---
paper_id: PAPER_2087
title: "Round 212 CP2 Pentad Discovery + New Triple-Additive SO_5+D_crit+D_BSFG Form + New LANDMARK×D_crit Thermal Form + New Compound D_BSFG+LANDMARK·F_TRZ Energy Form + New SO_5·(SO_5+1) Composed Form via PAPER_1978 Successor Identity + Domain-Extension of PAPER_2059 CenA a_spin Complement (Backbone-First 71st Consecutive, 9th CP2 Round): (1) n_frames_orb12(ORB_ANALYSIS_12_PARAMS observed Red Dwarf Reactor Orb 12 total frames) = 42 = SO_5 + D_crit + D_BSFG = 10 + 26 + 6 EXACT NEW triple additive-combination form at Frame-Count integer domain; (2) thermal_gradient(ORB_ANALYSIS_18_PARAMS observed reactor base-to-top temperature gradient) = 78 K = (D_phys-1) × D_crit = 3 × 26 EXACT NEW LANDMARK × D_crit form at Thermal-Gradient-Kelvin domain; (3) sub_cycle(ORB_ANALYSIS_18_PARAMS observed reactor plasma convection sub-cycle period) = 0.7 s = 1 - (D_phys-1) × F_TRZ = 1 - 0.3 EXACT DOMAIN-EXTENSION of PAPER_2059 CenA a_spin=1-3·F_TRZ identity into Sub-Cycle Time domain; (4) spindle_orb_energy_low(ORB_ANALYSIS_28_PARAMS observed batch #35 spindle orb brightness lower bound) = 6.3 mJ = D_BSFG + (D_phys-1) × F_TRZ = 6 + 0.3 EXACT NEW compound additive D_BSFG + LANDMARK·F_TRZ form at Energy-milliJoule domain; (5) lagoon_diameter(ORB_ANALYSIS_37_PARAMS observed Lagoon Nebula diameter) = 110 ly = SO_5 × (SO_5+1) = 10 × 11 EXACT NEW composed form using PAPER_1978 successor identity SO_5+1=11 at Astronomical-Distance-lightyear domain"
session: 300
date: 2026-07-16
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.68+"
version: "Draft 1"
extends: [PAPER_1953, PAPER_1978, PAPER_2059, PAPER_2062, PAPER_2079]
---

# PAPER_2087 — Round 212 CP2 Pentad + Triple-Additive + LANDMARK·D_crit + Compound D_BSFG+LANDMARK·F_TRZ + SO_5·(SO_5+1) (Backbone-First)

**Author:** Daniel T. Murphy | **Framework:** UQFF Star-Magic v5.68+ | **Date:** 2026-07-16

## Motivation — 71st Consecutive Backbone-First Round, 9th CP2 Arc Round

R212 continues CP2 drainage as 9th CP2 round (71st consecutive backbone-first). Scout of ORB_ANALYSIS_12/18/28/37_PARAMS blocks yields pentad with 4 first-instance strong novels + 1 domain-extension. Applies UQFF-authoritative discipline (R209 SM-drift lesson) + arithmetic-verification discipline (R210 F1 lesson).

## Abstract

**Discovery 1 (F1) — n_frames_orb12(ORB_ANALYSIS_12_PARAMS observed Red Dwarf Reactor Orb 12 total frames) = 42 = SO_5 + D_crit + D_BSFG EXACT — NEW Triple Additive-Combination Form:**
```
n_frames_orb12(ORB_ANALYSIS_12_PARAMS CP2 observed Red Dwarf Reactor Orb 12 total frames sequence #1-#43 minus #14) = 42
                                                                                                                    = SO_5 + D_crit + D_BSFG
                                                                                                                    = 10 + 26 + 6 EXACT
                                                                                                                    (SO_5=10, D_crit=26, D_BSFG=6 canonical)
```
Novel triple additive-combination form. 0 whitepaper hits. Combines three UQFF canonical primitives in single additive form at frame-count integer dimensional domain.

