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"twentyfoursevensports" => true "twitch" => true "twitter" => true "ustream" => true "vbox7" => true "veoh" => true "vevo" => true "videodetective" => true "vimeo" => true "vine" => true "vk" => true "vocaroo" => true "vox" => true "washingtonpost" => true "wavekit" => true "wistia" => true "wshh" => true "wsj" => true "xboxclips" => true "xboxdvr" => true "xenforo" => true "youku" => true "youmaker" => true "youtube" => true ] #consentedGroups: [] } "enableRtnProtect" => true "serviceWorkerPath" => null "language" => Language {#311 #id: "1" #options: array:18 [ "title" => "English (US)" "language_code" => "en-US" "date_format" => "M j, Y" "time_format" => "g:i A" "currency_format" => "{symbol}{value}" "decimal_point" => "." 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"widget.app_download_canvas" => "App download" "widget.become_a_member" => "Upgrade Your Account" "widget.canvas_menu" => "Canvas Menu" "widget.canvas_menu_social" => "Canvas menu social" "widget.donation" => "Help Cover Community Costs!" "widget.forum_overview_forum_statistics" => "" "widget.forum_overview_members_online" => "" "widget.forum_overview_new_posts" => "" "widget.forum_overview_new_profile_posts" => "" "widget.forum_overview_share_page" => "" "widget.latest_followed_profile_posts" => "Latest profile posts by followers" "widget.latest_posts" => "Latest posts" "widget.latest_profile_posts" => "Latest profile posts" "widget.latest_watched" => "Latest watched" "widget.leaderboards" => "Leaderboard: Posts" "widget.member_wrapper_find_member" => "" "widget.member_wrapper_newest_members" => "" "widget.nf_calendar_list_featured_events" => "" "widget.online_list_online_statistics" => "" "widget.sh_forumStats" => "Forum Statistics" "widget.sh_homeTrending" => "Trending Threads" "widget.sh_mediaSlider" => "Latest Media" "widget.sh_subscribe" => "Subscribe" "widget.thdonate_earnings" => "" "widget.thdonate_goals" => "" "widget.thdonate_topDonations" => "" "widget.thdonate_topDonors" => "" "widget.thuix_footer_aboutUsWidget" => "About us" "widget.uix_footer_forumStatistics" => "" "widget.uix_footer_newPosts" => "" "widget.uix_footer_onlineStatistics" => "" "widget.uix_footer_sharePage" => "" "widget.uix_sidebar_postNewThread" => "Can't find a topic?" "widget.unread_posts" => "Unread posts" "widget.whats_new_new_posts" => "" "widget.whats_new_new_profile_posts" => "" "widget.xfes_thread_view_below_quick_reply_similar_threads" => "" "widget.xfrm_forum_overview_new_resources" => "" "widget.xfrm_list_featured_resources" => "" "widget.xfrm_list_top_resources" => "" "widget.xfrm_overview_latest_reviews" => "" "widget.xfrm_overview_top_authors" => "" "widget.xfrm_whats_new_overview_new_resources" => "" "reactions.1_person" => "1 person" "reactions.deleted_user" => "(deleted member)" "reactions.threactplus_one_user" => "1 user" "reactions.threactplus_x_users" => "{count} users" "reactions.threactplus_you_and_x_others" => "You and {count} others" "reactions.user1" => "{user1}" "reactions.user1_and_user2" => "{user1} and {user2}" "reactions.user1_user2_and_user3" => "{user1}, {user2} and {user3}" "reactions.user1_user2_user3_and_1_other" => "{user1}, {user2}, {user3} and 1 other person" "reactions.user1_user2_user3_and_x_others" => "{user1}, {user2}, {user3} and {others} others" "reactions.x_people" => "{reactions} people" "reactions.you" => "You" "reactions.you_and_user1" => "You and {user1}" "reactions.you_user1_and_user2" => "You, {user1} and {user2}" "reactions.you_user1_user2_and_1_other" => "You, {user1}, {user2} and 1 other person" "reactions.you_user1_user2_and_x_others" => "You, {user1}, {user2} and {others} others" "reaction_title.1" => "Like" "reaction_title.2" => "Love" "reaction_title.3" => "Haha" "reaction_title.4" => "Wow" "reaction_title.5" => "Sad" "reaction_title.6" => "Angry" "trophy_title.1" => "First Real Post" "trophy_title.10" => "Old School Sniper's Hide" "trophy_title.11" => "Posts (Silent)" "trophy_title.12" => "Logging In (Silent)" "trophy_title.13" => "Post Media Items (Silent)" "trophy_title.136" => "Test Achievement 4" "trophy_title.14" => "Spotted" "trophy_title.15" => "Rifle Cleaner" "trophy_title.16" => "Completed Profile" "trophy_title.17" => "Gunsmith" "trophy_title.19" => "Community Contributor" "trophy_title.2" => "Just getting into Precision Rifle." "trophy_title.20" => "Marksman!" "trophy_title.22" => "Made America Great Again" "trophy_title.23" => "Professor" "trophy_title.25" => "Leaderboard Legend" "trophy_title.26" => "Commercial Sales Member" "trophy_title.27" => "Supporter" "trophy_title.3" => "Look Everyone I can Sell Now !" "trophy_title.4" => "Hide Addict !" "trophy_title.5" => "Members are Noticing" "trophy_title.6" => "Hide Rockstar, Lady Gaga Approved!" "trophy_title.7" => "They like me, they really like me!" "trophy_title.8" => "I want to have Lowlight's Love Child" "trophy_title.9" => "I LOVE IT LONG TIME" "a_moment_ago" => "A moment ago" "actions" => "Actions" "approve" => "Approve" "continue_reading" => "Continue reading..." "conversations" => "Conversations" "date_x_at_time_y" => "{date} at {time}" "day_friday" => "Friday" "day_friday_short" => "Fri" "day_monday" => "Monday" "day_monday_short" => "Mon" "day_saturday" => "Saturday" "day_saturday_short" => "Sat" "day_sunday" => "Sunday" "day_sunday_short" => "Sun" "day_thursday" => "Thursday" "day_thursday_short" => "Thu" "day_tuesday" => "Tuesday" "day_tuesday_short" => "Tue" "day_wednesday" => "Wednesday" "day_wednesday_short" => "Wed" "day_x_at_time_y" => "{day} at {time}" "delete" => "Delete" "edit_avatar" => "Edit avatar" "follow" => "Follow" "forums" => "Forums" "from_x_location" => "From {location}" "guest" => "Guest" "help" => "Help" "in_a_minute" => "In a minute" "in_a_moment" => "In a moment" "in_x_minutes" => "In {minutes} minutes" "later_today_at_x" => "Later today at {time}" "master_language" => "Master language" "master_style" => "Master style" "members" => "Members" "month_1" => "January" "month_10" => "October" "month_10_short" => "Oct" "month_11" => "November" "month_11_short" => "Nov" "month_12" => "December" "month_12_short" => "Dec" "month_1_short" => "Jan" "month_2" => "February" "month_2_short" => "Feb" "month_3" => "March" "month_3_short" => "Mar" "month_4" => "April" "month_4_short" => "Apr" "month_5" => "May" "month_5_short" => "May" "month_6" => "June" "month_6_short" => "Jun" "month_7" => "July" "month_7_short" => "Jul" "month_8" => "August" "month_8_short" => "Aug" "month_9" => "September" "month_9_short" => "Sep" "new_posts" => "New