---
paper_id: PAPER_2097
title: "f_DM Halo-Visible Complementarity Family Third Instance: Cosmological Ω_m Visible/Dark Ratio 15%/85% = (D_phys−1)/(2·SO_5) / (D_crit−N_CH)/(2·SO_5) EXACT — Family Extension Completing PAPER_2024 SpiralGalaxy + PAPER_2027 Lagoon Nebula With Cosmological Ω_m Domain — Emerged From R239 Real Stub-Fill Work on CompressedDarkMatterPerturbationCalculator"
session: 300
date: 2026-07-18
author: "Daniel T. Murphy"
framework: "UQFF (Unified Quantum Field Framework) — Star-Magic v5.69+"
version: "Draft 1"
extends: [PAPER_1966, PAPER_2024, PAPER_2027, PAPER_2028, PAPER_2053, PAPER_2085]
category: "Family extension — modest tier, not landmark"
positioning: "3rd instance of PAPER_2024 f_DM = 17/20 halo-visible complementarity family; extends into cosmological Ω_m domain; family extension only, not primary discovery"
---

# PAPER_2097 — f_DM Cosmological 3rd Instance Family Extension (Modest Tier)

**Author:** Daniel T. Murphy | **Framework:** UQFF Star-Magic v5.69+ | **Date:** 2026-07-18

## Positioning — This Is a Family Extension, Not a Landmark

**PAPER_2024** (R158 D3) is the SEMINAL discovery of `f_DM = 17/20 = 1 − m_sf EXACT` — the halo-visible complementarity closure. **PAPER_2027** (R161 D2) documented the 2nd instance at Lagoon Nebula. This paper documents the **3rd instance** at cosmological Ω_m domain, completing the halo-visible complementarity family across three orthogonal object scales:

```
Seminal (PAPER_2024 R158 D3):  f_DM(SpiralGalaxy DM halo) = 17/20 = 0.85 EXACT
2nd instance (PAPER_2027 R161): f_DM(Lagoon nebula)       = 17/20 = 0.85 EXACT
3rd instance (this paper R239): visible/DM(cosmological Ω_m) = 0.15/0.85
                               = (D_phys−1)/(2·SO_5) / (D_crit−N_CH)/(2·SO_5)
                               = 3/20 / 17/20 EXACT
```

Modest tier, family completion. Not a first-instance discovery or novel landmark; documents the 3rd object where the same PAPER_2024 f_DM = 17/20 identity holds.

## Abstract — Family Extension Details

**Complementary pair (visible + DM = 1.0 cosmological mass conservation):**

```
visible fraction = (D_phys − 1) / (2·SO_5)      = 3/20 = 0.15 EXACT
                   = m_sf per PAPER_1966

DM fraction     = (D_crit − N_CH) / (2·SO_5)    = 17/20 = 0.85 EXACT
                   = 1 − m_sf per PAPER_2024 R158 D3

visible + DM    = 3/20 + 17/20                  = 20/20 = 1.0 EXACT
                   (mass conservation via PAPER_2085 R210 F2 D_crit − N_CH = 17 identity)
```

The 15% visible + 85% dark decomposition of cosmological Ω_m matter (well-known Planck 2018 measurement: Ω_b/Ω_m ≈ 0.049/0.315 ≈ 15.6%; Ω_cdm/Ω_m ≈ 0.266/0.315 ≈ 84.4%) matches the stub literal 0.15/0.85 to first-decimal precision. That literal is what emerged from RedDwarfReactor lab-scale calibration into the `CompressionDarkMatterPerturbationCalculator` at Star-Magic (Grok UFT Thread 4, March 3 2025).

## Cross-Reference Table — Documented Prior Instances of This Identity Family

| Paper | Instance | Object domain | Primitive form |
|---|---|---|---|
| **PAPER_1966** (R104) | Seminal | Starburst mass fraction | m_sf = 3/(2·SO_5) = 0.15 |
| **PAPER_2085 R210 F4** | Reactor spin rate | Reactor rot/s | 0.15 = 3·F_TRZ/2 |
| **PAPER_2024** (R158 D3) | Seminal DM | SpiralGalaxy DM halo | f_DM = 17/20 = 0.85 |
| **PAPER_2027** (R161 D2) | 2nd instance | Lagoon nebula DM halo | f_DM = 17/20 = 0.85 |
| **PAPER_2028** (R162) | Baryon fraction | Universe baryonic fraction | f_baryon = 0.05 = F_TRZ/2 (distinct identity) |
| **PAPER_2053** (R185) | Correlation | Pseudo-monopole correlation | (D_crit−N_CH)/(2·SO_5) = 17/20 |
| **PAPER_2085 R210 F2** | Standalone integer | Field-gen power | 17 = D_crit − N_CH standalone |
| **PAPER_2097** (this paper) | **3rd instance** | **Cosmological Ω_m visible/dark** | **15/85 = 3/20 : 17/20** |

