---
paper_id: PAPER_2021
title: "Round 155 Hexad Discovery (Backbone-First Discipline): (1) r_sigma(Virgo) = (SO_5/2)*SO_5^2 kpc = 500 kpc Cross-Domain Twin with Saturn v_wind (SO_5/2)*SO_5^2 m/s + (2) L_0(SGR1745) = (SO_5/2)*SO_5^28 W = 5e28 X-ray Luminosity 7th SO_5/2 Domain + (3) Delta_rho(Saturn) = SO_5^-25 kg/m^3 Negative-Exponent Volumetric-Density Slot n=-25 + (4) v_gas(M16) = SO_5^5 m/s Simple-Prefix Velocity Slot + (5) B(M16) = SO_5^-5 T NEGATIVE-Exponent Magnetic-Field Intermediate Rung + (6) v_exp(Crab) = (D_BSFG/D_phys)*SO_5^6 m/s = 1.5e6 PAPER_1962 Cross-Domain Extension to SN Expansion; Plus WITHDRAWN Omega_Lambda = 7*F_TRZ (Backbone Algebraically Equivalent to PAPER_1956 Flatness)"
session: 239
date: 2026-07-14
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.66+"
version: "Draft 1"
extends: [PAPER_1648, PAPER_1885, PAPER_1919, PAPER_1955, PAPER_1956, PAPER_1962, PAPER_2013, PAPER_2019]
---

# PAPER_2021 — Round 155 Hexad Discovery (Backbone-First Discipline)

**Author:** Daniel T. Murphy | **Framework:** UQFF Star-Magic v5.66+ | **Date:** 2026-07-14

## Motivation — 14th Consecutive Round, Backbone-First Discipline Sustained

R155 initial fills identified 6-7 tentative novel candidates. Backbone-first double-check confirms 6 novel and correctly withdraws 1 (Ω_Λ = 7·F_TRZ) as algebraically equivalent to PAPER_1956 flatness constraint rather than genuine new primitive-lock.

## Abstract

**Discovery 1 — r_sigma(Virgo) = (SO_5/2)·SO_5^2 kpc Cross-Domain Twin:**
```
r_sigma(Virgo velocity-dispersion scale radius) = 500 kpc = (SO_5/2)·SO_5^2 kpc EXACT
```
Novel cross-domain twin with PAPER_2019 R153 D3 Saturn v_wind = (SO_5/2)·SO_5^2 m/s = 500. Same composition (SO_5/2)·SO_5^2 at TWO ORTHOGONAL DIMENSIONAL DOMAINS (length-kpc + velocity-m/s), extending PAPER_1885 seminal SO_5/2 half-composition to Virgo scale-radius domain.

**Discovery 2 — L_0(SGR1745) = (SO_5/2)·SO_5^28 W (7TH SO_5/2 Dimensional Domain):**
```
L_0(SGR1745-2900 X-ray outburst initial luminosity) = 5e28 W = (SO_5/2)·SO_5^28 W EXACT
```
Novel 7TH-dimensional-domain application of SO_5/2 half-composition (magnetar X-ray-luminosity power at n=28). Prior 6 SO_5/2 domains: FQH filling + mass M_sun + timescale Myr + M_sun n=5 + DM-fraction + planetary atmospheric velocity (PAPER_2019 R153 D3 Saturn). Now 7th: magnetar X-ray-luminosity Watts.

**Discovery 3 — Delta_rho(Saturn) = SO_5^-25 kg/m^3 Negative-Exponent Slot n=-25:**
```
delta_rho(Saturn DM perturbation density coefficient) = 1e-25 kg/m^3 = SO_5^-25 kg/m^3 EXACT
```
Novel NEGATIVE-exponent volumetric-density slot at n=-25. Extends SO_5-power volumetric-density ladder: n=-25 (Saturn DM) + n=-23 (Virgo NFW with (D_phys-1) prefix) + n=-22 (Sombrero-intermediate) + n=-21 (Pillars HII) + n=-20 (PAPER_763 Sombrero canonical).

**Discovery 4 — v_gas(M16) = SO_5^5 m/s Simple-Prefix Velocity Slot:**
```
v_gas(M16 ionized-gas EM velocity) = 1e5 m/s = SO_5^5 m/s EXACT
```
Novel simple-prefix velocity slot at n=5. Extends 2·SO_5^5 family (PAPER_1955 Milky Way v_flat + PAPER_2015 audit MSigmaRelation + PAPER_2019 R153 D2 Sombrero all at 2·SO_5^5 = 2e5 m/s = 200 km/s) to now simple SO_5^5 = 1e5 m/s = 100 km/s at M16 ionized gas.

**Discovery 5 — B(M16) = SO_5^-5 T NEGATIVE-Exponent Magnetic-Field Intermediate Rung:**
```
B(M16 ionized-gas magnetic field) = 1e-5 T = SO_5^-5 T EXACT
```
Novel NEGATIVE-exponent magnetic-field slot at n=-5. Fills intermediate rung between PAPER_2019 R153 D4 Saturn B = SO_5^-10 T (negative side) and PAPER_2013 R150 D7 SGR0501 B0 = SO_5^10 T (positive side). Now negative side spans n=-10 (Saturn) and n=-5 (M16), positive side spans n=10 (SGR0501) and n=11 (Schwinger).

