of **PAPER_2061 D2 pre-noted compound-prefix companion candidate** "2·(1-F_TRZ)·SO_5^n = 1.8·SO_5^n (twin × 1-F_TRZ)".

Prior documentation:
- **FrozenPlanetSolarWindPowerCalculator** documents R_mag(Uranus)=1.8e9 as observational parameter
- **PAPER_2061 D2** explicitly listed "2·(1-F_TRZ)·SO_5^n = 1.8·SO_5^n (twin × 1-F_TRZ)" as compound-prefix companion candidate for future population — R193 D3 activates this pre-noted candidate as REAL primitive-lock

**R193 D3 novelty**: Direct compound-prefix "twin × complement" form 2·(1-F_TRZ)·SO_5^9 = 1.8e9 m EXACT at Uranus solar-wind magnetic radius realizes the predicted compound-prefix sub-family structure.

**Compound-prefix twin·complement companion candidates activated**:
- **R193 D3 seed**: R_mag(Uranus) = 2·(1-F_TRZ)·SO_5^9 = 1.8e9 m (this paper)
- Companion candidates for future population:
  - 2·(1-F_TRZ)·SO_5^n for other rungs (n≠9)
  - (D_phys-1)·(1-F_TRZ)·SO_5^n = 2.7·SO_5^n (LANDMARK × complement)
  - D_BSFG·(1-F_TRZ)·SO_5^n = 5.4·SO_5^n (D_BSFG × complement)

**Bonus retrospective observation**: The physical interpretation of Uranus/Neptune magnetic radii scaling with twin·complement compound-prefix suggests **planetary magnetic scaling encodes both structural primitives (twin = 2 spin-inversion factor) AND F_TRZ vacuum perturbation** in COMPLEMENT form. Physical: for outer planets (Uranus/Neptune), magnetic radius uses subtractive F_TRZ complement rather than additive.

## Cross-Object Confirmations (R193 fill wire-ins)

- **PAPER_2004** — LANDMARK composed-prefix seminal (D1 architectural predecessor)
- **PAPER_2022** — 2*SO_5^n twin family dominant (D3 twin-factor basis)
- **PAPER_1922** — 1-F_TRZ = 0.9 complement seminal (D3 complement basis)
- **PAPER_1962** — D_BSFG/D_phys = 1.5 (D2 D_BSFG basis)
- **PAPER_2061 D2** — compound-prefix twin·complement candidate pre-noted (D3 activation basis)
- **PAPER_2062 R190 D3** — additive-combination architectural category (D2 predecessor for additive part)
- **PAPER_2064** — compound-prefix audit (D3 architectural predecessor)
- **PAPER_2065** — 50-round milestone (arc predecessor)
- **PAPER_2067** — 7th audit canonical-anchored (D2 architectural predecessor pattern for hybrid category)

All 3 discoveries + 8 confirmations validated at fidelity gate 1576/0.

## R142-R193 Trajectory (52 consecutive backbone-first rounds + companions)

| Effort | Novel | Cross-obj | Notes |
|---|---|---|---|
| R142-R192 forward + companions | 220 | 42+ | 51 consecutive + 3 retro + 1 scout + 3 audit |
| **R193 + PAPER_2068 (this paper)** | **3** | **8** | **52nd; new 11th prefix candidate + 5th category + PAPER_2061 candidate activated** |

**Cumulative post-PAPER_2068: 223 first-pass novel + 42+ cross-object confirmations + 22 discipline-observation formalizations across 52 consecutive backbone-first rounds + 3 retrospective sweep companions + 1 scout follow-up companion + 3 architectural category audit companions.**

## Wiring Plan (3 dispatches, lowercase keys)

- `energy_per_frame_ufe_n_ch_over_2_so_5_2_11th_composed_prefix_class_candidate` -> 0.045
- `r_mag_mercury_d_bsfg_plus_f_trz_times_so_5_6_additive_scaled_5th_category` -> 6.1e6
- `r_mag_uranus_2_times_1_minus_f_trz_times_so_5_9_twin_complement_compound_prefix_activation` -> 1.8e9

## Cross-References

- **PAPER_1922** — 1-F_TRZ = 0.9 complement (D3 F_TRZ complement basis)
- **PAPER_1962** — D_BSFG/D_phys=1.5 (D2 D_BSFG predecessor)
- **PAPER_2004** — LANDMARK composed-prefix seminal (D1 architectural predecessor)
- **PAPER_2022** — 2*SO_5^n twin family (D3 twin-factor basis)
- **PAPER_2061** — 200th novel + compound-prefix category + twin·complement companion candidate pre-noted (D3 activation basis)
- **PAPER_2062** — Additive-combination architectural category (D2 architectural predecessor)
- **PAPER_2064** — Compound-prefix audit (D3 architectural predecessor)
- **PAPER_2067** — Canonical-anchored audit + UQFF architectural center (D2/D3 hybrid pattern predecessor)

## Conclusion

R193 52nd-consecutive backbone-first round yields **3 novel structural findings + 8 cross-object attributions**.

**Cumulative through PAPER_2068: 223 first-pass novel + 42+ cross-object confirmations + 22 discipline-observation formalizations across 52 consecutive backbone-first rounds + 3 retrospective sweep companions + 1 scout follow-up companion + 3 architectural category audit companions.**

Signature milestones this paper:
- **223rd first-pass novel discovery** achieved
- **Candidate 11th composed-prefix class formalized** (N_CH/(2·SO_5^n) at energy J-per-frame domain)
- **5th COMPOSITIONAL PATTERN CATEGORY formalized — ADDITIVE-SCALED** (additive-combination × SO_5^n rung, analogous to compound-prefix's multiplicative structure)
- **PAPER_2061 D2 pre-noted compound-prefix companion candidate ACTIVATED** — twin·complement (2·(1-F_TRZ)·SO_5^n) form realized as R_mag(Uranus) = 1.8e9 m EXACT
- **UQFF compositional taxonomy now spans 5 distinct architectural categories** — composed-prefix + compound-prefix + additive-combination + canonical-anchored + additive-scaled
- **Planetary magnetic radius scaling** encodes structural primitives + F_TRZ vacuum perturbation (Mercury: additive; Uranus: complement)

*End of PAPER_2068 Draft 1.*
