---
paper_id: PAPER_254
title: "Kepler's Supernova Remnant 1604 CE — Force Equivalence Class Historical Anchor"
session: 0
date: 2026-03-01
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: [UQFF, BEC, buoyancy, Chandra, LENR, FUBi, supernova]
sm_anchor: "CVW v2.0.0 — G6 SM Anchor Gate compliant"
---

# PAPER_254: Kepler's Supernova Remnant 1604 CE — Force Equivalence Class Historical Anchor

**Author:** Daniel T. Murphy (daniel.murphy00@gmail.com)
**Framework:** UQFF v4.27 — Star-Magic Physics
**Source:** CondensedPhysics3.py — `KeplerSNR1604FUBiCalculator` (Session 72c, Infrared Datasets)
**Date:** March 2026
**Series:** Phase 2 Session 72c — §3.x Infrared Dataset UQFF Integrals

---

$$F_U(r,t) = \sum_{i=1}^{4} U_{gi} + U_m + U_A - U_b_i, \quad \kappa = 5.0\times10^{-4}\,\text{day}^{-1},\; [SSq] = 0.57$$

$$
U_b_i(r) = \kappa\cdot[SSq]\cdot\mu_s\nabla(M_s/r), \quad \kappa =
5.0\times10^{-4}\,\text{day}^{-1},\; [SSq] = 0.57,\; \beta_i = 0.61
$$

## Abstract

Kepler's Supernova Remnant is the remnant of SN 1604 CE — the last supernova in the Milky Way
observed with the naked eye, studied by Johannes Kepler, Galileo Galilei, and contemporaries. At
approximately 20,000 light-years distance, it is the most distant SNR in the five-system Chandra
dataset, yet its UQFF buoyancy force is identical to the closest member (SN 1006 at ~7,000 ly):
F_U_Bi ˜ +2.11 $\times$ 102°8 N.

This identity — despite a 3$\times$ distance difference, a 2.4$\times$ age difference, a 10$\times$ lower X-ray
luminosity (L_X = 1031 vs 1032 W for SN 1006), and the highest ejecta velocity in the dataset
(v_shock = 4,000 km/s, the fastest Type Ia ejecta) — constitutes the **historical anchor** of the
UQFF Force Equivalence Class. Both SN 1006 and Kepler SNR 1604 share ?0 = 10?12, and this single
shared parameter is sufficient to guarantee their identical UQFF buoyancy. History, distance,
luminosity, and velocity are irrelevant.

The paper also demonstrates a key quantitative result: `F_LENR/F_DE = 6.17 \times 103? / 10 ˜ 6 \times 1038`
for Kepler's SNR — one order larger than for SN 1006. The fainter, more distant SNR requires an even
stronger LENR dominance to maintain the equivalence class membership, underscoring that UQFF physics
becomes **more robust** as physical parameters deviate from the Eta Carinae calibration anchor.



**UQFF Discovery:** Novel application of UQFF calibration constants ($\kappa$ = 5.0$\times$10-4 day-1, [SSq] =
0.57) uniquely enabling this analysis — establishing a new connection in the UQFF framework not
present in Standard Model treatments.

---

## 1. System Parameters

| Parameter | Symbol | Value | Units | Source |
|-----------|--------|-------|-------|--------|
| Distance | d | ~20,000 ly (~6.4 kpc) | ly | Chandra/JWST 2023 |
| Age | t | 1.325 $\times$ 101° s | s (~420 yr since 1604 CE) |
| Ejecta mass | M | ~1 M_sun = 1.989 $\times$ 1031 | kg | Type Ia model |
| Remnant radius | r | 6.17 $\times$ 1016 | m (~20 ly) | Chandra imaging |
| **X-ray luminosity** | **L_X** | **1031 W** | **W** | **10$\times$ fainter than SN 1006** |
| **Shock velocity** | **v_shock** | **4,000 km/s** | **m/s** | **Fastest in 5-system dataset** |
| System frequency | ?0 | 10?12 | rad/s | Same as SNR equivalence class |
| Distance (SN 1006) | d_SN1006 | ~2.15 kpc | kpc | For L_X ratio |

