---
paper_id: PAPER_2081
title: "Round 206 CP2 Quad Discovery + F_TRZ 10th and 11th Sub-Family Candidates (Backbone-First 65th Consecutive, 3rd CP2 Round): (1) target_fps(VideoFrameSettingsCalculator CP2 video target frame-per-second rate) = 60 = A_5 EXACT FIRST-INSTANCE at Frame-Rate-FPS Dimensional Domain; (2) spin_resonance(FieldGeneratorCorrelationV3Calculator CP2 reactor-field spin resonance) = 0.92 = 1 - 2·D_phys·F_TRZ^2 = 1 - 8·F_TRZ^2 EXACT NEW COMPOSITE-INTEGER COEFFICIENT × F_TRZ^2 COMPLEMENT FORM Candidate 10TH F_TRZ COMPOSITIONAL SUB-FAMILY — Extends PAPER_2060 8th Sub-Family (Integer-Multiple Higher-Power c=1,2 n=3) into Composite Integer Coefficient (c=2·D_phys=8, n=2) Regime; (3) non_local_ghost(FieldGeneratorCorrelationV3Calculator CP2 non-locality ghost detection efficiency) = 0.88 = 1 - F_TRZ - 2·F_TRZ^2 EXACT NEW MULTI-TERM F_TRZ SUBTRACTIVE SERIES Candidate 11TH F_TRZ COMPOSITIONAL SUB-FAMILY — First Documented Multi-Term Subtractive Combination Analog to PAPER_2075 R198 D1 3-Term Geometric-Additive Series 1+F_TRZ+F_TRZ^2 for Λ Observational; (4) omega_s(UniversalPermanenceCalculator CP2 permanence equation angular frequency) = 37699.11 rad/s = 2π × D_BSFG × SO_5^3 EXACT NEW π-CANONICAL × COMPOSED-PREFIX HYBRID Combining PAPER_2073 π-Canonical 2π-Anchored Sub-Family with PAPER_2025 D_BSFG·SO_5^n 3rd Composed-Prefix Class at Angular-Frequency Rad/s Dimensional Domain"
session: 299
date: 2026-07-15
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.68+"
version: "Draft 1"
extends: [PAPER_2025, PAPER_2060, PAPER_2070, PAPER_2073, PAPER_2075, PAPER_2079, PAPER_2080]
---

# PAPER_2081 — Round 206 CP2 Quad Discovery (Backbone-First Discipline)

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

## Motivation — 65th Consecutive Backbone-First Round, 3rd CP2 Arc Round

R206 continues the CP2 drainage arc as the 3rd CP2 round (65th consecutive backbone-first overall). Follows R204 CP2 arc opening quad (PAPER_2079) + R205 CP2 triad (PAPER_2080). Scout of VideoFrameSettings + FieldGeneratorCorrelationV3 + UniversalPermanence surfaces STRONG QUAD DISCOVERY with two candidate NEW F_TRZ compositional sub-family forms (10th + 11th).

## Abstract

**Discovery 1 (F1) — target_fps(VideoFrameSettingsCalculator CP2 target frame-per-second rate) = 60 = A_5 EXACT — First-Instance at Frame-Rate FPS Dimensional Domain:**
```
target_fps(VideoFrameSettingsCalculator CP2 target frame-per-second video rate) = 60 fps
                                                                                = A_5 EXACT
                                                                                (since A_5 = 60 icosahedral group order primitive)
```
Novel first-instance bare A_5 primitive at frame-rate-FPS dimensional domain. Extends A_5=60 primitive applications into video frame-rate domain.

**Discovery 2 (F3) — spin_resonance(FieldGeneratorCorrelationV3 CP2 reactor-field spin resonance dimensionless) = 0.92 = 1 - 2·D_phys · F_TRZ² EXACT — NEW Composite-Integer × F_TRZ² Complement Form Candidate 10TH F_TRZ Sub-Family:**
```
spin_resonance(FieldGeneratorCorrelationV3Calculator CP2 reactor-field spin resonance) = 0.92
                                                                                        = 1 - 2·D_phys · F_TRZ²
                                                                                        = 1 - 8 · F_TRZ²
                                                                                        = 1 - 8 · 0.01
                                                                                        = 1 - 0.08 EXACT
                                                                                        (since 2·D_phys = 8 per PAPER_2035 5th composed-prefix, F_TRZ² = 0.01)
```
Novel composite-integer × F_TRZ² complement form. Extends PAPER_2060 8th F_TRZ sub-family (1 - c·F_TRZ^n integer-multiple higher-power complement with c=1,2 n=3) into composite integer coefficient regime (c=2·D_phys=8, n=2).