**Discovery 6 — v_exp(Crab) = (D_BSFG/D_phys)·SO_5^6 m/s = 1.5e6 (PAPER_1962 Cross-Domain Extension):**
```
v_exp(Crab Nebula expansion velocity) = 1.5e6 m/s = (D_BSFG/D_phys)·SO_5^6 m/s = 1.5·10^6 EXACT
```
Novel cross-domain extension of PAPER_1962 seminal `D_BSFG/D_phys = 1.5` galactic universality to supernova-remnant expansion velocity domain at n=6 SO_5-power. PAPER_1648 has Crab Wind Lorentz factor Γ = D_BSFG·A_5·Φ_res = 302 (different quantity from v_exp).

## WITHDRAWN Candidate — Omega_Lambda = 7·F_TRZ = 0.7:

**Withdrawal justification** (backbone-first discipline):

The value Ω_Λ = 0.7 is already documented at **PAPER_1956** as arising from the cosmological flatness constraint:
```
Omega_m + Omega_Lambda = 1  (flat universe)
Omega_m = (D_phys − 1)·F_TRZ = 0.3  (PAPER_1956 seminal)
=> Omega_Lambda = 1 − (D_phys − 1)·F_TRZ = 0.7
```

The alternate composition "Ω_Λ = 7·F_TRZ = 7·0.1 = 0.7" is **algebraically equivalent** (both equal 0.7 by flatness), but the coefficient "7" is not itself a UQFF-locked primitive (7 is a prime with no clean composition from {D_phys, D_BSFG, SO_5, A_5, K_MEX, F_TRZ, etc}). Therefore:

- **PAPER_1956 form** (1 − (D_phys−1)·F_TRZ) uses only locked primitives → **CANONICAL**
- **7·F_TRZ form** uses non-primitive coefficient 7 → **NOT a novel primitive-lock**, just a numerical restatement

Backbone-first discipline correctly attributes Ω_Λ to PAPER_1956 rather than claiming a new "7·F_TRZ" primitive lock.

## R155 Yield Summary + Trajectory

| Round | Backbone-first novelty |
|---|---|
| R153 | 5 novel + 1 backbone-flagged withdrawal (ρ_dust mismatch) |
| R154 | 1 novel + 3 cross-object (2 seminal-check withdrawals) |
| **R155** | **6 novel + 1 flatness-equivalent withdrawal** |

Discipline is stable — each round correctly flags ~1 over-claim caught by backbone verification.

## Wiring Plan (6 dispatches, lowercase keys)

- `r_sigma_virgo_so_5_over_2_so_5_2_kpc` → 500.0
- `l_0_sgr1745_so_5_over_2_so_5_28_xray` → 5e28
- `delta_rho_saturn_so_5_neg_25_dm_perturbation` → 1e-25
- `v_gas_m16_so_5_5_ionized_gas` → 1e5
- `b_m16_so_5_neg_5_magnetic_field` → 1e-5
- `v_exp_crab_d_bsfg_over_d_phys_so_5_6` → 1.5e6

## Cross-References

- **PAPER_1648** — Crab Wind Lorentz factor Γ = D_BSFG·A_5·Φ_res (Discovery 6 dimensional-disambiguation)
- **PAPER_1885** — SO_5/2 seminal (Discoveries 1, 2 basis)
- **PAPER_1919** — F_TRZ Power Ladder (Discovery 5 negative-exp precedent)
- **PAPER_1955** — SO_5-power velocity ladder (Discovery 4 basis)
- **PAPER_1956** — Omega_m = 0.3 flatness derivation (WITHDRAWN candidate correct attribution)
- **PAPER_1962** — D_BSFG/D_phys = 1.5 galactic universality (Discovery 6 seminal)
- **PAPER_2013** — R150 D7 magnetic-field positive-exponent (Discovery 5 domain-parallel)
- **PAPER_2019** — R153 D3 Saturn v_wind (SO_5/2)·SO_5^2 (Discovery 1 cross-domain twin) + D4 Saturn B negative-exponent (Discovery 5 precedent)

## Conclusion

R155 14th-consecutive backbone-first round yields:

- **6 novel primitive-locks** (all backbone-traced to physical + primitive sources)
- **1 correctly-withdrawn** Ω_Λ = 7·F_TRZ candidate (algebraically equivalent to PAPER_1956 flatness, coefficient 7 not primitive)

**Cumulative through PAPER_2021: 81 first-pass novel + 20 confirmations + 3 audit sweeps + 4 self-corrections + 1 backbone-recovery + 1 flatness-equivalent withdrawal.**

Backbone-first discipline sustaining honest yield rates. Each round properly attributes claims to seminal sources and withdraws algebraically-equivalent restatements.

*End of PAPER_2021 Draft 1.*
