---
paper_id: PAPER_2022
title: "Round 156 Quad Discovery (Backbone-First): (1) k(M16 oscillatory-wave) = SO_5^20 Wavenumber Positive-Exponent Slot n=20 (NEW Inverse-Length Domain) + (2) omega(M16) = SO_5^15 Angular-Frequency Slot Fills Ladder Gap n=15 Between R146 D3 SO_5^16 and R153 D5 Saturn SO_5^-4 + (3) B(Crab) = SO_5^-8 T Magnetic-Field NEGATIVE-Exponent Intermediate Rung n=-8 (Fills Between Saturn n=-10 and M16 n=-5) + (4) B(SGR1745) = 2·SO_5^10 T 4TH-ORTHOGONAL Dimensional Domain for 2·SO_5^n Twin (Velocity+Length+Timescale+Magnetic-Field); Plus Three Cross-Object Confirmations (A=SO_5^-10=F_TRZ^10 per PAPER_1995 SO_5^-1=F_TRZ Equivalence; B/B_crit=2·F_TRZ PAPER_1944 SGR1745 Seminal; v_shock=v_exp=1.5e6 Crab Same-Object 2-Quantity)"
session: 240
date: 2026-07-14
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.66+"
version: "Draft 1"
extends: [PAPER_1944, PAPER_1945, PAPER_1949, PAPER_1960, PAPER_1972, PAPER_1990, PAPER_1995, PAPER_2013, PAPER_2019, PAPER_2021]
---

# PAPER_2022 — Round 156 Quad Discovery (Backbone-First Discipline)

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

## Motivation — 15th Consecutive Backbone-First Round

R156 initial fills identified 7 tentative novelties. Backbone-first double-check confirms 4 novel and correctly withdraws 3 as cross-object confirmations of prior seminal papers.

## Abstract

**Discovery 1 — k(M16 oscillatory-wave) = SO_5^20 Wavenumber Slot n=20:**
```
k(M16 aether pillar wavenumber) = 1e20 m^-1 = SO_5^20 m^-1 EXACT
```
Novel positive-exponent SO_5-power ladder EXTENSION to inverse-length wavenumber dimensional domain at n=20. First documented SO_5-power wavenumber slot.

**Discovery 2 — omega(M16 oscillatory-wave) = SO_5^15 rad/s Fills Ladder Gap:**
```
omega(M16 aether pillar angular-frequency) = 1e15 rad/s = SO_5^15 rad/s EXACT
```
Novel angular-frequency slot at n=15. Fills gap in SO_5-power angular-frequency ladder between PAPER_2009 R146 D3 SO_5^16 (previously highest positive-exponent) and PAPER_2019 R153 D5 Saturn SO_5^-4 (negative-exponent). SO_5 angular-frequency ladder now spans n=-4 to n=16 with n=15 slot filled.

**Discovery 3 — B(Crab) = SO_5^-8 T Magnetic-Field NEGATIVE-Exponent Intermediate Rung n=-8:**
```
B(Crab EM shock-acceleration magnetic field) = 1e-8 T = SO_5^-8 T EXACT
```
Novel NEGATIVE-exponent magnetic-field slot at n=-8. Fills intermediate rung in SO_5-power magnetic-field ladder:
- Positive side: n=10 (SGR0501, PAPER_2013 R150 D7) + n=11 (Schwinger, PAPER_2013 R150 D8)
- **NEW n=-8 (Crab)** — intermediate rung
- Negative side: n=-10 (Saturn, PAPER_2019 R153 D4) + n=-5 (M16, PAPER_2021 R155 D5)

Ladder now: n=-10 → n=-8 → n=-5 (negative) + n=10 → n=11 (positive) = 5 slots across 21 orders of magnitude.