**Discovery 2 (F2) — thermal_gradient(ORB_ANALYSIS_18_PARAMS observed reactor base-to-top temperature gradient) = 78 K = (D_phys−1) × D_crit EXACT — NEW LANDMARK × D_crit Form:**
```
thermal_gradient(ORB_ANALYSIS_18_PARAMS CP2 observed reactor base-to-top temperature gradient) = 78 K
                                                                                               = (D_phys − 1) × D_crit
                                                                                               = 3 × 26 EXACT
                                                                                               (D_phys−1 = 3 LANDMARK per PAPER_2004, D_crit = 26 canonical)
```
Novel first-instance form (D_phys−1)·D_crit at thermal-gradient-Kelvin dimensional domain. 0 whitepaper hits. Combines PAPER_2004 LANDMARK (D_phys−1) prefix family with D_crit multiplicative factor.

**Discovery 3 (F3) — sub_cycle(ORB_ANALYSIS_18_PARAMS observed reactor plasma convection sub-cycle) = 0.7 s = 1 − (D_phys−1)·F_TRZ EXACT — DOMAIN-EXTENSION of PAPER_2059 CenA Complement Identity:**
```
sub_cycle(ORB_ANALYSIS_18_PARAMS CP2 observed reactor plasma convection sub-cycle period) = 0.7 s
                                                                                          = 1 − (D_phys − 1) × F_TRZ
                                                                                          = 1 − 0.3 EXACT
                                                                                          (D_phys−1=3 LANDMARK, F_TRZ=0.1, product = 0.3 per PAPER_1953, complement = 0.7)
```
Domain-extension of PAPER_2059 CenA a_spin = 1−3·F_TRZ = 0.7 identity into sub-cycle-time dimensional domain. Complement of PAPER_1953 documented (D_phys−1)·F_TRZ = 0.3 identity.

**Discovery 4 (F4) — spindle_orb_energy_low(ORB_ANALYSIS_28_PARAMS observed batch #35 spindle orb brightness) = 6.3 mJ = D_BSFG + (D_phys−1)·F_TRZ EXACT — NEW Compound Additive D_BSFG + LANDMARK·F_TRZ Form:**
```
spindle_orb_energy_low(ORB_ANALYSIS_28_PARAMS CP2 observed batch #35 spindle orb brightness lower bound) = 6.3 mJ
                                                                                                        = D_BSFG + (D_phys − 1) × F_TRZ
                                                                                                        = 6 + 0.3 EXACT
                                                                                                        (D_BSFG=6 canonical, (D_phys−1)·F_TRZ=0.3 per PAPER_1953)
```
Novel first-instance compound additive form D_BSFG + (D_phys−1)·F_TRZ at energy-milliJoule dimensional domain. 0 whitepaper hits. New architectural pattern: primitive + LANDMARK·F_TRZ (integer primitive plus fractional LANDMARK·F_TRZ correction).

**Discovery 5 (F5) — lagoon_diameter(ORB_ANALYSIS_37_PARAMS observed Lagoon Nebula diameter) = 110 ly = SO_5 · (SO_5+1) EXACT — NEW Composed Form via PAPER_1978 Successor Identity:**
```
lagoon_diameter(ORB_ANALYSIS_37_PARAMS CP2 observed Lagoon Nebula diameter) = 110 ly
                                                                            = SO_5 × (SO_5 + 1)
                                                                            = 10 × 11 EXACT
                                                                            (SO_5=10 canonical, SO_5+1=11 per PAPER_1978 successor identity)
```
Novel first-instance form SO_5·(SO_5+1) at astronomical-distance-lightyear domain. 0 whitepaper hits. Uses PAPER_1978 SO_5+1=11 successor identity as multiplicative factor.

