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	import numpy as np
	import matplotlib.pyplot as plt

	z = np.linspace(0, 3, 500)
	a = 1/(1+z)

	plt.figure(figsize=(8,5))
	plt.plot(z, a, 'b-', label='Scale factor a(z)')
	plt.xlabel('Redshift z')
	plt.ylabel('Scale factor a')

	Log uploaded on Saturday, December 6, 2025, 2:32:29 PM
	Loaded mods:
	Harmony(brrainz.harmony)[mv:2.4.2.0]: 0Harmony(2.4.1), HarmonyMod(2.4.2)
	Core(Ludeon.RimWorld): (no assemblies)
	Royalty(Ludeon.RimWorld.Royalty): (no assemblies)
	Ideology(Ludeon.RimWorld.Ideology): (no assemblies)
	Biotech(Ludeon.RimWorld.Biotech): (no assemblies)
	Anomaly(Ludeon.RimWorld.Anomaly): (no assemblies)
	Odyssey(Ludeon.RimWorld.Odyssey): (no assemblies)
	Vehicle Framework(SmashPhil.VehicleFramework): SmashTools(av:1.6.0,fv:1.6.0), UpdateLogTool(av:1.6.0,fv:1.6.0), Vehicles(av:1.6.0,fv:1.6.0)

	\documentclass[11pt]{article}
	\usepackage{amsmath,amssymb}
	\usepackage{hyperref}
	\usepackage[a4paper,margin=1in]{geometry}

	\title{Photonic Universe Hypothesis (PUH v6):\\Identical Redshift of Photons and Gravitational Waves}
	\author{Brian Martell}
	\date{4 December 2025}

	\begin{document}

	Log uploaded on Saturday, December 6, 2025, 2:31:37 PM
	Loaded mods:
	Harmony(brrainz.harmony)[mv:2.4.2.0]: 0Harmony(2.4.1), HarmonyMod(2.4.2)
	Faster Game Loading(Taranchuk.FasterGameLoading): FasterGameLoading(1.0.0)
	Loading Progress(ilyvion.LoadingProgress): ilyvion.LoadingProgress(0.9.5)
	Core(Ludeon.RimWorld): (no assemblies)
	Royalty(Ludeon.RimWorld.Royalty): (no assemblies)
	Biotech(Ludeon.RimWorld.Biotech): (no assemblies)
	HugsLib(UnlimitedHugs.HugsLib)[ov:12.0.0]: 0Harmony(av:2.4.1,fv:1.2.0.1), HugsLib(av:1.0.0,fv:12.0.0)
	Vanilla Expanded Framework(OskarPotocki.VanillaFactionsExpanded.Core): 0ModSettingsFramework(1.0.0), 0PrepatcherAPI(1.2.0), KCSG(av:1.1.2,fv:25.11.14), MVCF(2.0.0.1), Outposts(av:3.0.0,fv:1.0.0), PipeSystem(av:1.0.1,fv:22.7.29), VEF(av:1.1.7,fv:1.1.9)

	#EXTM3U url-tvg="https://iptv-epg.org/files/epg-cz.xml"

	#EXTINF:-1 tvg-id="Jednotka.cz" tvg-name="JEDNOTKA" tvg-logo="https://grgopitic.github.io/piconstv/all/jednotka.png", JEDNOTKA
	http://212.102.38.45/live/test_jednotka_25p/playlist.m3u8
	#EXTINF:-1 tvg-id="Dvojka.cz" tvg-name="DVOJKA" tvg-logo="https://grgopitic.github.io/piconstv/all/stv2.png", DVOJKA
	http://212.102.38.45/live/test_dvojka_25p/playlist.m3u8
	#EXTINF:-1 tvg-id="Markíza.cz" tvg-name="Markíza" tvg-logo="https://i.postimg.cc/Cxpd03D6/markiza.png", Markiza
	http://212.102.38.45/live/test_markiza_25p/playlist.m3u8
	#EXTINF:-1 tvg-id="Markíza KRIMI.cz" tvg-name="Markíza KRIMI" tvg-logo="https://i.postimg.cc/SsPNv3kd/markizakrimi.png", Markiza KRIMI
	http://212.102.38.45/live/test_markiza_krimi_hevc/playlist.m3u8

	// SPDX-License-Identifier: MIT
	// OpenZeppelin Contracts (last updated v5.0.0) (access/Ownable.sol)

	pragma solidity ^0.8.20;

	import {Context} from "../utils/Context.sol";

	/**
	* @dev Contract module which provides a basic access control mechanism, where
	* there is an account (an owner) that can be granted exclusive access to

	def part2(data: Seq[String]): Long = {
	val grid: Grid[Char] = data.dropRight(1).toArray.map(_.toCharArray).transpose

	var grandTotal: Long = 0
	var curTotal: Long = 0
	var op: Op = null
	data.last.zipWithIndex.foreach { case (ch, idx) =>
	if (ch == '+') {
	curTotal = grid(idx).mkString.trim.toLong
	op = (a, b) => a + b

	# This code snippet is dedicated to the Public Domain, or licensed under CC0 if you prefer.

	printf -v _start '%.0f' $(( EPOCHREALTIME * 1000 ))
	::
	::: COMMANDS TO MEASURE HERE :::
	::
	printf -v _end '%.0f' $(( EPOCHREALTIME * 1000 ))

	_elapsed=$(( _end - _start ))