posts" "new_profile_posts" => "New profile posts" "no_items_to_display" => "No items to display" "none" => "None" "one_minute_ago" => "1 minute ago" "realms_realm_quiz_user" => "Realm Quiz User" "s9e_MediaSites_Footer_Credit" => "Media embeds via s9e/MediaSites" "show_hidden_content_by_x" => "Show hidden content by {names}" "show_ignored_content" => "Show ignored content" "showing_all_items" => "Showing all items" "showing_x_of_y_items" => "Showing {count} of {total} items" "spoiler" => "Spoiler" "staff_member" => "Staff member" "th_progress_bar_color_will_change_donate" => "Once this milestone has been reached the progress bar will change to this color. If left blank it will display the default color from your color palette." "there_are_x_items_in_total" => "There are {total} items in total" "time_am_lower" => "am" "time_am_upper" => "AM" "time_pm_lower" => "pm" "time_pm_upper" => "PM" "title_page_x" => " | Page {page}" "today_at_x" => "Today at {time}" "tomorrow_at_x" => "Tomorrow at {time}" "unfollow" => "Unfollow" "ungrouped" => "Ungrouped" "upload_file" => "Upload file" "viewing_an_error" => "Viewing an error" "x_b" => "{number}B" "x_bytes" => "{size} bytes" "x_gb" => "{size} GB" "x_k" => "{number}K" "x_kb" => "{size} KB" "x_m" => "{number}M" "x_mb" => "{size} MB" "x_minutes_ago" => "{minutes} minutes ago" "x_tb" => "{size} TB" "xfmg_browse_albums" => "Browse albums" "xfmg_x_seconds" => "{count} second(s)" "xfrm_resource_icon" => "Resource icon" "yesterday_at_x" => "Yesterday at {time}" "your_account" => "Your account" "th_reactplus_show_hidden_low_quality_content" => "Show hidden low quality content" "thcovers_no_edit_permissions" => "You are not allowed to edit this cover." ] #phrasesToLoad: array:1 [ 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1586271288 => array:1 [ …1] 1586301543 => array:1 [ …1] 1586351104 => array:1 [ …1] 1586356882 => array:1 [ …1] 1717893457 => array:1 [ …1] 1719841650 => array:1 [ …1] 1726082187 => array:1 [ …1] 1726084660 => array:1 [ …1] 1731899295 => array:1 [ …1] 1732552619 => array:1 [ …1] 1727469645 => array:1 [ …1] 1727814018 => array:1 [ …1] 1730756848 => array:1 [ …1] ] } "style" => Style {#321 #id: "27" #lastModified: 1731439652 #properties: array:696 [ "adavAchievementCriteria" => array:3 [ …3] "adavAchievementCriterionProgressBar" => array:5 [ …5] "adavAchievementCriterionProgressBarInner" => array:3 [ …3] "adavAchievementCriterionProgressBarStatus" => array:1 [ …1] "adavAchievementExperience" => array:3 [ …3] "adavAchievementTitle" => array:2 [ …2] "adst_shepherdElement" => array:3 [ …3] "animationSpeed" => "0.2s" "audapp_primaryColor" => "#677e9a" "audapp_secondaryColor" => "#677e9a" "avatarBg" => "rgb(27,27,27)" "avatarBorderRadius" => "8px" "badge" => array:4 [ …4] "bbCodeBlock" => array:6 [ …6] "bbCodeBlockTitle" => array:3 [ …3] "bbCodeInlineCode" => array:9 [ …9] "blockBorder" => array:5 [ …5] "blockBorderRadius" => "8px" "blockFilterBar" => array:3 [ …3] "blockFooter" => array:5 [ …5] "blockFooterBg" => "rgb(45,45,45)" "blockFooterTextColor" => "rgba(255, 255, 255, 0.6)" "blockHeader" => array:6 [ …6] "blockLink" => array:4 [ …4] "blockLinkSelected" => array:5 [ …5] "blockMinorHeader" => array:6 [ …6] "blockMinorTabHeader" => array:5 [ …5] "blockMinorTabHeaderSelected" => array:2 [ …2] "blockPaddingH" => "16px" "blockPaddingV" => "16px" "blockTabHeader" => array:6 [ …6] "blockTabHeaderBg" => "transparent" "blockTabHeaderSelected" => array:2 [ …2] "blockTabHeaderTextColor" => "rgba(255, 255, 255, 0.6)" "blockTextHeader" => array:3 [ …3] "borderColor" => "rgba(255,255,255,.14)" "borderColorAccentContent" => "#677e9a" "borderColorAttention" => "#677e9a" "borderColorFaint" => "rgba(255,255,255,.14)" "borderColorFeature" => "#677e9a" "borderColorHeavy" => "rgba(255,255,255,.14)" "borderColorHighlight" => "#677e9a" "borderColorLight" => "rgba(255,255,255,.14)" "borderRadiusLarge" => "12px" "borderRadiusMedium" => "8px" "borderRadiusSmall" => "8px" "borderSize" => "0px" "borderSizeFeature" => "2px" "buttonBase" => array:8 [ …8] "buttonBg" => "fade(rgba(255, 255, 255, 0.8), 14%)" "buttonCta" => array:3 [ …3] "buttonCtaBg" => "#677e9a" "buttonDefault" => array:3 [ …3] "buttonDisabled" => array:4 [ …4] "buttonPrimary" => array:3 [ …3] "buttonPrimaryBg" => "#677e9a" "buttonTextColor" => "rgba(255, 255, 255, 0.8)" "chip" => array:5 [ …5] "chipHover" => array:1 [ …1] "chromeBg" => "mix(#677e9a, rgb(27,27,27), 10%)" "chromeTextColor" => "rgb(36,36,36)" "contentAccentBase" => array:2 [ …2] "contentAccentBg" => "mix(#677e9a, rgb(27,27,27), 10%)" "contentAccentLink" => array:1 [ …1] "contentAltBase" => array:2 [ …2] "contentAltBg" => "rgb(36,36,36)" "contentBase" => array:2 [ …2] "contentBg" => "rgb(27,27,27)" "contentHighlightBase" => array:2 [ …2] "contentHighlightBg" => "rgb(45,45,45)" "dataListFooter" => array:5 [ …5] "dataListHeader" => array:7 [ …7] "dataListPaddingH" => "16px" "dataListPaddingV" => "16px" "dataListSection" => array:5 [ …5] "editorBg" => "rgb(45,45,45)" "editorButtonActiveColor" => "rgba(255, 255, 255, 0.8)" "editorButtonColor" => "fade(mix(rgba(255, 255, 255, 0.8), rgb(255, 255, 255)), 85%)" "editorButtonDisabledColor" => "mix(rgb(27,27,27), rgba(255, 255, 255, 0.6), 60%)" "editorButtonHoverBg" => "fade(rgba(255, 255, 255, 0.8), 15%)" "editorButtonHoverColor" => "rgba(255, 255, 255, 0.8)" "editorButtonSelectedBg" => "fade(rgba(255, 255, 255, 0.8), 15%)" "editorButtonSize" => "18px" "editorColor" => "rgba(255, 255, 255, 0.8)" "editorFocusBg" => "xf-intensify(rgb(45,45,45), 1%)" "editorFocusColor" => "rgba(255, 255, 255, 0.8)" "editorImageHandles" => "#677e9a" "editorSelectionBg" => "rgb(36,36,36)" "editorSelectionColor" => "rgba(255, 255, 255, 0.8)" "editorToolsFocusBg" => "linear-gradient(180deg, rgb(45,45,45), xf-intensify(rgb(45,45,45), 1%))" "editorToolsOverflowBg" => "xf-intensify(rgb(45,45,45), 3%)" "elementSpacer" => "16px" "emailBg" => "rgb(18,18,18)" "emailBorderColor" => "rgba(255,255,255,.14)" "emailContentAltBg" => "rgb(36,36,36)" "emailContentBg" => "rgb(27,27,27)" "emailFont" => "ui-sans-serif,system-ui,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji" "emailHeaderColor" => "rgba(255, 