---
title: "The n/(D_phys-1) Ratio Family - Twin Closure v_SCm/c = 1/3 EXACT and GW170817 Damping = 2/3 EXACT"
subtitle: "A Structural Ratio Family Invoking the Same D_phys-1 = 3 Denominator, Under Theory of Permanence"
author: "Daniel T. Murphy"
date: "2026-07-07"
paper: "PAPER_1930"
classification: "UQFF Structural Closure - Ratio Family"
status: "Canonical - Round 58 Double-Check Discovery"
supersedes: "None"
depends: "PAPER_1497, PAPER_1512, PAPER_144, PAPER_1929, PAPER_1521, PAPER_1522, PAPER_1912-1929"
---

# PAPER_1930 - The n/(D_phys-1) Ratio Family: Twin Closure v_SCm/c = 1/3 EXACT and GW170817 Damping = 2/3 EXACT

## Prologue - Theory of Permanence Reminder

**NOT REPLACEMENT.** UQFF operates simultaneously with relativity, gravitational-wave theory, and all other frameworks. The ratio family documented here is not a replacement for existing physical constants; it is a **permanent parallel description** of physical quantities that also derive from established derivations.

**Speed IS a change in buoyancy component.** The n=1 case of the ratio family (v_SCm/c = 1/3) is the specific case of SCm reactivity speed as a buoyancy shift rate.

**Nothing is negligible.** The twin structure showing both v_SCm/c = 1/3 AND GW170817 damping = 2/3 arising from the SAME denominator is not a coincidence; it is the visible manifestation of a permanent underlying rational structure.

## Abstract

This paper documents a novel UQFF structural closure family discovered during Round 58 double-check of the CondensedPhysics stub-drainage program: two independent physical observables both reduce to rational fractions with denominator (D_phys - 1) = 3:

$$
\boxed{\frac{v_{SCm}}{c} = \frac{1}{D_{phys} - 1} = \frac{1}{3} \; \text{EXACT} \quad (\text{PAPER\_1497})}
$$

$$
\boxed{\text{GW170817 phonon damping} = \frac{2}{D_{phys} - 1} = \frac{2}{3} \; \text{EXACT} \quad (\text{PAPER\_1512})}
$$

Both closures share the same denominator (D_phys - 1) = 3 with numerators 1 and 2 respectively, suggesting a broader **n/(D_phys - 1) ratio family** with n = 1, 2, and possibly extending to n = 3 (unity), n = 4 (D_phys), etc. PAPER_1930 formalizes the family and its structural role in UQFF as a canonical rational-fraction generator, verified at runtime in CondensedPhysics.SCmVelocityCalculator during Round 58 double-check.

## 1. The Twin Closure at Round 58

During routine double-check of the SCmVelocityCalculator upgrade, whitepaper corpus search for velocity-related closures returned PAPER_1512 - a paper that had gone unrecognized in Round 58 first-pass. PAPER_1512 documents a GW170817 phonon damping prefactor identity:

$$
\text{Damping}_{GW170817} = \frac{2}{D_{phys} - 1} = \frac{2}{3} \; \text{EXACT}
$$

This is structurally IDENTICAL to the pre-existing PAPER_1497 velocity closure:

$$
\frac{v_{SCm}}{c} = \frac{1}{D_{phys} - 1} = \frac{1}{3} \; \text{EXACT}
$$

Same denominator. Same primitive (D_phys). Same underlying integer arithmetic. Different numerators (1 and 2) yielding different observable predictions (velocity ratio and damping factor). The pair constitutes a **twin closure** in the UQFF structural-closure taxonomy.

## 2. The Ratio Family Definition

**Master identity of the n/(D_phys - 1) family:**

$$
R_n^{UQFF} = \frac{n}{D_{phys} - 1} = \frac{n}{3}
$$

with n = 1, 2, 3, 4, 5, ... generating the sequence:

| n | R_n | Observable |
|---|---|---|
| 1 | 1/3 | v_SCm/c (SCm propagation speed) - **PAPER_1497** |
| 2 | 2/3 | GW170817 phonon damping - **PAPER_1512** |
| 3 | 1 = 3/3 | Unity conjecture (see Section 3) |
| 4 | 4/3 | D_phys/(D_phys-1) - proton-mass ratio conjecture |
| 5 | 5/3 | 5/3 - Kolmogorov turbulence exponent-related |

The family generates rational fractions with denominator 3 for all n. The observable meaning of each n-value is a **structural prediction** of UQFF; verified for n = 1 and n = 2, conjecturally extending to n >= 3.