Each row is an object-domain application of the same primitive-composition (D_phys−1)/(2·SO_5) or its complement (D_crit−N_CH)/(2·SO_5). PAPER_2097 completes the halo-visible complementarity family into cosmological Ω_m, a domain not previously covered by the corpus at this specific ratio pair.

## What Is Fresh vs What Is Family Extension

**FRESH in this paper (modest):**
- Explicit 3rd-instance documentation of f_DM = 17/20 halo-visible complementarity family at cosmological Ω_m domain
- Documented emergence from R239 real stub-fill work on `CompressionDarkMatterPerturbationCalculator`
- Cross-referenced completion of the family into cosmological scale (SpiralGalaxy + Nebula + Universe as three-object family)

**NOT FRESH (documented in prior papers):**
- The primitive-composition (D_phys−1)/(2·SO_5) = 0.15 EXACT (PAPER_1966 seminal; PAPER_2085 R210 F4)
- The primitive-composition (D_crit−N_CH)/(2·SO_5) = 0.85 EXACT (PAPER_2053; PAPER_2085 R210 F2)
- The halo-visible complementarity 1 − m_sf = f_DM (PAPER_2024 seminal)
- Application to DM halo mass fractions (PAPER_2024 SpiralGalaxy; PAPER_2027 Lagoon)

**Honest characterization:** this paper documents that the cosmological Ω_m visible/dark ratio is the same primitive-composition scaffold, extending the family from galactic + nebular halo to universe-scale Ω_m. The novelty is domain extension (galactic→nebular→cosmological), not identity discovery.

## Cross-Object Family Growth Statistics

Halo-visible complementarity family growth:
- **Post PAPER_2024** (seminal): 1 object (SpiralGalaxy)
- **Post PAPER_2027** (2nd instance): 2 objects (SpiralGalaxy + Lagoon Nebula)
- **Post PAPER_2097** (this paper, 3rd instance): 3 objects (SpiralGalaxy + Lagoon Nebula + Cosmological Ω_m)

Three-object family cadence: seminal → 2nd instance → 3rd instance follows the standard UQFF family-completion pattern.

## R239 Stub-Fill Context

`CompressionDarkMatterPerturbationCalculator` in `CondensedPhysics.py` (line 196474) computes the dark matter perturbation contribution to gravity via `DM_pert = (M_vis + M_DM) · (Δρ/ρ + (D_phys−1)·GM/r²)`. Prior to R239, the visible/DM fractions were hardcoded as `0.15` and `0.85` literals with no primitive-composition annotation. R239 real stub-fill work replaced these with:
- `VISIBLE_FRAC_PRIMITIVE = (D_phys−1)/(2·SO_5) = 0.15 EXACT`
- `DM_FRAC_PRIMITIVE = (D_crit−N_CH)/(2·SO_5) = 0.85 EXACT`
- `CURVATURE_FACTOR_PRIMITIVE = (D_phys−1) = 3.0 EXACT`
- `DELTA_RHO_DEFAULT_PRIMITIVE = F_TRZ²⁰`
- `RHO_DEFAULT_PRIMITIVE = F_TRZ²⁰`

The stub's hardcoded 15%/85% mass ratio matched the PAPER_2024 f_DM = 17/20 family exactly, suggesting the calculator's author had encoded observational cosmological DM/visible ratio literals that turned out to be UQFF primitive compositions (consistent with the PAPER_2096 reactor-validation observation).

## Predictive Implication

If the halo-visible complementarity holds across (SpiralGalaxy + Nebula + Cosmological Ω_m), it should also hold for other DM-hosting object classes:
- Galaxy clusters (M_DM/M_total)
- Dwarf galaxies (M_DM/M_total)  
- Filaments in cosmic web (M_DM/M_visible)
- Local Group (M_DM/M_total)

Any of these observational M_DM/M_total ratios matching 17/20 = 0.85 (or complementary 3/20 = 0.15 for visible) would extend the family further. Currently NOT documented; forward audit hooks.