255, 255, 0.8)" "emailLinkColor" => "#677e9a" "emailTextColor" => "rgba(255, 255, 255, 0.8)" "emailTextColorMuted" => "rgba(255, 255, 255, 0.6)" "fixedMessage" => array:7 [ …7] "flashMessage" => array:5 [ …5] "fontFamilyBody" => "ui-sans-serif,system-ui,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji" "fontFamilyUi" => "ui-sans-serif,system-ui,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji" "fontSizeLarge" => "1.6rem" "fontSizeLarger" => "2.0rem" "fontSizeLargest" => "2.4rem" "fontSizeNormal" => "1.6rem" "fontSizeSmall" => "1.4rem" "fontSizeSmaller" => "1.4rem" "fontSizeSmallest" => "1.1rem" "formExplain" => array:2 [ …2] "formHint" => array:2 [ …2] "formLabel" => array:3 [ …3] "formRowPaddingHInner" => "16px" "formRowPaddingHOuter" => "16px" "formRowPaddingV" => "16px" "formSectionHeader" => array:6 [ …6] "formSubmitRow" => array:3 [ …3] "globalActionColor" => "#677e9a" "inlineModBar" => array:6 [ …6] "inlineModHighlightColor" => "mix(#677e9a, rgb(27,27,27), 10%)" "input" => array:10 [ …10] "inputBgColor" => "rgb(45,45,45)" "inputDisabled" => array:2 [ …2] "inputFocus" => array:3 [ …3] "inputFocusBgColor" => "xf-intensify(rgb(45,45,45), 1%)" "inputTextColor" => "rgba(255, 255, 255, 0.8)" "link" => array:2 [ …2] "linkColor" => "#677e9a" "linkHover" => array:2 [ …2] "linkHoverColor" => "xf-intensify(#677e9a, 17%)" "majorHeadingBg" => "transparent" "majorHeadingTextColor" => "rgb(255, 255, 255)" "memberHeader" => array:3 [ …3] "memberHeaderBlurbContainerBanner" => array:4 [ …4] "memberHeaderName" => array:2 [ …2] "memberTooltipBlurbContainerBanner" => array:5 [ …5] "memberTooltipHeader" => array:4 [ …4] "memberTooltipName" => array:1 [ …1] "menu" => array:6 [ …6] "menuBorderRadius" => "8px" "menuFeatureBorderColor" => "rgba(255,255,255,.14)" "menuFooter" => array:6 [ …6] "menuHeader" => array:5 [ …5] "menuLinkRow" => array:2 [ …2] "menuLinkRowSelected" => array:3 [ …3] "menuTabHeader" => array:5 [ …5] "menuTabHeaderSelected" => array:2 [ …2] "messageNewIndicator" => array:8 [ …8] "messagePadding" => "16px" "messagePaddingSmall" => "16px" "messageSignature" => array:7 [ …7] "messageUserBlock" => array:3 [ …3] "messageUserElements" => array:9 [ …9] "metaThemeColor" => "#677e9a" "minorBlockContent" => array:3 [ …3] "minorHeadingTextColor" => "rgba(255, 255, 255, 0.8)" "nodeIconReadColor" => "#fff" "nodeIconUnreadColor" => "#fff" "nodeListDescriptionDisplay" => "inline" "overlayHeader" => array:8 [ …8] "overlayMaskColor" => "rgba(0, 0, 0, .3)" "paddingLarge" => "16px" "paddingLargest" => "24px" "paddingMedium" => "16px" "paddingSmall" => "8px" "pageBackground" => array:1 [ …1] "pageBg" => "rgb(18,18,18)" "pageEdgeSpacer" => "30px" "paletteAccent1" => "#677e9a" "paletteAccent2" => "#677e9a" "paletteAccent3" => "#677e9a" "paletteColor1" => "rgb(27,27,27)" "paletteColor2" => "rgb(36,36,36)" "paletteColor3" => "rgb(45,45,45)" "paletteColor4" => "rgb(18,18,18)" "paletteColor5" => "mix(#677e9a, rgb(27,27,27), 10%)" "paletteNeutral1" => "rgb(255, 255, 255)" "paletteNeutral2" => "rgba(255, 255, 255, 0.6)" "paletteNeutral3" => "rgba(255, 255, 255, 0.8)" "profilePostCommentToggle" => 1 "progressBarColor" => "#677e9a" "publicFaviconUrl" => "styles/snipershide/snipershide/sh-favicon.svg" "publicFooter" => array:2 [ …2] "publicFooterLink" => array:1 [ …1] "publicHeader" => array:3 [ …3] "publicHeaderAdjustColor" => "" "publicIconUrl" => "data/assets/logo/192.png" "publicIconUrlLarge" => "data/assets/logo/512.png" "publicLogoHeight" => "60" "publicLogoUrl" => "styles/snipershide/snipershide/logo-top.svg" "publicLogoWidth" => "417" "publicMetadataLogoUrl" => "https://snipershide.com/shooting/styles/snipershide/snipershide/SHMetaplatev2.png" "publicNav" => array:3 [ …3] "publicNavCollapseWidth" => "1000px" "publicNavPaddingH" => "12px" "publicNavSelected" => array:2 [ …2] "publicNavTab" => array:5 [ …5] "publicNavTabHover" => array:2 [ …2] "publicNavTabMenuOpen" => array:1 [ …1] "publicStaffBar" => array:5 [ …5] "publicSubNav" => array:5 [ …5] "publicSubNavElHover" => array:1 [ …1] "publicSubNavElMenuOpen" => array:1 [ …1] "publicSubNavPaddingV" => "2px" "responsiveEdgeSpacerRemoval" => "1000px" "responsiveWide" => "1000px" "scrollJumpButtons" => "both" "sidebarSpacer" => "16px" "sidebarWidth" => "300px" "standaloneTab" => array:4 [ …4] "standaloneTabSelected" => array:2 [ …2] "starEmptyColor" => "rgba(255,255,255,.14)" "starFullColor" => "#677e9a" "styleType" => "dark" "subNavBg" => "rgb(45,45,45)" "subNavTextColor" => "rgba(255, 255, 255, 0.6)" "textColor" => "rgba(255, 255, 255, 0.8)" "textColorAccentContent" => "#677e9a" "textColorAttention" => "#677e9a" "textColorDimmed" => "rgba(255, 255, 255, 0.6)" "textColorEmphasized" => "#677e9a" "textColorFeature" => "rgba(255, 255, 255, 0.8)" "textColorMuted" => "rgba(255, 255, 255, 0.6)" "th_nodeBody" => array:1 [ …1] "th_reactplus_countStyling" => array:8 [ …8] "thdonate_progressBar" => array:1 [ …1] "thdonate_progressBarContainer" => array:3 [ …3] "thfeature_slider" => array:1 [ …1] "thuix_webapp_backgroundColor" => "#677e9a" "thxpress_dotsNavigation" => 1 "thxpress_postExcerptTitle" => array:4 [ …4] "tl_backgroundColor" => "rgb(45,45,45)" "tl_backgroundLightColor" => "rgb(27,27,27)" "tl_fontColor" => "rgba(255, 255, 255, 0.8)" "tl_fontDarkColor" => "rgba(255, 255, 255, 0.8)" "tl_fontExtraLightColor" => "rgba(255, 255, 255, 0.6)" "tl_fontLightColor" => "rgba(255, 255, 255, 0.6)" "tl_lineColor" => "rgba(255,255,255,.14)" "tl_lineLightColor" => "rgba(255,255,255,.14)" "tl_overlayColor" => "rgb(45,45,45)" "tl_primaryColor" => "#677e9a" "tl_secondaryColor" => "#677e9a" "tooltip" => array:8 [ …8] "uix_abridgedSignatures" => 1 "uix_activeNavTitle" => 0 "uix_activeNavTitleStyle" => array:7 [ …7] "uix_additionalCss" => "ac_app.less,realms.less" "uix_alertsUnread" => 0 "uix_avatarShape" => "1" "uix_backstretch" => 0 "uix_backstretchDuration" => "4000" "uix_backstretchFade" => "500" "uix_backstretchImages" => ""styles/acui/images/bg/1.jpg", "styles/acui/images/bg/2.jpg", "styles/acui/images/bg/3.jpg"" "uix_backstretchSelector" => "body" "uix_betaMode" => 0 "uix_blockBody" => [] "uix_blockContainer" => array:3 [ …3] "uix_blockMessage" => array:3 [ …3] "uix_blockOuter" => array:1 [ …1] "uix_blockTabHeaderTab" => [] "uix_borderRadiusJs" => 