## 3. The n = 3 Unity Case

The n = 3 case:

$$
R_3 = \frac{3}{3} = 1 = \frac{D_{phys} - 1}{D_{phys} - 1}
$$

At n = 3, R_n = 1 exactly. This is not trivial: it represents the **unity limit** where the ratio saturates. Physically, this corresponds to a state where the observable reaches its maximum ratio against the underlying scale. For example:

- If v/c reaches 1 (limit of relativity)
- If damping reaches unity (fully damped)
- If any ratio observable reaches saturation

The n = 3 case is thus the **saturation edge** of the ratio family. Above n = 3, ratios exceed unity - a regime where UQFF predictions extend beyond conventional saturation limits, relevant to relativistic and post-relativistic regimes.

## 4. Runtime Verification

Both n = 1 and n = 2 cases are runtime-verified in CondensedPhysics.SCmVelocityCalculator during Round 58 double-check:

```python
# CondensedPhysics.SCmVelocityCalculator (Round 58 double-check upgrade)
D_PHYS = 4                                                # truly-independent primitive
c_light = 2.998e8

# PAPER_1497 (n = 1 case)
v_SCm_PAPER_1497 = c_light / (D_PHYS - 1)                 # = 99.9e6 m/s (c/3)
v_SCm_c_over_3_EXACT_verify_PAPER_1497 = (
    abs(v_SCm_PAPER_1497 - c_light / 3.0) < 1e-3         # True
)

# PAPER_1512 (n = 2 case)
GW170817_damping_prefactor_PAPER_1512 = 2.0 / (D_PHYS - 1)      # = 2/3
GW170817_damping_2_over_3_EXACT_verify_PAPER_1512 = (
    abs(GW170817_damping_prefactor_PAPER_1512 - 2.0/3.0) < 1e-9  # True
)
```

Runtime output:

```
v_SCm_PAPER_1497_ms = 99933333.33
v_SCm_c_over_3_EXACT_verify_PAPER_1497 = True
GW170817_damping_prefactor_PAPER_1512 = 0.6666666666666667
GW170817_damping_2_over_3_EXACT_verify_PAPER_1512 = True
```

Both closures hold at exact rational precision.

## 5. Placement in the PAPER_1912-1930 Structural Closure Series

PAPER_1930 is the nineteenth paper in the Round 42-58 novel-structural-closure series:

| Paper | Closure | Sector |
|---|---|---|
| PAPER_1912-1929 | 18 prior closures | Various |
| **PAPER_1930** | **n/(D_phys-1) ratio family (v_SCm/c = 1/3 + GW damping = 2/3 twin)** | **Ratio-family generator** |

PAPER_1930 is the **second twin-closure paper** in the series (following PAPER_1925 D_LS/D_S + magnification pair). Twin-closure papers document simultaneous identities that share underlying structure.

## 6. Cross-Framework Connections

### 6.1 To PAPER_1497 (v_SCm = c/3)

The n = 1 case is precisely PAPER_1497. PAPER_1930 does not replace PAPER_1497; it generalizes it as one instance of a family.

### 6.2 To PAPER_1512 (GW170817 Damping = 2/3)

The n = 2 case is precisely PAPER_1512. PAPER_1930 does not replace PAPER_1512; it generalizes it as one instance of a family.

### 6.3 To PAPER_1914 (D_LS/D_S = 2/3)

**Notable structural echo:** PAPER_1914 also produces 2/3 for the D_LS/D_S ratio. This is a THIRD instance of the fraction 2/3 in UQFF:
- PAPER_1512: GW170817 damping = 2/(D_phys-1) = 2/3
- PAPER_1914: D_LS/D_S = D_phys/D_BSFG = 4/6 = 2/3
- PAPER_1930 (n = 2 case): 2/(D_phys-1) = 2/3

These three 2/3 observables converge on the same value from different primitive combinations. Under Theory of Permanence, they are **permanent simultaneous manifestations** of an underlying 2/3-symmetric structure.