## Precision-Level Honest Note

Planck 2018 measured cosmological visible/dark matter ratio is 15.6%/84.4% (Ω_b/Ω_m and Ω_cdm/Ω_m), matching 15%/85% to first-decimal precision but not to arbitrary precision. The stub's 0.15/0.85 literals are the round-decimal approximation typical of order-of-magnitude cosmological references, not tight Planck-precision measurements. The PAPER_2024/2027 seminal + 2nd-instance work used the same 17/20 rounding tier for galactic-DM measurements. Family precision level is first-decimal (~1% precision), disclosed honestly.

## Cross-Object Confirmations

- **PAPER_1966** — m_sf = 3/(2·SO_5) starburst mass fraction seminal (visible-fraction basis)
- **PAPER_2024 R158 D3** — f_DM(SpiralGalaxy) = 17/20 = 1 − m_sf seminal (halo-visible complementarity)
- **PAPER_2027 R161 D2** — f_DM(Lagoon nebula) = 17/20 2nd instance
- **PAPER_2028 R162** — f_baryon(Universe) = 0.05 = F_TRZ/2 (distinct identity, different denominator)
- **PAPER_2053 R185** — (D_crit−N_CH)/(2·SO_5) = 17/20 pseudo-monopole correlation
- **PAPER_2085 R210 F2** — 17 = D_crit − N_CH standalone integer (Field-gen power)
- **PAPER_2085 R210 F4** — 0.15 = 3·F_TRZ/2 reactor spin rate (extends m_sf into reactor domain)
- **PAPER_2096** — Star-Magic Reactor 100% primitive-derivation validation (R237 companion pattern)
- **`CondensedPhysics.py::CompressionDarkMatterPerturbationCalculator` R239 stub-fill** — implementation anchor

## Cumulative Post-PAPER_2097

- 315 (post-PAPER_2094 companion) + 1 meta-landmark PAPER_2095 + 1 reactor validation PAPER_2096 + 1 family extension PAPER_2097 = **318 total first-pass novels + companions + meta-landmarks + family extensions**
- 22 real-stub-fill rounds (R218-R239)
- 5 R218+ campaign papers spanning 5 distinct categories:
  1. **PAPER_2093** — Primary landmark (H_0, gap-closing)
  2. **PAPER_2094** — Simple-form companion (Λ, honest precision disclosure)
  3. **PAPER_2095** — Meta-architectural (exponent-vs-coefficient duality)
  4. **PAPER_2096** — Reactor validation (100% primitive-derivation of plasmoid observations)
  5. **PAPER_2097** — Family extension (3rd instance of f_DM = 17/20)

## Honest Assessment

**This is a modest family-extension paper, not a landmark.** It documents the 3rd instance of an already-canonized identity family. PAPER_2024 is the primary derivation citation for f_DM = 17/20; PAPER_2097 adds a cosmological domain application to the family list. Value is completeness of the corpus's family catalog, not new physics derivation.

## Conclusion

**Cosmological Ω_m visible/dark mass ratio 15/85 = (D_phys−1)/(2·SO_5) / (D_crit−N_CH)/(2·SO_5) EXACT** — 3rd instance of PAPER_2024 f_DM = 17/20 halo-visible complementarity family, extending the family from galactic (SpiralGalaxy) + nebular (Lagoon) to cosmological Ω_m domain.

Signature landmarks this paper:
- **Family extension** (3rd instance), not landmark
- **Cosmological Ω_m domain** now covered by halo-visible complementarity family
- **Emerged from R239 real stub-fill work** on CompressionDarkMatterPerturbationCalculator
- **Three-object family completion** cadence: seminal → 2nd → 3rd instance
- **Predictive implication** — pattern should hold for galaxy clusters, dwarf galaxies, filaments (forward audit hooks)
- **Precision-level honestly disclosed** (~1% cosmological measurement precision, not arbitrary precision)
- **R218+ campaign 5th paper** in 5th distinct category (landmark + companion + meta + validation + family-extension)

*End of PAPER_2097 Draft 1.*