0 "uix_borderRadiusSelectors" => ".p-footer-inner, .uix_extendedFooter, .p-nav, .p-sectionLinks, .p-staffBar, .p-header, #wpadminbar" "uix_bottomBreadcrumbLocation" => "belowMainContainer" "uix_brandmarkImage__breakpoint" => "0" "uix_breadcrumbItem" => array:1 [ …1] "uix_breadcrumbItem__active" => array:1 [ …1] "uix_breadcrumbStyle" => array:1 [ …1] "uix_breadcrumbWrapper" => [] "uix_breadcrumbWrapperBottom" => array:1 [ …1] "uix_buttonActive" => array:2 [ …2] "uix_buttonCtaActive" => [] "uix_buttonCtaHover" => array:1 [ …1] "uix_buttonHover" => array:2 [ …2] "uix_buttonLink" => array:4 [ …4] "uix_buttonPrimaryActive" => [] "uix_buttonPrimaryHover" => array:1 [ …1] "uix_buttonRipple" => 1 "uix_buttonSmall" => array:5 [ …5] "uix_canvas" => array:2 [ …2] "uix_canvasHeader" => [] "uix_canvasNavItem" => array:2 [ …2] "uix_canvasNavItemActive" => array:2 [ …2] "uix_canvasNavItemHover" => array:1 [ …1] "uix_canvasNavSubItem" => array:2 [ …2] "uix_categoryCollapse" => 1 "uix_categoryDescription" => array:5 [ …5] "uix_categoryDescriptionDisplay" => "tooltip" "uix_categoryIconStyle" => array:3 [ …3] "uix_categoryStrip" => array:5 [ …5] "uix_categoryStripIcons" => 0 "uix_categoryStripOutsideWrapper" => 0 "uix_clickableThreads" => 0 "uix_collapseExtraInfo" => 1 "uix_collapseStaffbarLinks" => 1 "uix_collapseibleSubForums" => 0 "uix_collapsibleSidebar" => 1 "uix_collapsibleStickyThreads" => 1 "uix_condenseVisitorTabs" => 0 "uix_contentWrapper" => "0" "uix_contentWrapperStyle" => array:3 [ …3] "uix_copyrightOrder" => "30" "uix_defaultNavIcon" => 1 "uix_defaultSidebarIcon" => 1 "uix_detachedNavigation" => 1 "uix_discussionList" => array:1 [ …1] "uix_discussionListAnimation" => 0 "uix_discussionListCollapseWidth" => "1000px" "uix_discussionListItem" => [] "uix_discussionListItemDeleted" => [] "uix_discussionListItemEven" => "" "uix_discussionListItemHover" => "" "uix_discussionListItemModerated" => [] "uix_discussionListItemSticky" => [] "uix_discussionListTitle" => array:3 [ …3] "uix_discussionListTitleUnread" => array:1 [ …1] "uix_dropdownHover" => 0 "uix_elevation1" => "0 10px 20px rgba(0,0,0,0.09), 0 6px 6px rgba(0,0,0,0.15)" "uix_elevation2" => "0 3px 10px 2px rgba(0,0,0,.1), 0 1px 18px 0px rgba(0, 0, 0, 0.12), 0 3px 5px 0 rgba(0, 0, 0, 0.2)" "uix_enableExtendedFooter" => 0 "uix_enableMainTabs" => 0 "uix_enableWelcomeHeaderImage" => 0 "uix_extendedFooterOrder" => "10" "uix_extendedFooterStyle" => array:6 [ …6] "uix_extendedFooter__whiteText" => 0 "uix_externalLinkIcon" => 1 "uix_fab" => "mobile" "uix_fabBarBackground" => "rgb(27,27,27)" "uix_fabScroll" => 0 "uix_fabVw" => "1000px" "uix_footerChooser" => array:2 [ …2] "uix_footerChooserHover" => array:1 [ …1] "uix_footerCopyrightRow" => array:4 [ …4] "uix_footerIcons" => 0 "uix_footerInsideContent" => 0 "uix_footerLinkHover" => array:2 [ …2] "uix_footerMenu" => array:1 [ …1] "uix_footerMenuOrder" => "20" "uix_footerWidget" => array:4 [ …4] "uix_footerWidgetBody" => [] "uix_footerWidgetFooter" => array:4 [ …4] "uix_footerWidgetHeader" => array:5 [ …5] "uix_footerWidgetPadding" => "16px" "uix_footerWidgetRow" => array:2 [ …2] "uix_footerWidgetWidth" => "280px" "uix_forceCoverCopyright" => 0 "uix_forceCoverExtendedFooter" => 0 "uix_forceCoverFooterMenu" => 0 "uix_glyphCategoryIcon" => "" "uix_glyphForumIcon" => "" "uix_glyphLinkIcon" => "" "uix_glyphPageIcon" => "" "uix_googleFonts" => "" "uix_headerWhiteSpace" => "0px" "uix_headerWrapper" => array:1 [ …1] "uix_headingFont" => "ui-sans-serif,system-ui,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji" "uix_headingFontWeight" => "400" "uix_headingFontWeightHeavy" => "700" "uix_hideElementsDuringJSLoad" => 1 "uix_hideExtendedFooterMobile" => 0 "uix_hideNodeLastPost" => 0 "uix_hideNodeStats" => 0 "uix_hideSingleCrumb" => 1 "uix_hideStyleChoose" => 0 "uix_hideTopPagenavMobile" => 1 "uix_homeCrumbIcon" => 1 "uix_iconFont" => array:1 [ …1] "uix_iconFontFamily" => "material" "uix_iconSize" => "18px" "uix_iconSizeLarge" => "24px" "uix_imageForumIcon" => array:2 [ …2] "uix_imageForumUnreadIcon" => array:2 [ …2] "uix_imageIcon" => array:1 [ …1] "uix_imageLinkIcon" => array:2 [ …2] "uix_imagePageIcon" => array:2 [ …2] "uix_imagePath" => "styles/acui" "uix_jsPath" => "acui" "uix_lazyLoadSupport" => 0 "uix_loginStyle" => "link" "uix_loginTriggerPosition" => "navigation" "uix_logoIcon" => "mdi mdi-tune" "uix_logoIconStyle" => array:2 [ …2] "uix_logoSmall" => "" "uix_logoText" => "UI.X" "uix_logoTextBreakpoint" => "650px" "uix_logoText__style" => array:4 [ …4] "uix_logoWidth" => "222.4px" "uix_mainTabsBarStyling" => array:1 [ …1] "uix_mainTabsHeight" => "50px" "uix_mainTabsSticky" => 0 "uix_materialAvatars" => 1 "uix_message" => array:2 [ …2] "uix_messageActionBar" => [] "uix_messageAnimation" => 0 "uix_messageAttachments" => array:3 [ …3] "uix_messageBody" => array:3 [ …3] "uix_messageControl" => array:7 [ …7] "uix_messageControlHover" => array:3 [ …3] "uix_messageLikes" => array:5 [ …5] "uix_messageMain" => array:1 [ …1] "uix_messageMeta" => array:4 [ …4] "uix_messageNotice" => array:2 [ …2] "uix_metaCell" => [] "uix_mobileTabsNav" => 1 "uix_navAboveHeader" => 0 "uix_navLogoVertSpacing" => "11px" "uix_navTabIconStyle" => array:2 [ …2] "uix_navTabIcons" => 0 "uix_navigationBarHeight" => "72px" "uix_navigationType" => "default" "uix_newNodeMarker" => 1 "uix_newNodeMarkerStyle" => array:8 [ …8] "uix_nodeAnimations" => 0 "uix_nodeBlockBody" => array:2 [ …2] "uix_nodeBody" => array:2 [ …2] "uix_nodeBodyEven" => "" "uix_nodeBodyHover" => array:2 [ …2] "uix_nodeClickable" => 1 "uix_nodeContainer" => array:4 [ …4] "uix_nodeDescription" => array:3 [ …3] "uix_nodeIconImages" => 0 "uix_nodeIconStyle" => array:4 [ …4] "uix_nodeIconWidth" => "51px" "uix_nodePadding" => "16px" "uix_nodeStatsHover" => 0 "uix_nodeStatsIcons" => 1 "uix_nodeTitle" => array:4 [ …4] "uix_nodeTitle__unread" => [] "uix_noticeLocation" => "aboveMainContainer" "uix_onlineIndicator" => "default" "uix_originalPoster" => "icon" "uix_pageAnimation" => 0 "uix_pageStyle" => "covered" "uix_pageTitle" => array:3 [ …3] "uix_pageWidthToggle" => "fixed" "uix_pageWrapper" => array:4 [ …4] "uix_parallax" => 0 "uix_parallaxImage" => "styles/acui/images/welcome-banner.png" "uix_parallaxPosition" => "center" "uix_parallaxSelector" => ".uix_welcomeSection" "uix_postBitAvatarSize" => "small" "uix_postBitIcons" => 