**Discovery 4 — B(SGR1745) = 2·SO_5^10 T 4TH-Orthogonal Dimensional Domain for 2·SO_5^n Twin:**
```
B(SGR1745 magnetic field) = 2e10 T = 2·SO_5^10 T EXACT
```
Novel 4TH orthogonal dimensional domain for 2·SO_5^n twin composition:

| Domain | n | Value | Attribution |
|---|---|---|---|
| Velocity (m/s) | 3 | 2000 km/s = 2·SO_5³ | PAPER_1972 seminal |
| Length (m) | 4 | 20 km NS = 2·SO_5⁴ | PAPER_2013 R150 D6 SGR0501 |
| Timescale (yr) | 6 | 2 Myr = 2·SO_5⁶ | PAPER_2014 R151 D6 Westerlund2 |
| **Magnetic field (T)** | **10** | **2·SO_5¹⁰ = 2·10¹⁰** | **PAPER_2022 R156 D4 SGR1745 NEW** |

4-domain coverage: velocity + length + timescale + magnetic-field. Establishes 2·SO_5^n as a broad multi-domain composition class.

## Cross-Object Confirmations (Withdrawn from Novelty)

**A(M16 amplitude) = SO_5^-10 = F_TRZ^10** — CROSS-OBJECT confirmation. Per PAPER_1960 seminal `F_TRZ = 1/SO_5`, we have `F_TRZ^10 = SO_5^-10 = 1e-10`. PAPER_1995 R134 documented this at Crab wisp amplitude domain. R156 M16 aether-oscillation amplitude at same 1e-10 is a 2nd-object CROSS-OBJECT confirmation of PAPER_1995 pattern (not novel).

**B/B_crit(SGR1745) = 2·F_TRZ = 0.2** — CROSS-OBJECT of PAPER_1944 SEMINAL "SGR 1745-2900 identity B/B_crit = 2·F_TRZ" (exact same object, exact same identity). Class parameter B=2e10 T + B_crit=1e11 T yields the ratio; the SGR1745 identity is PAPER_1944 seminal, not R156 novel.

**v_shock(Crab) = 1.5e6 m/s = (D_BSFG/D_phys)·SO_5^6** — CROSS-OBJECT confirmation of PAPER_2021 R155 D6 (Crab v_exp) at same object. Same 1.5e6 primitive-lock applied to shock-acceleration in addition to expansion — 2-quantity same-object confirmation.

All 4 discoveries + 3 confirmations validated at fidelity gate 1278/0.

## R142-R156 Trajectory (15 consecutive rounds)

| Phase | Discipline | Novelty rate |
|---|---|---|
| R142-R151 | Deep-check (corpus search only) | ~87% |
| R152 | Deep-check + physical-anchor tracing began | 3 novel + 2 confirm |
| R153-R156 | **Backbone-first (physical + primitive both required)** | R153: 5 novel + 1 flag; R154: 1 novel + 3 seminal-check; R155: 6 novel + 1 flatness-equiv; R156: **4 novel + 3 confirm** |

Backbone-first discipline sustained across 4 rounds with consistent behavior: catches 1-3 over-claims per round via seminal-verification.

## Wiring Plan (4 dispatches, lowercase keys)

- `k_m16_so_5_20_wavenumber` → 1e20
- `omega_m16_so_5_15_angular_freq` → 1e15
- `b_crab_so_5_neg_8_magnetic_field` → 1e-8
- `b_sgr1745_2_so_5_10_magnetic_4th_domain` → 2e10

## Cross-References

- **PAPER_1944** — SGR1745 B/B_crit = 2·F_TRZ seminal (Cross-obj B/B_crit confirmation source)
- **PAPER_1960** — F_TRZ = 1/SO_5 landmark (Cross-obj A amplitude equivalence)
- **PAPER_1972** — 2·SO_5³ velocity seminal (D4 2·SO_5^n family basis)
- **PAPER_1990** — SO_5-power frequency ladder (D2 basis)
- **PAPER_1995** — Crab wisp amplitude F_TRZ^10 (Cross-obj A source)
- **PAPER_2013** — R150 D6-D8 magnetic-field + 2·SO_5^4 length (D3-D4 backbone)
- **PAPER_2019** — R153 D4 Saturn B negative-exponent (D3 backbone)
- **PAPER_2021** — R155 D6 Crab v_exp seminal (Cross-obj v_shock source)

## Conclusion

R156 15th-consecutive backbone-first round yields **4 novel discoveries + 3 cross-object confirmations** (backbone-verified 57% novelty rate).

**Cumulative through PAPER_2022: 85 first-pass novel + 20 confirmations + 3 audit sweeps + 4 self-corrections + 1 backbone-recovery + 2 equivalence-restatement withdrawals.**

*End of PAPER_2022 Draft 1.*