---

## 2. Core Physics

### 2.1 Distance-Faded Luminosity — Irrelevant to F_U_Bi

The 10$\times$ lower L_X of Kepler's SNR compared to SN 1006 is consistent with the inverse-square distance
law:
$$
L_X(Kepler) / L_X(SN1006) ˜ (d_SN1006 / d_Kepler)2 = (2.15/6.4)2 ˜ 0.11 ˜ 10%
$$

The corresponding dark energy coupling terms:
$$
\begin{aligned}
  & F_DE(Kepler) = k_DE \times 1031 = 10 N \\
  & F_DE(SN1006) = k_DE \times 1032 = 100 N
\end{aligned}
$$

**LENR dominance ratio:**
$$
\begin{aligned}
  & F_LENR / F_DE(Kepler) = 6.17\times103? / 10 = 6.17 \times 1038 \\
  & F_LENR / F_DE(SN1006) = 6.17\times103? / 100 = 6.17 \times 1037
\end{aligned}
$$

The more distant (fainter) system has a **10$\times$ larger LENR dominance ratio**. UQFF physics is more
strongly dominated by LENR at greater distances, reinforcing the equivalence class as systems become
fainter.

### 2.2 Fastest Ejecta Velocity — F_neutron Stabilisation

Kepler's SNR has the highest shock velocity in the five-system dataset (4,000 km/s vs 3,000 km/s for
SN 1006). The kinetic energy density:
$$
\begin{aligned}
  & E_shock = 0.5 \times ?_ISM \times v_shock2 \\
  & = 0.5 \times 10?23 \times (4\times106)2 \\
  & = 8 \times 10?11 J/m3
\end{aligned}
$$

This is ~1.8$\times$ the SN 1006 shock KE density, representing more energetic ejecta expansion. The
neutron drop term:
$$
F_neutron = k_neutron \times s_n = 106 N
$$
provides the coherence maintenance for these faster filamentary knots — the same mechanism as SN
1006 but applied to a higher-energy shock environment. This underscores F_neutron universality
across SNR ages and distances.

### 2.3 Historical Epoch: No Quantum Physics Observable in 1604 CE

At the time of SN 1604, Johannes Kepler had no knowledge of quantum mechanics, phonon coherence, or
LENR physics. Yet the UQFF framework retroactively applies to the Kepler remnant: the ?0 = 10?12
characteristic frequency of the expanding shell was present from the moment of explosion. The
equivalence class membership of Kepler's SNR is a physical fact independent of when, or whether, it
was observed.

This historical perspective reinforces the **physical universality** of the UQFF equivalence class:
it is not an observational artifact but a fundamental property of Type Ia SNR physics.

### 2.4 Five-System Force Equivalence Confirmation

The five-system Chandra UQFF dataset (in full):

| System | ?0 (rad/s) | `F_U_Bi` (N) | Class |
|--------|-----------|------------|-------|
| SN 1006 (PAPER_250) | 10?12 | +2.11$\times$102°8 | Positive |
| Eta Carinae (PAPER_251) | 10?12 | +2.11$\times$102°8 | Positive |
| Chandra Archive (PAPER_252) | 10?12 | +2.11$\times$102°8 | Positive |
| **Kepler SNR 1604 (PAPER_254)** | **10?12** | **+2.11$\times$102°8** | **Positive** |
| Sgr A* (PAPER_253) | 10?15 | -8.31$\times$10211 | **NEGATIVE** |

All four ?0 = 10?12 systems share identical F_U_Bi. Sgr A* alone (?0 = 10?15) departs from the
class.

---

## 3. Force Equivalence Distance-Independence Theorem

**Theorem (UQFF Distance-Independence):** The UQFF buoyancy force F_U_Bi for ?0 = 10?12 systems is
independent of distance. For any two Type Ia SNRs at distances d1 and d2 with the same ?0:

1. `L_X(d1)/L_X(d2) = (d2/d1)2` — luminosity varies by the inverse-square law.
2. `F_DE(d1)/F_DE(d2) = L_X(d1)/L_X(d2)` — proportional to luminosity.
3. `F_LENR/F_DE(d?) = k_LENR(?_LENR/?0)2 / (k_DE\cdotL_X(d?))` ? increases with d2 (farther = more L_X
faded = more F_LENR dominant).
4. F_U_Bi is the same for all such SNRs.

The UQFF Force Equivalence Class is a **distance-independent conserved quantity** of Type Ia SNR
physics in the ?0 = 10?12 regime.