1 "uix_prefixAccent" => "#677e9a" "uix_prefixBlue" => "#2196F3" "uix_prefixGray" => "#616161" "uix_prefixGreen" => "#4CAF50" "uix_prefixLightGreen" => "#8BC34A" "uix_prefixOlive" => "#689F38" "uix_prefixOrange" => "#FF9800" "uix_prefixPrimary" => "#677e9a" "uix_prefixRed" => "#D32F2F" "uix_prefixRedSkyBlue" => "#03A9F4" "uix_prefixRoyalBlue" => "#0D47A1" "uix_prefixSilver" => "#CFD8DC" "uix_prefixYellow" => "#FFEB3B" "uix_primaryColor" => "#677e9a" "uix_primaryColorDarker" => "#677e9a" "uix_removeBottomBreadcrumb" => 0 "uix_removeHeaderWrapper" => 1 "uix_removeIndexPageTitle" => 0 "uix_removeMessageArrow" => 1 "uix_removePageAction" => 0 "uix_removeRegisterText" => 0 "uix_removeVisitorTabsText" => 1 "uix_removeWhatsNewButtons" => 1 "uix_responsiveLogoFontSize" => "" "uix_rightAlignNavigation" => 0 "uix_scrollableSidebar" => 0 "uix_searchBar" => array:5 [ …5] "uix_searchBarFocus" => array:1 [ …1] "uix_searchBarHeight" => "36px" "uix_searchBarPlaceholderColor" => "rgba(255, 255, 255, 0.6)" "uix_searchBarPlaceholderFocusColor" => "rgba(255, 255, 255, 0.8)" "uix_searchBarWidth" => "250px" "uix_searchButton" => 0 "uix_searchIcon" => array:6 [ …6] "uix_searchIconBehavior" => "expandMobile" "uix_searchIconFocusColor" => "rgba(255, 255, 255, 0.6)" "uix_searchPosition" => "header" "uix_search_maxResponsiveWidth" => "10000px" "uix_secondaryColor" => "#677e9a" "uix_sectionBg" => "#677e9a" "uix_sectionLinksStickyStyle" => array:1 [ …1] "uix_separateThreads" => 1 "uix_shareWidgetModal" => 1 "uix_sideNavCollapsed" => 0 "uix_sideNavigationAnimation" => 0 "uix_sidebarBlockRow" => [] "uix_sidebarBreakpoint" => "1000px" "uix_sidebarIcons" => 0 "uix_sidebarLocation" => "right" "uix_sidebarMobileCanvas" => 1 "uix_sidebarNavWidth" => "210px" "uix_sidebarNavigationStyle" => array:1 [ …1] "uix_sidebarTriggerPhrase" => 0 "uix_sidebarTriggerPosition" => "sectionLinks" "uix_sidebarWidgetAnimations" => 0 "uix_sidebarWidgetFooter" => [] "uix_sidebarWidgetHeading" => array:3 [ …3] "uix_sidebarWidgetWrapper" => array:1 [ …1] "uix_signatureHoverEnabled" => 0 "uix_signatureMaxHeight" => "100" "uix_similarScrollNotice" => 1 "uix_socialMediaIcon" => array:1 [ …1] "uix_socialMediaPosition" => "copyright" "uix_staffBarBreakpoint" => "1000px" "uix_staffBarTab" => array:4 [ …4] "uix_staffBarTabHover" => array:2 [ …2] "uix_stickyCategoryStrips" => 0 "uix_stickyNavHeight" => "72px" "uix_stickyNavigationStyle" => array:2 [ …2] "uix_stickySectionLinkHeight" => "40px" "uix_stickySidebar" => "disabled" "uix_stickySidebarCalcDelay" => "100" "uix_stickySidenav" => 1 "uix_stickyStaffBar" => 1 "uix_stickyStaffBarHeight" => "40px" "uix_stickyStaffbarStyle" => [] "uix_structPaddingH" => "16px" "uix_structPaddingV" => "16px" "uix_subForumTitle" => array:1 [ …1] "uix_swipeSupport" => 0 "uix_tabBarLocation" => "header" "uix_tablinksInSideNav" => 1 "uix_tag" => [] "uix_tagHover" => [] "uix_textSelection" => array:2 [ …2] "uix_threadField" => array:3 [ …3] "uix_threadListSeparator" => array:4 [ …4] "uix_titlebar" => array:5 [ …5] "uix_titlebarLocation" => "mainContainerTop" "uix_topBreadcrumbLocation" => "aboveMainContainer" "uix_transition" => "cubic-bezier(0.4, 0, 0.2, 1)" "uix_userTabsPosition" => "navigation" "uix_version" => "2.2.15.0.2" "uix_viewportCenterLogo" => "0px" "uix_viewportCollapseStaffLinks" => "1000px" "uix_viewportCollapseStats" => "1000px" "uix_viewportCondenseVisitorTabs" => "10000px" "uix_viewportRemoveRegisterText" => "650px" "uix_viewportRemoveVisitorTabsText" => "100000px" "uix_viewportShowLogoBlock" => "100%" "uix_viewportWidthRemoveSubNav" => "1px" "uix_visitorPanelIcons" => 0 "uix_visitorTabsMobile" => "initial" "uix_voteActionButton" => "mobile" "uix_welcomeSectionForumListOnly" => 1 "uix_welcomeSectionIcon__style" => array:3 [ …3] "uix_welcomeSectionInner" => array:2 [ …2] "uix_welcomeSectionLocation" => "sidebar" "uix_welcomeSectionOverlay" => "" "uix_welcomeSectionText__style" => array:4 [ …4] "uix_welcomeSectionTitle__style" => array:2 [ …2] "uix_welcomeSectionVisible" => "guests" "uix_welcomeSection__buttonText" => "Register" "uix_welcomeSection__icon" => "" "uix_welcomeSection__style" => array:3 [ …3] "uix_welcomeSection__text" => "Get access to live stream, lessons, the post exchange, and chat with other snipers." "uix_welcomeSection__title" => "Join the Hide community" "uix_welcomeSection__url" => "register" "uix_widgetPadding" => "16px" "xpress_articleListLayout" => "list" "xpress_authorBlock" => array:10 [ …10] "xpress_dropcap" => 0 "xpress_featuredArticleStyle" => "carousel" "xpress_featuredExcerptLength" => "150" "xpress_featuredItemsCount" => "3" "xpress_removeFeaturedExcerpt" => 1 "adavAchievement" => [] "adavAchievementCriterionTitle" => [] "adavAchievementCriterionTitleCompleted" => array:1 [ …1] "adavAchievementTitleCommon" => [] "adavAchievementTitleEpic" => array:1 [ …1] "adavAchievementTitleLegendary" => array:1 [ …1] "adavAchievementTitleRare" => array:1 [ …1] "adavAchievementTitleUncommon" => array:1 [ …1] "adavAchievementTitleUnique" => array:1 [ …1] "adav_memberLevelBadeLocation" => "stats" "audfeeds_chromeless_tabs" => 0 "audfeeds_tabbar_location" => "aboveMainContent" "audfeeds_tabsWrapper" => [] "avatarDefaultImage" => "" "avatarDefaultTextContent" => "?" "avatarDefaultType" => "text" "avatarDynamicFont" => "'Arial', sans-serif" "avatarDynamicLineHeight" => "1.04" "avatarDynamicTextPercent" => "60" "badgeHighlighted" => array:2 [ …2] "bbCodeBlockExpandHeight" => "150px" "bbCodeImgFloatMargin" => "0.25em" "bbCodeImgFloatMarginAfter" => "1.35em" "bbCodeImgLarge" => "512px" "bbCodeImgMedium" => "128px" "bbCodeImgSmall" => "64px" "borderSizeMinorFeature" => "2px" "editorToolsBg" => "transparent" "emailPublicLogoUrl" => "" "errorBg" => "rgb(253, 233, 233)" "errorColor" => "rgb(200, 68, 72)" "errorFeatureColor" => "rgb(200, 68, 72)" "findThreadsNavStyle" => "tabs" "fontAwesomeWeight" => "400" "fontFamilyCode" => "Monaco, Menlo, Consolas, 'Roboto Mono', 'Andale Mono', 'Ubuntu Mono', monospace" "fontWeightHeavy" => "700" "fontWeightLight" => "300" "fontWeightNormal" => "400" "formLabelWidth" => "33%" "formResponsive" => "540px" "formSubmitSticky" => 1 "lineHeightDefault" => "1.4" "memberHeaderNameBanner" => array:1 [ …1] "memberTooltipNameBanner" => array:1 [ …1] "messageSingleColumnWidth" => "650px" "messageUserBlockWidth" => "120px" "nfCalendarDateIcons" => 