**F_TRZ Compositional Architecture — Candidate 10th Sub-Family**:

| # | Form | Coefficient type | Example | Seminal |
|---|---|---|---|---|
| 8 | 1 - c·F_TRZ^n | Integer c (1, 2) | 0.998 (c=2, n=3) | PAPER_2060 |
| **10 candidate** | **1 - c·F_TRZ² with c composite** | **Composite c (2·D_phys=8)** | **0.92 (c=8, n=2)** | **PAPER_2081 R206 F3** |

**Discovery 3 (F4) — non_local_ghost(FieldGeneratorCorrelationV3 CP2 non-locality ghost detection efficiency dimensionless) = 0.88 = 1 - F_TRZ - 2·F_TRZ² EXACT — NEW Multi-Term F_TRZ Subtractive Series Candidate 11TH F_TRZ Sub-Family:**
```
non_local_ghost(FieldGeneratorCorrelationV3Calculator CP2 non-locality ghost detection efficiency) = 0.88
                                                                                                   = 1 - F_TRZ - 2·F_TRZ²
                                                                                                   = 1 - 0.1 - 0.02
                                                                                                   = 0.88 EXACT
```
Novel multi-term F_TRZ subtractive series. First documented 3-term subtractive combination of F_TRZ powers.

**Structural analog with PAPER_2075 R198 D1**: PAPER_2075 R198 D1 established Λ observational = (1+F_TRZ+F_TRZ²)·SO_5^-52 EXACT as 3-term geometric-ADDITIVE series (Ramanujan-like at first 3 terms). PAPER_2081 R206 F4 establishes analog 3-term SUBTRACTIVE series (1 - F_TRZ - 2·F_TRZ²).

**F_TRZ Compositional Architecture — Candidate 11th Sub-Family**:

| # | Form | Structure | Example | Seminal |
|---|---|---|---|---|
| Geometric-additive | 1 + F_TRZ + F_TRZ² | 3-term additive series | 1.11 (× SO_5^-52 for Λ) | PAPER_2075 |
| **11 candidate** | **1 - F_TRZ - c·F_TRZ²** | **3-term subtractive series** | **0.88 (c=2)** | **PAPER_2081 R206 F4** |

**Discovery 4 (F5) — omega_s(UniversalPermanenceCalculator CP2 permanence equation angular frequency) = 37699.11 rad/s = 2π × D_BSFG × SO_5^3 EXACT — π-Canonical × Composed-Prefix Hybrid at Angular Frequency Rad/s Domain:**
```
omega_s(UniversalPermanenceCalculator CP2 permanence equation angular frequency parameter) = 37699.11 rad/s
                                                                                            = 2π × 6000
                                                                                            = 2π × D_BSFG × SO_5^3 EXACT
                                                                                            (since 2π canonical per PAPER_2073, D_BSFG×SO_5^3 = 6000 per PAPER_2025 3rd composed-prefix + PAPER_2062 R190 D2)
```
Novel π-canonical × composed-prefix hybrid architectural form. Combines:
- **PAPER_2073 π-canonical 2π-anchored sub-family** (angular frequency ω = 2π·f canonical mechanism, 95+ instances via ω_SCm)
- **PAPER_2025 D_BSFG·SO_5^n 3rd composed-prefix class** (D_BSFG × SO_5³ = 6000, established R190 D2 spooky-action)

**Cross-category architectural hybrid**: R206 F5 demonstrates that UQFF architectural categories can COMBINE in hybrid forms — π-canonical × composed-prefix = 2π × D_BSFG × SO_5³. Similar to R204 F2 compound-prefix "primitive × (1+F_TRZ)" which combines integer primitive × F_TRZ compositional family element. Suggests architectural taxonomy allows nested/hybrid compositions.

**Structural interpretation**: Universal Permanence equation angular frequency parameter uses 2π (canonical angular-frequency conversion) × D_BSFG (DPM structural primitive) × SO_5³ (mid-range SO_5 ladder rung) = 37699.11 rad/s. Physical intuition: permanence equation ω_s naturally scales with structural primitive amplified by SO_5 ladder rung in angular frequency canonical form.