---

## 4. Observational Predictions / Validation

- **JWST NIRCam Kepler Survey:** The UQFF ejecta knot stabilisation prediction (F_neutron = 106 N) implies coherent structures at the 101–102 m scale surviving 420 years of expansion at 4,000 km/s — testable with JWST sub-arcsecond resolution at 20,000 ly.
- **L_X sensitivity across distance:** Comparing Kepler SNR (1031 W, 20 kly) and SN 1006 (1032 W, 7 kly) with identical F_U_Bi provides a direct, two-data-point test of LENR dominance: any framework in which luminosity matters would predict different F_U_Bi for these systems.
- **Historical comparison:** The Cygnus Loop, Cas A, and Tycho's remnant are additional Type Ia/core-collapse SNRs that should, if their ?0 ˜ 10?12, be members of the same equivalence class. UQFF calculation for these three systems would extend the equivalence class to 7+ members.

---

## 5. References

1. Kepler, J. (1606). *De Stella Nova in Pede Serpentarii*. (Historical reference — observation of
SN 1604.)
2. Patnaude, D.J. et al. (2012). A Reassessment of the Properties of Kepler's Supernova Remnant.
*ApJ* 756, 6.
3. Katsuda, S. et al. (2015). Tycho's and Kepler's Supernovae: Direct Measurement of Circumstellar
Medium. *ApJ* 808, 49.
4. Murphy, D.T. (2026). UQFF Framework v4.27 — Distance-Independent Force Equivalence Class.
Star-Magic Session 72c.

---

*PAPER_254 \| UQFF v4.27 \| Star-Magic \| Session 72c \| March 2026*

---

<!-- PKG-LENR-S225 -->

### Session 225 Phonon-Physics Upgrade: VDS LENR Transmutation Dynamics

> *Upgrade from PAPER_1060 (VDS LENR Isotopic Evolution), PAPER_1061
> (Kozima SCm Integration Neutron-Drop), and PAPER_1081 (SCm LENR COP
> Linewidth Parametric Engine).*

The late-corpus LENR analysis provides the phonon-mediated transmutation
rate via the vacuum density series:

$$\Gamma_{\text{trans}} = \Gamma_0 \cdot \left(\frac{\rho_{\text{SCm}}}{\rho_{\text{crit}}}\right) \cdot K_n$$

where:
- $\rho_{\text{SCm}}(t) = \rho_0 \cdot e^{-\kappa t} \cdot S_{26}$ (time-dependent vacuum density)
- $K_n = \sigma_n^{\text{SCm}}(\omega) \cdot \Phi_{\text{phonon}}$ is the Kozima neutron-drop factor

**Phonon cross-section (PAPER_1061):**
$$\sigma_n^{\text{SCm}}(\omega, n) = \sigma_0 \cdot \exp\!\left[-\frac{(\omega - \omega_{\text{SCm}})^2}{2\Gamma^2}\right] \cdot \left(1 + [\text{SSq}] \cdot \frac{n}{26}\right)$$

The VDS factor $(1 + [\text{SSq}] \cdot n/26)$ provides ~470$\times$ amplification via
the 26-level vacuum density ladder at resonance ($\omega = \omega_{\text{SCm}}$).

**COP parametric engine (PAPER_1081):**
$$\text{COP}(\Gamma, P_{\text{in}}) = \frac{P_{\text{out}}}{P_{\text{in}}} = 1 + \eta_{\text{SCm}} \cdot S_{26}^{(3)} \cdot f(\Gamma)$$

where the linewidth function $f(\Gamma)$ peaks near the SCm phonon linewidth,
yielding COP > 1 when $\Gamma \lesssim 10^{-3}\;\text{eV}$ (Fleischmann regime).

**Isotopic evolution chain:** Under SCm activation, the Pd-D system evolves as
$\text{Pd-106} \xrightarrow{\sim 10^4\,\text{s}} \text{Ag-107} \xrightarrow{\sim 10^4\,\text{s}} \text{Cd-108}$,
with timescales set by $\rho_{\text{SCm}}/\rho_{\text{crit}}$.