0 "nodeListSubDisplay" => "menu" "noticeScrollInterval" => "6" "overlayMaskBlur" => "0px" "overlayTopMargin" => "4vh" "pageNavStyle" => "mixed" "pageWidthMax" => "1200px" "publicIconsMaskable" => 0 "publicLogoUrl2x" => "" "publicNavPaddingV" => "8px" "publicNavSticky" => "primary" "publicPushBadgeUrl" => "styles/default/xenforo/bell.png" "publicPwaInstallVideoUrl" => "styles/default/xenforo/add_to_home.mp4" "publicSubNavPaddingH" => "8px" "reactionSummaryOnLists" => "" "responsiveMedium" => "650px" "responsiveNarrow" => "480px" "successBg" => "rgb(218, 243, 216)" "successColor" => "rgb(61, 121, 63)" "successFeatureColor" => "rgb(99, 178, 101)" "th_backgroundSelector_nodes" => ".node--id{node_id} > .node-body" "th_enableGrid_nodes" => 0 "th_enableGrid_nodes_advanced" => 0 "th_enableNodeFooter_nodes" => 1 "th_enableStyling_nodes" => 0 "th_imageOverlay" => "rgba(0,0,0,.4)" "th_nodeGutter" => "10px" "th_reactplus_condensedSummary" => 0 "th_reactplus_countMin" => "1" "th_reactplus_showCounter" => 0 "th_textSelector_nodes" => ".node--id{node_id} > .node-body, .node--id{node_id} > .node-body a" "th_uix_staffMessageBlock" => [] "th_uix_staffMessageNewIndicator" => [] "th_uix_staffMessageSignature" => [] "th_uix_staffMessageUserBlock" => [] "th_uix_threadStarterMessageBlock" => [] "th_uix_threadStarterMessageNewIndicator" => [] "th_uix_threadStarterMessageSignature" => [] "th_uix_threadStarterMessageUserBlock" => [] "thdonate_separateCompletedCampaigns" => 0 "thfeature_defaultFeatureBackground" => "" "thfeature_display_style" => "default" "thfeature_firstPost_article" => 1 "thfeature_firstPost_author" => 1 "thfeature_firstPost_style" => array:2 [ …2] "thfeature_icon_size" => "l" "thfeature_icon_style" => "default" "thfeature_pageTitle" => 0 "thmonetize_userUpgradeCurrency" => array:1 [ …1] "thmonetize_userUpgradeLength" => array:1 [ …1] "thmonetize_userUpgradeOccurrence" => array:1 [ …1] "thmonetize_userUpgradePrice" => array:1 [ …1] "thmonetize_userUpgradeShapeBorderWidth" => "12px" "thmonetize_userUpgradeShapeWidth" => "220px" "thnodes_enable_header_styling_categoryView" => 0 "thnodes_enable_header_styling_forumView" => 0 "thnodes_enable_header_styling_threadView" => 0 "thnodes_enable_icons" => 0 "thnodes_show_header_icon" => 0 "thuix_webapp_icon192x192" => "" "thuix_webapp_icon512x512" => "" "thxpress_articleFeaturedImageCover" => 1 "thxpress_carouselItems" => "1" "thxpress_excerpt" => 1 "thxpress_excerptLimit" => "55" "thxpress_hideSignature" => 0 "thxpress_postThumbnails" => 1 "thxpress_showFunctionalTags" => 0 "voteNegativeColor" => "rgb(200, 68, 72)" "votePositiveColor" => "rgb(99, 178, 101)" "warningBg" => "rgb(251, 247, 226)" "warningColor" => "rgb(132, 101, 61)" "warningFeatureColor" => "rgb(220, 218, 84)" "whatsNewNavStyle" => "tabs" "xfmgCategoryList" => "container" "xpress_articleThumbnailSize" => "thumbnail" "xpress_categoryScroller" => 1 "xpress_removeFeaturedMeta" => 0 "xpress_vwColumnBreakpoint" => "650px" "zIndexMultiplier" => "100" ] #options: array:14 [ "style_id" => 27 "parent_id" => 26 "parent_list" => array:6 [ …6] "title" => "Realms: Sniper's Hide (Dark)" "description" => "" "assets" => [] "effective_assets" => [] "user_selectable" => true "designer_mode" => null "th_product_id_uix" => 0 "th_product_version_uix" => null "th_primary_child_uix" => false "th_child_style_xml_uix" => "" "th_child_style_cache_uix" => [] ] } "isRtl" => false "options" => ArrayObject {#229 -storage: array:573 [ "acpSearchExclude" => [] "activitySummaryEmail" => array:4 [ …4] "activitySummaryEmailBatchLimit" => "100" "ad_lb_alertTop" => "15" "ad_lb_awardTop" => "10" "ad_lb_cache" => "5" "ad_lb_defaultSort" => "weekly" "ad_lb_enable_pagination" => "1" "ad_lb_incrementNumber" => "5" "ad_lb_rankChanges" => "1" "ad_lb_types" => array:5 [ …5] "ad_lb_userEntry" => "1" "ad_lb_userEntry_rank" => "1" "adav_level_formula" => "logarithmic" "adav_level_formula_data" => array:4 [ …4] "adca_dismissDuration" => "0" "adca_dismissible" => "1" "adca_notifyCutoff" => "7" "adca_notifyUserAfter" => "7" "addBanUserGroup" => "23" "adminRequireTfa" => "0" "adsDisallowedTemplates" => """ error\n login\n login_password_confirm\n login_two_step\n message_page\n register_complete\n register_connected_account\n register_confirm\n register_form """ "akismetKey" => "8be4acf584c1" "alertExpiryDays" => "3" "alertsPerPage" => "25" "alertsPopupExpiryDays" => "7" "allowGuestRte" => "1" "allowVideoUploads" => array:2 [ …2] "allowedCodeLanguages" => """ apacheconf\n applescript\n aspnet\n bash\n c\n clike\n coffeescript\n cpp\n csharp\n css\n diff\n git\n html\n http\n ini\n java\n javascript\n json\n jsx\n less\n makefile\n markdown\n nginx\n objectivec\n perl\n php\n python\n ruby\n sass\n scss\n sql\n svg\n swift\n wiki\n xml\n yaml """ "approveSharedBannedRejectedIp" => array:2 [ …2] "attachmentExtensions" => """ zip\n txt\n pdf\n png\n jpg\n jpeg\n jpe\n gif """ "attachmentMaxDimensions" => array:2 [ …2] "attachmentMaxFileSize" => "25000" "attachmentMaxPerMessage" => "25" "attachmentThumbnailDimensions" => "150" "audapi_oauthEncryptionKey" => "hacxn11Rc7qZVYsNav1FwiFV3dkluCMUZw81Czgdjg0=" "audapi_oauthPrivateKey" => """ -----BEGIN PRIVATE KEY-----\n MIIEvwIBADANBgkqhkiG9w0BAQEFAASCBKkwggSlAgEAAoIBAQDq+QDCK3Xe/IMi\n 0SgreLG/PSnt6AK5L1DNvjpWmic4EjMMcAej7SB9J5gxUUQAoPClERbAwrplb7Zl\n Fq2udfIR6HXVkGKYq6uiLKeNKgKT4cFSjoQ73JnfPHJQwQG7aHvLyz8Bz6u2u9fJ\n YlBRu2oFhDEmie0kgAbXYD9by3jYTv/hSp7gTDT8TdHnMc4GKqcfk5qhnJn++uKy\n QzNSLsZsq86bANUfu8y6HEMV8qwjGpzZ8X3TlbmcCxuvNN3EDiU4GGPdsuyQbMXv\n II2FSE4OfSwAPp6uBJuTDhSD6pUyV6Byk7x6iKis25KndHBcRqVSY7G1Uw3VzRFg\n 4RiwczvvAgMBAAECggEBAJm9UkG5LeY4UZT2RNIsph/6ZPTEWQPRcY0saf8/3WlS\n fxQkONuIyzkYLvwVr+i5ZLqb88crocm8zhpWPE1p3njZIEAbuGcr66CwlvBGDGm1\n zEe3980zCXqGkkVEA14bfuRYl2EX/8IQJaAeM29GsJfrZj1RAVhgbBl/X/UvrGHa\n DZ8ppq4duRn9VBg3oHLeS42jZbgAwoW2RS9ffHpby4Ju9PDTo8IeArJamndofB7E\n QaaTPVkNp4RULEFvQb4p58DHK7JBbNvLVMcp+bmdTRXKYjAoXUdjqg+USdabKZsj\n /HZ6DFHICWa5/RubC9mBvm67CK1xADKeVrrf1th/bAECgYEA9dZFk67dnCwrm4Yn\n N53q2aMSAv7zM+gS1LBBKFNpolSfDvGiW1AQ83gXa7x9ULjQkE7bzg+lrA5YjwU+\n cp+09vKzy8HPC14oVJfuPUD/sh9X57cFDAIr5VWvAtTjwX6XOx3TMnwN9FCg2fk6\n aI54/+jH4l9po2QzFDK9MfOrfDUCgYEA9K/AnWQ5QJmNTfCjFcV8kHjJgCoS42BP\n iTKyTniDASSxGUNMxt0Hqu1m9jDwduHhi4X+KibVTaMexdkta6KPNgpFYSCWgwcj\n