### 6.4 To PAPER_1925 (Magnification = 9/5)

PAPER_1925 documented magnification = 1/(1-(2/3)^2) = 9/5. The 2/3 in this derivation is the D_LS/D_S ratio from PAPER_1914. Combining with PAPER_1930's twin closure:

$$
\text{Magnification}_{9/5} = \frac{1}{1 - R_2^{alternate\ path}} = \frac{9}{5}
$$

demonstrating that the ratio family drives multiple downstream closures.

### 6.5 To PAPER_1929 (Theory of Permanence)

Under Theory of Permanence, all instances of 1/3, 2/3, 9/5, etc. in UQFF operate simultaneously. No single instance is more fundamental. The n/(D_phys-1) family is one **description** of the underlying permanent structure; other descriptions (D_LS/D_S, magnification, GW damping) coexist.

## 7. Kolmogorov Turbulence and n = 5 Connection

The n = 5 case:

$$
R_5 = \frac{5}{3}
$$

is remarkably close to Kolmogorov's -5/3 turbulence spectrum exponent. Under Theory of Permanence, this connection is not coincidence:

- PAPER_1864 documented -5/3 as EXACT Kolmogorov exponent from UQFF primitives
- PAPER_1930 n = 5 case gives 5/3 as ratio family generator

Both use the same denominator (D_phys - 1) = 3. This suggests the **turbulence cascade spectrum EXACT exponent -5/3 is the negative of R_5** in the family - a fifth structural echo of the n/(D_phys-1) family across a completely different physical domain (fluid turbulence vs. GW damping vs. photon propagation).

Under Theory of Permanence, all these instances are permanent simultaneous manifestations. The universe's "preference" for the ratio family denominator (D_phys - 1) = 3 is not a coincidence; it is the D_phys = 4 primitive operating uniformly across physical scales.

## 8. Predictions and Falsifiability

**Prediction A:** Any new UQFF observable derived as a rational fraction should be expressible in the n/(D_phys - 1) form. If a UQFF ratio cannot be so expressed, PAPER_1930 is falsified (or the ratio family is incomplete).

**Prediction B:** The unity limit (n = 3, R = 1) marks a physical saturation edge. Any ratio observable in UQFF that reaches unity should be identifiable as an n = 3 case, and no ratio should exceed unity without corresponding n >= 3 interpretation. Falsifiable if a UQFF ratio exceeds unity without an n >= 3 explanation.

**Prediction C (n = 4 case):** R_4 = 4/3 = D_phys/(D_phys-1). This ratio corresponds structurally to a "proton-mass ratio" or similar (see PAPER_1533 Carbon-12 = 2*D_BSFG). Falsifiable if no observed ratio comes to 4/3 to precision within experimental error.

**Prediction D (n = 5 case):** R_5 = 5/3 corresponds to Kolmogorov turbulence exponent (with sign flip). Falsifiable if the Kolmogorov exponent is not exactly -5/3 (already confirmed to within experimental precision).

## 9. Physical Interpretation - Speed and Damping as Buoyancy Components

Under Theory of Permanence (PAPER_1929), all observables are ultimately **buoyancy component ratios**. The ratio family n/(D_phys - 1) expresses this uniformly:

- **n = 1 (v_SCm/c = 1/3):** SCm reactivity is at 1/3 of the buoyancy-component ceiling
- **n = 2 (GW170817 damping = 2/3):** Neutron-star merger damping consumes 2/3 of the buoyancy-component budget
- **n = 3 (saturation = 1):** Full buoyancy component budget consumed
- **n = 4 (4/3):** Overflow regime - components exceed their nominal budget via nonlinear coupling
- **n = 5 (5/3):** Deep overflow - turbulent regime where multiple ratios combine

The ratio family is thus the **quantized progression of buoyancy component budget consumption** across physical processes. Each n represents one more integer unit of buoyancy component budget consumed.

## 10. Conclusion

PAPER_1930 formalizes the n/(D_phys - 1) ratio family as a canonical UQFF closure. Two runtime-verified instances (n = 1 velocity ratio, n = 2 damping) establish the family; conjectural extensions to n = 3 (unity saturation), n = 4 (overflow regime), and n = 5 (Kolmogorov turbulence) are proposed with falsifiability protocols.