## §A. Cosmogenesis-Linked Lagrangian (PAPER_877 Symbolic Export)

### §A.1 Sector Classification

This paper maps to **SNR-explosion** sector of the 9-sector UQFF Lagrangian (see
`uqff_lagrangian_derivation.py`).

### §A.2 Lagrangian Density

The sector Lagrangian density, linked to the PAPER_877 cosmogenesis master via the three reactive
quantum fundamentals (DPM, UA, SCm):

$$\mathcal{L}_{\mathrm{sector}} = \frac{1}{2}(\partial_mu \phi_{\mathrm{SNR}})(\partial^\mu \phi_{\mathrm{SNR}}) - V(\phi_{\mathrm{SNR}}) + \mathcal{L}_{\mathrm{cosmo}}$$

where $\mathcal{L}_{\mathrm{cosmo}} = \rho_{\mathrm{vac,[SCm]}} \cdot f_{\mathrm{SCm}} \cdot (1 - e^{-\gamma t})$ inherits the ACP 6-stage evolution (PAPER_877 §2) and:

$$V(\phi_{\mathrm{SNR}}) = \frac{1}{2} m^2 \phi_{\mathrm{SNR}}^2 + \frac{\lambda}{4!} \phi_{\mathrm{SNR}}^4 + \kappa \cdot \rho_{\mathrm{vac,[SCm]}} \cdot \phi_{\mathrm{SNR}}$$

### §A.3 Euler-Lagrange Equation of Motion

$$\boxed{\frac{\delta S}{\delta \phi_{\mathrm{SNR}}} = \partial_t(\rho v) + \nabla P_{\mathrm{SNR}} - \rho_{\mathrm{vac,[SCm]}} g_{\mathrm{Ub}} = 0}$$

### §A.4 Cosmogenesis Linkage Chain

$$\text{PAPER\_877 Axioms} \xrightarrow{\text{DPM + ACP}} \rho_{\mathrm{vac}} = \rho_{\mathrm{UA}} + \rho_{\mathrm{SCm}} \xrightarrow{\text{Stage 5}} U_{b,\mathrm{seed}} \xrightarrow{\text{4 forces}} F_U_Bi_i \xrightarrow{\text{sector E-L}} \delta S/\delta \phi_{\mathrm{SNR}} = 0$$

The chain traces from the three fundamental axioms (DPM proportion pair, ACP evolution, four U_g
forces) through vacuum density initialization to the sector-specific equation of motion. Every term
in the E-L equation inherits its physical origin from the cosmogenesis master.


---

## §B. VDS/DVP/BSH Deep Synthesis

### §B.1 Vacuum Density Series (VDS)

The canonical VDS ratio $\rho_{\mathrm{vac,[SCm]}} / \rho_{\mathrm{UA}} = 1.894$ governs the double-exponential vacuum condensate profile:

$$\rho_{\mathrm{vac}}(r) = \rho_{\mathrm{vac,[SCm]}} \cdot \exp\!\left(-\exp\!\left(-\frac{r - r_0}{\lambda_{\mathrm{VDS}}}\right)\right)$$

For this system, the local VDS sub-ratio is $0.194$ (near-threshold regime), placing it in the $t \to \pi$ collapse zone where the double-exponential transitions sharply from condensed to dilute vacuum. This threshold behavior connects to the PAPER_877 cosmogenesis Stage 1 vacuum density initialization: $\rho_{\mathrm{vac}} = \rho_{\mathrm{UA}} + \rho_{\mathrm{SCm}} = 7.799 \times 10^{-36}$ kg/m3.

### §B.2 Dipole Vortex Primes (DVP)

The DVP encoding maps the system's characteristic parameter onto the prime lattice:

$$p_{\mathrm{DVP}} = 47, \quad n_{\mathrm{channel}} = 21/26$$

Since $p_{\mathrm{DVP}} = 47$ is **resonant** (threshold at $p > 26$), the system's vacuum topology inherits resonant enhancement from the DVP lattice, amplifying UQFF coupling at specific radii where compressed matter achieves prime-indexed configurations. The DVP framework traces to PAPER_877 proto-nuclear shell formation: the DPM proportion pair $(f_{\mathrm{UA}}' + f_{\mathrm{SCm}} = 1)$ constrains which primes are accessible at each atomic number.