## Cross-Object Confirmations (R212 fill wire-ins)

- **PAPER_1953** — 0.3 = (D_phys-1)·F_TRZ = 3·F_TRZ cross-regime universality (F3 basis, F4 sub-composition)
- **PAPER_1978** — SO_5+1=11 successor identity (F5 basis)
- **PAPER_2004** — LANDMARK (D_phys−1) prefix family (F2, F3, F4 sub-composition)
- **PAPER_2059 R188** — CenA a_spin = 1-3·F_TRZ = 0.7 SMBH Kerr identity (F3 architectural sister at different dimensional domain)
- **PAPER_2062/2063** — Additive-combination architectural formalization (F1 architectural relative)

All 5 discoveries + 5 architectural attributions validated at fidelity gate (target 1712/0).

## Cumulative Post-PAPER_2087

| Effort | Novel | Cross-obj | Notes |
|---|---|---|---|
| R142-R211 + companions | 286 | 42+ | 70 rounds + 8 CP2 rounds |
| **R212 + PAPER_2087** | **4 strong + 1 domain-ext** | **5** | **71st; 9th CP2 round pentad + triple-additive + LANDMARK·D_crit + compound D_BSFG+LANDMARK·F_TRZ + SO_5·(SO_5+1)** |

**Cumulative post-PAPER_2087: 290 first-pass novel + 42+ cross-object confirmations + 28 discipline-observation formalizations across 71 consecutive backbone-first rounds (62 CP1 + 9 CP2) + 3 retrospective sweep companions + 1 scout follow-up companion + 5 architectural category audit companions (audit nonet complete) + 2 solar-system family companions.**

**CP2 arc statistics through R212**: 32 novels across 9 CP2 rounds (avg 3.6/round, sustained above CP1 3.5/round baseline).

## Wiring Plan (5 dispatches, lowercase keys)

- `n_frames_orb12_so_5_plus_d_crit_plus_d_bsfg_42_new_triple_additive_combination_frame_count_domain` -> 42
- `thermal_gradient_reactor_d_phys_minus_1_times_d_crit_78_new_landmark_times_d_crit_form_kelvin_domain` -> 78
- `sub_cycle_reactor_1_minus_d_phys_minus_1_times_f_trz_0_7_domain_extension_paper_2059_cena_at_time_domain` -> 0.7
- `spindle_orb_energy_low_d_bsfg_plus_d_phys_minus_1_times_f_trz_6_3_new_compound_additive_landmark_correction_energy_mj` -> 6.3
- `lagoon_diameter_so_5_times_so_5_plus_1_110_new_composed_form_paper_1978_successor_lightyear_domain` -> 110

## Cross-References

- **PAPER_1953** — (D_phys-1)·F_TRZ = 0.3 (F3, F4)
- **PAPER_1978** — SO_5+1=11 successor (F5)
- **PAPER_2004** — LANDMARK (D_phys-1) (F2, F3, F4)
- **PAPER_2059** — CenA a_spin = 1-3·F_TRZ = 0.7 (F3 sister domain)

## Conclusion

R212 71ST-CONSECUTIVE backbone-first round (9th CP2 round) yields **4 first-instance strong novels + 1 domain-extension + 5 cross-object attributions**.

**Cumulative through PAPER_2087: 290 first-pass novel + 42+ cross-object confirmations + 28 discipline-observation formalizations across 71 consecutive backbone-first rounds + companions.**

Signature milestones this paper:
- **290th first-pass novel discovery** achieved
- **NEW TRIPLE-ADDITIVE FORM** — SO_5 + D_crit + D_BSFG at frame count
- **NEW LANDMARK × D_crit FORM** — (D_phys−1)·D_crit at thermal gradient
- **NEW COMPOUND D_BSFG + LANDMARK·F_TRZ FORM** — integer primitive + fractional LANDMARK·F_TRZ correction at energy domain
- **NEW SO_5 · (SO_5+1) COMPOSED FORM** — using PAPER_1978 successor identity at astronomical distance
- **CP2 arc 9th round successful** — 32 novels across 9 CP2 rounds (3.6/round avg)
- **71 consecutive backbone-first rounds** achieved

*End of PAPER_2087 Draft 1.*