## Cross-Object Confirmations (R206 fill wire-ins)

- **PAPER_2007 R144 hexad** — 0.15 = (D_phys-1)/(2·SO_5) (F2 cross-object at rotation-rate rps)
- **PAPER_2025** — D_BSFG·SO_5^n 3rd composed-prefix class (F5 basis)
- **PAPER_2035** — 2·D_phys=8 5th composed-prefix (F3 basis)
- **PAPER_2060** — 8th F_TRZ sub-family 1-c·F_TRZ^n (F3 predecessor)
- **PAPER_2062 R190 D2** — D_BSFG·SO_5³=6000 spooky-action (F5 predecessor)
- **PAPER_2070** — 9th F_TRZ sub-family 1-F_TRZ²/2 (F3 predecessor)
- **PAPER_2073** — π-canonical audit 2π-anchored sub-family (F5 basis)
- **PAPER_2075** — 3-term geometric-additive series Λ obs (F4 analog predecessor)

All 4 discoveries + 8 confirmations validated at fidelity gate 1664/0.

## Cumulative Post-PAPER_2081

| Effort | Novel | Cross-obj | Notes |
|---|---|---|---|
| R142-R205 + companions | 265 | 42+ | 64 rounds + 3 CP2 rounds |
| **R206 + PAPER_2081** | **4** | **8** | **65th; 3rd CP2 round quad + candidate F_TRZ 10th+11th sub-families** |

**Cumulative post-PAPER_2081: 269 first-pass novel + 42+ cross-object confirmations + 27 discipline-observation formalizations across 65 consecutive backbone-first rounds (62 CP1 + 3 CP2) + 3 retrospective sweep companions + 1 scout follow-up companion + 5 architectural category audit companions (audit nonet complete) + 2 solar-system family companions.**

## Wiring Plan (4 dispatches, lowercase keys)

- `target_fps_60_a_5_video_frame_rate_first_instance_bare_a_5_primitive` -> 60
- `spin_resonance_0_92_1_minus_2_d_phys_f_trz_2_candidate_10th_f_trz_sub_family` -> 0.92
- `non_local_ghost_0_88_1_minus_f_trz_minus_2_f_trz_2_candidate_11th_f_trz_multi_term_subtractive` -> 0.88
- `omega_s_universal_permanence_2_pi_d_bsfg_so_5_3_pi_canonical_composed_prefix_hybrid` -> 37699.11

## Cross-References

- **PAPER_2025** — D_BSFG·SO_5^n 3rd composed-prefix (F5 basis)
- **PAPER_2035** — 5th composed-prefix 2·D_phys (F3 basis)
- **PAPER_2060/2070** — 8th/9th F_TRZ sub-families (F3 predecessor)
- **PAPER_2062** — R190 D2 D_BSFG·SO_5³=6000 (F5 predecessor)
- **PAPER_2073** — π-canonical 2π-anchored sub-family (F5 basis)
- **PAPER_2075** — 3-term geometric-additive series (F4 analog predecessor)
- **PAPER_2079/2080** — CP2 arc opening + 2nd round (R206 predecessors)

## Conclusion

R206 65th-consecutive backbone-first round (3rd CP2 round) yields **4 novel structural findings + 8 cross-object attributions**.

**Cumulative through PAPER_2081: 269 first-pass novel + 42+ cross-object confirmations + 27 discipline-observation formalizations across 65 consecutive backbone-first rounds + 3 retrospective sweep companions + 1 scout follow-up companion + 5 architectural category audit companions + 2 solar-system family companions.**

Signature milestones this paper:
- **269th first-pass novel discovery** achieved
- **CANDIDATE 10TH F_TRZ COMPOSITIONAL SUB-FAMILY** — composite-integer coefficient × F_TRZ² complement (c=2·D_phys=8, R206 F3)
- **CANDIDATE 11TH F_TRZ COMPOSITIONAL SUB-FAMILY** — multi-term F_TRZ subtractive series (1 - F_TRZ - 2·F_TRZ², R206 F4)
- **A_5 primitive** extends to frame-rate FPS dimensional domain (R206 F1)
- **π-canonical × composed-prefix hybrid architectural form** documented (R206 F5)
- **CP2 arc 3rd round strong yield** — 4/5 = 80% novel-yield ratio at CP2 3rd round (matches R204 CP2 opening)
- **65 consecutive backbone-first rounds** achieved

*End of PAPER_2081 Draft 1.*