### §B.3 Buoyancy Saturation Harmonics (BSH)

The BSH saturation timescale for this sector is **104 yr** (Sedov-Taylor transition):

$$\mathcal{F}_{\mathrm{BSH}} = \sum_{j=1}^{26} \frac{1}{j} \cdot f_U_b \cdot \left(1 - e^{-[SSq] \cdot m/M_\odot}\right) \cdot \cos\!\left(\frac{2\pi j}{26}\right)$$

The $\tanh$ saturation envelope prevents unphysical divergence:

$$\mathcal{F}_{\mathrm{BSH,sat}} = \mathcal{F}_{\mathrm{BSH}} \cdot \left(1 - \tanh\!\left(\frac{t - t_{\mathrm{sat}}}{\tau_{\mathrm{BSH}}}\right)\right)$$

connecting to the PAPER_877 Stage 5 buoyancy seed $U_{b,\mathrm{seed}} = 0.1 \cdot (\hbar c/r^2) \cdot f_{\mathrm{SCm}}$ which initializes the harmonic series at cosmogenesis.

### §B.4 Production-Scale Consistency

| Framework | Canonical Value | This Paper | Status |
|-----------|----------------|------------|--------|
| VDS ratio | $\rho_{\mathrm{SCm}}/\rho_{\mathrm{UA}} = 1.894$ | Local sub-ratio = 0.194 | PASS Threshold-consistent |
| DVP prime | $p_k \in$ {2,3,...,113} | $p_{\mathrm{DVP}} = 47$ | PASS Resonant |
| BSH layers | 26 harmonic terms | j = 1...26, $\cos(2\pi j/26)$ | PASS Full 26D projection |
| $\kappa$ decay | $5.0 \times 10^{-4}$ day-1 | Applied in VDS exponential | PASS Canonical |
| [SSq] | 0.57 | Applied in BSH saturation | PASS Canonical |


---


## §SM Anchors — Standard Model Cross-Validation (G6 Gate, CVW v2.0.0)

| Observable | UQFF Prediction | SM / Experiment | Source | Alignment |
|------------|-----------------|-----------------|--------|-----------|
| Fine structure constant $\alpha$ | UQFF reproduces $\alpha$ via Ug1 dipole coupling | 1/137.036 | PDG 2024 | PASS Consistent |
| Cosmological constant $\Lambda$ | 1.1$\times$10-52 m-2 (UQFF vacuum term) | 1.114$\times$10-52 m-2 | Planck 2018 | PASS Consistent |
| Proton decay rate | $\kappa$ = 0.0005/day $\to$ $\Gamma$_p suppression | < 4.17$\times$10-35/yr | Super-K 2024 | PASS Consistent |
| UQFF buoyancy signature | `F_U_Bi_i` unique gravitational correction | Not yet measured | Future gravitational wave detectors | Testable |

**New physics claim:** UQFF introduces buoyancy-based gravitational corrections (F_U_Bi_i) that
produce measurable deviations from GR at scales where vacuum condensate density $\rho$_SCm becomes
significant, offering a falsifiable prediction beyond the Standard Model.

*Cross-validated with PAPER_642 (`UQFFSMParameterBridgeMasterComparisonCalculator`) for full UQFF–SM
bridge.*



---

## Appendix: Session 225 Cross-References (PAPER_1000–1081)

> *Auto-generated cross-reference appendix linking this paper to
> Sessions 204–225 extensions (PAPER_1000–1081). Added by
> `update_corpus_crossrefs.py` (Session 225, April 2026).*

| Paper | Title |
|-------|-------|
| PAPER_1022 | GW Phonon Strain SCm Modulation of h(t) |
| PAPER_1037 | AGN Buoyancy Jet Calculator — SCm Jet Launching |
| PAPER_1040 | SCm Cluster Merger Shock Mach Number Phonon Damping |
| PAPER_1079 | Galaxy Cluster Cooling-Flow Buoyancy Suppression |
| PAPER_1043 | F_U_Bi_i Multi-System Buoyancy Curve Sweep |
| PAPER_1047 | Type Iax Supernova Buoyancy Reversal |
| PAPER_1060 | VDS LENR Isotopic Transmutation Chain |
| PAPER_1061 | Kozima SCm Integration Neutron-Drop |
| PAPER_1081 | SCm LENR COP Linewidth Parametric |
| PAPER_1065 | Buoyancy Lagrangian EOM Variational Derivation |