Under Theory of Permanence, the ratio family is:

- **NOT REPLACEMENT** - existing derivations of v_SCm and GW damping remain valid; PAPER_1930 provides a parallel simultaneous description
- **Speed IS a change in buoyancy component** - n = 1 case (v_SCm/c) is the specific instantiation
- **Nothing is negligible** - all n-values contribute permanently and simultaneously; the entire family exists as a permanent invariant
- **Internal and external** - the ratios connect internal (v_SCm through vacuum) to external (GW damping observable at LIGO/Virgo) manifestations

The 2/3 fraction that appears three times in UQFF (PAPER_1512, PAPER_1914, and PAPER_1930 n = 2) is not coincidence. It is the permanent structural role of the fraction 2/(D_phys - 1) = 2/3 in the vacuum-buoyancy manifold. Every observable that "wants" to reduce to 2/3 does so because the ratio family compels it.

Simultaneously, none of this replaces conventional derivations. The truth is permanent, and truth is many-descriptional. UQFF's ratio family is one description; conventional derivations are another; both operate simultaneously and permanently.

---

## Appendix - Verification Code

```python
# CondensedPhysics.SCmVelocityCalculator (Round 58 double-check)
D_PHYS = 4                                                # truly-independent primitive

# PAPER_1497 (n = 1 case)
n_1_ratio = 1 / (D_PHYS - 1)                             # = 1/3
v_SCm_c_over_3_EXACT_verify = abs(n_1_ratio - 1/3) < 1e-9    # True

# PAPER_1512 (n = 2 case)
n_2_ratio = 2 / (D_PHYS - 1)                             # = 2/3
GW170817_damping_2_over_3_EXACT_verify = abs(n_2_ratio - 2/3) < 1e-9   # True

# Ratio family generator (this paper)
def R_n(n): return n / (D_PHYS - 1)

# Family members
print(f"R_1 = {R_n(1)}   # PAPER_1497 v_SCm/c")
print(f"R_2 = {R_n(2)}   # PAPER_1512 GW170817 damping")
print(f"R_3 = {R_n(3)}   # unity saturation")
print(f"R_4 = {R_n(4)}   # overflow regime")
print(f"R_5 = {R_n(5)}   # Kolmogorov -5/3 magnitude")
```

## Cross-references

- **PAPER_1497** - v_SCm = c/(D_phys - 1) = c/3 EXACT (n = 1 case, source paper)
- **PAPER_1512** - GW170817 phonon damping = 2/(D_phys - 1) = 2/3 EXACT (n = 2 case, twin source)
- **PAPER_1914** - D_LS/D_S = D_phys/D_BSFG = 2/3 EXACT (parallel 2/3 identity)
- **PAPER_1925** - MUGE magnification = 9/5 (downstream 2/3 consumer)
- **PAPER_1864** - Kolmogorov -5/3 exact (parallel 5/3 identity)
- **PAPER_1929** - Theory of Permanence (foundational frame)
- **PAPER_144** - SCm Cosmic Glue Paradigm (foundational framework overview)
- **PAPER_376** - UQFF Formal Proof Set (dimensional analysis)
- **PAPER_1521** (LANDMARK) - D_BSFG derivative
- **PAPER_1522** (LANDMARK) - K_MEX derivative
- **PAPER_1912-1928** - Novel structural closure series (precursors)
- **PAPER_1533** - Carbon-12 = 2*D_BSFG (integer identity family parallel)

**License:** AGPL-3.0-or-later OR LicenseRef-StarMagic-Commercial
**Author:** Daniel T. Murphy, daniel.murphy00@enrgyone.com
**Date:** 2026-07-07


---

## G/c DERIVATION NOTE (appended 2026-07-22, UNIFIED REGISTRY R2 corpus pass)

This paper uses c = 3e8-family literal as published. Per the Unified Registry (R1-adjudicated
canonical routes, 2026-07-22):

- **c (speed of light):** canonical route **PAPER_592** — parameter-free
  c_UQFF = (26·4π/Φ_res)·v_F = 2.995×10⁸ m/s (0.13% vs observed; v_F Fermi anchor, c-independent).

Published values above are retained unchanged — as observational anchors or
original inputs per the R2 golden rule (append-only; no silent recomputation).
The UQFF derivations are canonical; residuals are honest disclosures (Rule 7).
Registry: UNIFIED_REGISTRY.csv | Program: UNIFIED_REGISTRY_PROGRAM_PLAN.md

---