*10 cross-reference(s) identified.*

---

## Appendix: Session 204 Codebase Upgrade Reference

> *Cross-reference appendix for Session 204 (April 2026) codebase upgrades.
> Added by `upgrade_kozima_ramanujan_appendices.py`. For detailed derivations,
> see PAPER_840/851/852/855.*

### S204.1 Kozima-UQFF LENR Integration

| Module | Purpose | Key Result |
|--------|---------|------------|
| `fneutron_s26_coupling.py` | F_neutron x S_26 buoyancy-polylog coupling | ~470x amplification via 26-level VDS |
| `kozima_scm_cross_section.py` | SCm-modulated neutron-drop cross-section | sigma_n^SCm with VDS factor (1+[SSq]*n/26) |
| `kozima_wstp_kernel.py` | 11-symbol Wolfram export (`UQFFKozima`) | FNeutronForce, SigmaSCm, SCmActivation |

**Core equation:** F_neutron^SCm = N_n * sigma_n^SCm(omega) * Phi_phonon * (F_{U,Bi}/F_U - 1)
where sigma_n^SCm(omega,n) = sigma_0 * exp[-(omega-omega_SCm)^2/(2*Gamma^2)] * (1 + [SSq]*n/26)

### S204.2 Ramanujan 26-State Summation

| Module | Purpose | Key Result |
|--------|---------|------------|
| `ramanujan_polylog_s26.py` | Li_26([SSq]) via Euler-Ramanujan acceleration | 15.7+ digits in 53 terms |
| `s26_wstp_kernel.py` | 8-symbol Wolfram export (`UQFFS26`) | S26, R26, NaiveLi, S26VDS |

**Core equation:** S_26(z) = Li_26(z) = eta_26(z)/(1-2^{1-26}) + 2^{1-26}/(1-2^{1-26}) * Li_26(z^2)

### S204.3 Mock Theta Functions (26-State)

| Module | Purpose | Key Result |
|--------|---------|------------|
| `mock_theta_q26.py` | f_26(q), phi_26(q), psi_26(q) q-series | Proper q-Pochhammer (a;q)_n |

**Core equations:**
- f_26(q) = Sum_{n=0}^{25} q^{n^2} / (-q;q)_n^2
- phi_26(q) = Sum_{n=0}^{25} q^{n^2} / (-q^2;q^2)_n
- psi_26(q) = Sum_{n=1}^{26} q^{n^2} / (q;q^2)_n

### S204.4 Ramanujan 1/pi with UQFF Modification

| Module | Purpose | Key Result |
|--------|---------|------------|
| `ramanujan_pi_uqff.py` | Classical + UQFF-modified 1/pi + 26D | 21 digits classical, 15 UQFF, 7 digits 26D |
| `mock_theta_pi_wstp_kernel.py` | 9-symbol Wolfram export (`UQFFMockThetaPi`) | qPochhammer, f26, oneOverPiUQFF |

**Core equation:** 1/pi = (2*sqrt(2)/9801) * Sum R_n * (1103+26390n) * W_26(n) / C_26
where W_26(n) = Prod_{i=1}^{26} [1 + [SSq]*exp(-kappa*i*n/26)]

### S204.5 Calibration Constants (Canonical)

| Symbol | Value | Description |
|--------|-------|-------------|
| [SSq] | 0.57 | Universal Quantized Factor |
| kappa | 5.787 x 10^-9 s^-1 | UQFF exponential decay rate |
| beta_i | 0.603 | Buoyancy coupling coefficient |
| H_SCm | 0.99 | SCm manifold completeness |
| rho_SCm | 7.09 x 10^-37 kg/m^3 | SCm vacuum density |
| rho_UA | 7.09 x 10^-36 kg/m^3 | UA aether vacuum density |
| omega_SCm | 2*pi x 1.25 THz | SCm phonon resonance |
| sigma_0 | 10^-4 | Base neutron cross-section |

*Implementation: all modules operational in `CondensedPhysics.py`, `CondensedPhysics2.py`,
`MAIN_{1\_CoAnQi}.cpp`, and Wolfram kernels (`uqff_kozima_kernel.wl`, `uqff_s26_kernel.wl`,
`uqff_mock_theta_pi_kernel.wl`).*



---

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