SwVv0xxoqiYGv1n5TTpcPM+4tVgSSdNiQsj2x3CaQXRH4W9rd3FBqI/bSb6kXgEV\n uu2fl7DNdBMCgYEAh9quvotfKmP6gUrkt0aMt1L3rDIqQmAYr/LrPxbBhJTRBZgh\n Cec4RuPxxXb3pblMgMMjkz9wZaHT7M2QEhYSEnpTQ+HJwlV5Yi5H2Q/nfg72LDYn\n EtjMW0M7oQv3BUIo3uF/iiGmMIKyMWMalRdO5NVGSOJDZakE1T+o8EbhWJUCgYEA\n lOMUqzC+/aXxq4lPUwIWJ7q3sbroP17tRqiIguMlo951vM+MujzoW4OVcRyaVVxg\n 54si+vciN9mX8f+SeboytklNqiowK45+VTn7r1PMBCybUngnEG0Ajyg+Vmo+xplP\n Yx/xua20zzs4Od6YX9eUgkL2xkqwrVqvpEzPHXhBq+0CgYBHTUVg6HTCS7/70ckk\n Za3OGmtn7OSlUIr5+RlMuYKZJ9qPEevkasyZ7lVKd8wzXOcYWRVCS39WbFQSp5r/\n g+uewXlkn5alw2g3zbctmqqkGuIOn3HwC/uNsJ4sWWYhDvSXt4no8S1uAisBANIK\n mTCpQEzuFWBAp/LmHDEZJ9Np8g==\n -----END PRIVATE KEY-----\n """ "audapi_oauthPublicKey" => """ -----BEGIN PUBLIC KEY-----\n MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEA6vkAwit13vyDItEoK3ix\n vz0p7egCuS9Qzb46VponOBIzDHAHo+0gfSeYMVFEAKDwpREWwMK6ZW+2ZRatrnXy\n Eeh11ZBimKuroiynjSoCk+HBUo6EO9yZ3zxyUMEBu2h7y8s/Ac+rtrvXyWJQUbtq\n BYQxJontJIAG12A/W8t42E7/4Uqe4Ew0/E3R5zHOBiqnH5OaoZyZ/vriskMzUi7G\n bKvOmwDVH7vMuhxDFfKsIxqc2fF905W5nAsbrzTdxA4lOBhj3bLskGzF7yCNhUhO\n Dn0sAD6ergSbkw4Ug+qVMlegcpO8eoiorNuSp3RwXEalUmOxtVMN1c0RYOEYsHM7\n 7wIDAQAB\n -----END PUBLIC KEY-----\n """ "audapp_appConfig" => array:4 [ …4] "audapp_appConfigFailures" => "0" "audapp_appConfigKey" => "d3ZYUjJEUEFxdERyOWlWbQ==" "audapp_appId" => "com.snipershide.app" "audapp_appleBid" => "com.snipershide.app.ios" "audapp_appleEnvironment" => "default" "audapp_appleSharedSecret" => "f0673ec43fea4ce69a9cab6b362d3738" "audapp_darkStyleId" => "22" "audapp_enableAppInstallBanner" => "1" "audapp_enableExtraNodeData" => "1" "audapp_enableInlineAds" => "1" "audapp_enableInterstitialAds" => "1" "audapp_enablePushLog" => "0" "audapp_featureToggles" => array:11 [ …11] "audapp_googleClientEmail" => "[email protected]" "audapp_googlePackageName" => "com.snipershide.app.android" "audapp_googlePrivateKey" => "-----BEGIN PRIVATE KEY-----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\nSrUfD9J1NACHWIyn0VfLwuXB\n-----END PRIVATE KEY-----\n" "audapp_googleProjectId" => "pc-api-8550534343379152468-165" "audapp_iOSAppStoreId" => "" "audapp_isSetup" => "1" "audapp_killApp" => "0" "audapp_killPushNotifications" => "0" "audapp_lightStyleId" => "21" "audapp_logPushApiErrors" => "0" "audapp_newPostDisplayMode" => "thread" "audapp_pageDisplayTypes" => array:5 [ …5] "audav_earn_alerts" => "first" "audav_level_alerts" => "1" "audav_showEarnOnModal" => "0" "audentioapi_oauthAccessTokenTTL" => "2592000" "audentioapi_oauthRefreshTokenTTL" => "5184000" "audentiocommunity_lastReportEval" => "0" "audentiocommunity_reportScore" => "0" "audentioleaderboards_pageSize" => "25" "audfeeds_ajaxTabs" => "1" "audfeeds_ajaxUpdate" => "1" "audfeeds_ajaxUpdateRate" => "5" "audfeeds_availablePrefixFilters" => [] "audfeeds_availableTTFilters" => [] "audfeeds_cachePageCount" => "1" "audfeeds_cacheTime" => "5" "audfeeds_cacheTimeLong" => "24" "audfeeds_createButton" => array:7 [ …7] "audfeeds_curatedLimit" => "100" "audfeeds_curatedMaxDays" => "30" "audfeeds_decay" => "exp" "audfeeds_dropdownSelect" => "1" "audfeeds_enableCustomOrder" => "0" "audfeeds_enableNodeFilter" => "1" "audfeeds_enablePage" => "1" "audfeeds_entriesPerPage" => "25" "audfeeds_excludeNodeIds" => [] "audfeeds_filterAutoSave" => "0" "audfeeds_filterWidgetPosition" => "sidenav" "audfeeds_hideGuestMedia" => "1" "audfeeds_holdPromotionX" => "60" "audfeeds_maxPages" => "1000" "audfeeds_newsFeedReactions" => "0" "audfeeds_promoteEverySocialX" => "60" "audfeeds_promoteEveryX" => "60" "audfeeds_redirectWhatsNew" => "0" "audfeeds_unlimitedScroll" => "1" "audfeeds_unreadIndicators" => "1" "audfeeds_weightComment" => "1000" "audfeeds_weightPost" => "1000" "audfeeds_weightRating" => "1000" "audfeeds_weightReaction" => "100" "audfeeds_weightReactionSocial" => "100" "audfeeds_weightView" => "1" "audlive_logApiErrors" => "0" "autoEmbedMedia" => array:2 [ …2] "boardActive" => "1" "boardDescription" => "Sniper's Hide Forum" "boardInactiveMessage" => "Sniper's Hide is currently undergoing an upgrade. Check back in a few hours!" "boardShortTitle" => "" "boardTitle" => "Sniper's Hide Forum" "boardUrl" => "https://www.snipershide.com/shooting" "boardUrlCanonical" => "0" "bounceEmailAddress" => "" "captcha" => "ReCaptcha" "categoryOwnPage" => "0" "censorCharacter" => "*" "censorWords" => [] "changeLogLength" => "60" "collectServerStats" => array:4 [ …4] "contactEmailAddress" => "[email protected]" "contactEmailSenderHeader" => "0" "contactUrl" => array:3 [ …3] "conversationPopupExpiryHours" => "72" "convertMarkdownToBbCode" => "0" "cookieConsent" => array:1 [ …1] "cookieConsentLogLength" => "90" "currentVersionId" => "2021672" "defaultEmailAddress" => "[email protected]" "defaultEmailStyleId" => "15" "defaultLanguageId" => "1" "defaultStyleId" => "27" "disallowedCustomTitles" => """ admin\n moderator """ "discourageBlankChance" => "10" "discourageDelay" => array:2 [ …2] "discourageFloodMultiplier" => "10" "discourageRedirectChance" => "15" "discourageRedirectUrl" => "" "discourageSearchChance" => "40" "discussionPreview" => "1" "discussionRssContentLength" => "500" "discussionsPerPage" => "20" "displayVisitorCount" => "title_and_icon" "dynamicAvatarEnable" => "1" "editHistory" => array:2 [ …2] "editLogDisplay" => array:2 [ …2] "editorDropdownConfig" => array:1 [ …1] "editorToolbarConfig" => array:4 [ …4] "emailBounceHandler" => array:7 [ …7] "emailConversationIncludeMessage" => "1" "emailDkim" => array:5 [ …5] "emailFileCheckWarning" => array:2 [ …2] "emailSenderName" => "" "emailShare" => "1" "emailSoftBounceThreshold" => array:3 [ …3] "emailTransport" => array:7 [ …7] "emailUnsubscribeHandler" => array:7 [ …7] "emailWatchedThreadIncludeMessage" => "1" "emojiSource" => array:2 [ …2] "emojiStyle" => "emojione" "enableMemberList" => "0" "enableNewsFeed" => "1" "enableNotices" => "1" "enablePush" => "1" "enableSearch" => "1" "enableTagging" => "1" "enableTrophies" => "0" "enableVerp" => "1" "extraCaptchaKeys" => array:2 [ …2] "facebookLike" => "1" "floodCheckLength" => "30" "floodCheckLengthDiscussion" => "180" "forumsDefaultPage" => "forums" "geoLocationUrl" => "https://maps.google.com/maps?q={location}" "giphy" => array:3 [ …3] "googleAnalyticsAnonymize" => "1" "googleAnalyticsWebPropertyId" => "UA-91918309-1" "gravatarEnable" => "0" "guestShowSignatures" => "0" "guestTimeZone" => "America/New_York" "homePageUrl" => "https://thehide.tv/" "imageCacheRefresh" => "0" "imageCacheTTL" => "7" "imageLibrary" => "gd" "imageLinkProxy" => array:2 [ …2] "imageLinkProxyKey" => "" "imageLinkProxyLogLength" => "90" "imageLinkProxyReferrer" => array:2 [ …2] "imageProxyBypass" => array:2 [ …2] "imageProxyMaxSize" => "51200" "import_vb_table" => "xf_import_vbulletin5_log" "includeCaptchaPrivacyPolicy" => "1" "includeTitleInUrls" => "1" "indexRoute" => "forums/" "ipInfoUrl" => "http://whatismyipaddress.com/ip/{ip}" "ipLogCleanUp" => array:2 [ …2] "jQuerySource" => "local" "jobRunTrigger" => "server" "jsLastUpdate" => "1725390632" "lastPageLinks" => "3" "lightBoxUniversal" => "0" "linkShare" => "1" "loginLimit" => "block" "logoLink" => "0" "lostPasswordCaptcha" => "1" "lostPasswordTimeLimit" => "180" "maxContentSpamMessages" => "2" "maxContentTags" => "10" "maxContentTagsPerUser" => "10" "maximumSearchResults" => "200" "membersPerPage" => "20" "messageMaxImages" => "25" "messageMaxLength" => "1000000" "messageMaxMedia" => "20" "messagesPerPage" => "50" "moderatorLogLength" => "0" "multiQuote" => "1" "newsFeedMaxItems" => "15" "newsFeedMessageSnippetLength" => "140" "nfCalendarAgendaViews" => "1" "nfCalendarBoundaryFilterDistance" => array:2 [ …2] "nfCalendarDefaultListView" => "listMonth" "nfCalendarDefaultView" => "agendaWeek" "nfCalendarEventCalLimit" => "5" "nfCalendarEventFromLimit" => "5" "nfCalendarEventUnreadCounter" => "0" "nfCalendarEventsPerPage" => "20" "nfCalendarGoogleApi" => "" "nfCalendarIncludeBirthdays" => array:2 [ …2] "nfCalendarIncludeWeekends" => "1" "nfCalendarIndexBirthdays" => "1" "nfCalendarIndexFutureBirthdays" => "1" "nfCalendarLayoutType" => "calendar" "nfCalendarLocationComplete" => "1" "nfCalendarMaxMessageLength" => "10000" "nfCalendarMinMessageLength" => "0" "nfCalendarNLP" => "0" "nfCalendarPrefillDateTime" => "1" "nfCalendarSelectable" => "0" "nfCalendarWeekStart" => "1" "oEmbedCacheRefresh" => "0" "oEmbedCacheTTL" => "7" "oEmbedLogLength" => "90" "oEmbedRequestReferrer" => array:2 [ …2] "onlineStatusTimeout" => "15" "pinterestShare" => "0" "pollMaximumResponses" => "10" "preRegAction" => array:3 [ …3] "preventDiscouragedRegistration" => "1" "privacyPolicyForceWhitelist" => "" "privacyPolicyLastUpdate" => "0" "privacyPolicyUrl" => array:2 [ …2] "profilePostMaxLength" => "500" "pushKeysVAPID" => array:2 [ …2] "readMarkingDataLifetime" => "30" "realms_createAchievements" => "1" "realms_logApiErrors" => "0" "realms_overrideLoginRegister" => "1" "realms_primaryRealmId" => "1" "realms_syncAchievements" => "0" "realms_syncQuizzes" => "0" "redditShare" => "0" "registrationCheckDnsBl" => array:3 [ …3] "registrationDefaults" => array:16 [ …16] "registrationSetup" => array:7 [ …7] "registrationTimer" => "15" "registrationWelcome" => array:13 [ …13] "reportIntoForumId" => "0" "romanizeUrls" => "0" "rootBreadcrumb" => "forums" "s9e_MediaSites_AMAZON_ASSOCIATE_TAG" => "" "s9e_MediaSites_AMAZON_ASSOCIATE_TAG_CA" => "" "s9e_MediaSites_AMAZON_ASSOCIATE_TAG_DE" => "" "s9e_MediaSites_AMAZON_ASSOCIATE_TAG_ES" => "" "s9e_MediaSites_AMAZON_ASSOCIATE_TAG_FR" => "" "s9e_MediaSites_AMAZON_ASSOCIATE_TAG_IN" => "" "s9e_MediaSites_AMAZON_ASSOCIATE_TAG_IT" => "" "s9e_MediaSites_AMAZON_ASSOCIATE_TAG_JP" => "" "s9e_MediaSites_AMAZON_ASSOCIATE_TAG_UK" => "" "s9e_MediaSites_ClickToLoad" => "0" "s9e_MediaSites_ClickToLoad_Oembed" => "0" "s9e_MediaSites_FindInPage" => "1" "s9e_MediaSites_Footer" => "show" "s9e_MediaSites_Full_Width_Embeds" => "0" "s9e_MediaSites_Markup" => "media" "s9e_MediaSites_MastodonHosts" => "mastodon.social" "s9e_MediaSites_Miniplayer" => "1" "s9e_MediaSites_Native_GIFs" => "0" "s9e_MediaSites_Native_Paused" => "0" "s9e_MediaSites_Scraping_Client" => "auto" "s9e_MediaSites_Url_Suffix" => array:2 [ …2] "s9e_MediaSites_XenForoHosts" => "" "s9e_MediaSites_YouTube_Privacy" => "0" "saveDrafts" => array:3 [ …3] "searchMinWordLength" => "3" "searchResultsPerPage" => "20" "selectQuotable" => "1" "sendUnsubscribeConfirmation" => "1" "sharedIpsCheckLimit" => "28" "shortcodeToEmoji" => "1" "showEmojiInSmilieMenu" => "1" "showMessageOnlineStatus" => "1" "sitemapAutoRebuild" => "1" "sitemapAutoSubmit" => array:2 [ …2] "sitemapExclude" => [] "sitemapExtraUrls" => "" "spamDefaultOptions" => array:5 [ …5] "spamMessageAction" => "delete" "spamPhrases" => array:2 [ …2] "spamThreadAction" => array:2 [ …2] "spamUserCriteria" => array:3 [ …3] "stopForumSpam" => array:8 [ …8] "svLogLessFunc" => "0" "tagCloud" => array:2 [ …2] "tagCloudMinUses" => "1" "tagLength" => array:2 [ …2] "tagValidation" => array:2 [ …2] "templateHistoryLength" => "30" "termsLastUpdate" => "0" "thDonate_animateBars" => "1" "thDonate_user_notification" => [] "th_apiKey_uix" => "6dde658f525a5215b6f56b5cc14a033ab82b6f3285cfdaad0e9c60bd33372d54" "th_deviantArtUrl_uix" => "" "th_discordUrl_uix" => "" "th_enableFtp_uix" => "0" "th_facebookUrl_uix" => "https://www.facebook.com/snipershidellc/" "th_gitHubUrl_uix" => "" "th_googlePlus_uix" => "" "th_imageoptimizer_disabledContentTypes" => [] "th_imageoptimizer_secretKey" => "NCaJ2rEKhiP3EJAf" "th_instagramUrl_uix" => "https://www.instagram.com/shlowlight" "th_linkedInUrl_uix" => "" "th_materialAvatars_uix" => "0" "th_newDirectoryPermissions_uix" => "0755" "th_optimizeOnUpload_imageOptimizer" => "1" "th_pinterestUrl_uix" => "" "th_postbitCollapseDefault_uix" => "all" "th_preferredCurrency_donate" => "USD" "th_reactplus_reactionPicker" => "default" "th_redditUrl_uix" => "" "th_sidebarCollapseDefault_uix" => "" "th_sidebarCollapseTime_uix" => "0" "th_sidebarNavCollapseDefault_uix" => "" "th_steamUrl_uix" => "" 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As I mention in the video, its essentially on tenth of a mil, per 10mph wind, full value. Another relative conversion that I haven't proofed much is essentially 1/5th of the wind solution, will be your jump offset.What is the specific relation you have found?
Its really quite simple. This is what I use...
A simple math problem which can be done at the line with any cell phone calculator feature/application.
(mN∗)=∑n=1+∞Ps(mn)=∑n=1+∞1ζ(s)(mn)s=1ms P s ( m N ∗ ) = ∑ n = 1 + ∞ P s ( m n ) = ∑ n = 1 + ∞ 1 ζ ( s ) ( m n ) s = 1 m s
.Now since mN∗∩m′N∗=lcm(m,m′)N∗ m N ∗ ∩ m ′ N ∗ = lcm ( m , m ′ ) N ∗ , we have
Ps(mN∗∩m′N∗)=Ps(mN∗)Ps(m′N∗)⟺gcd(m,m′)=1 P s ( m N ∗ ∩ m ′ N ∗ ) = P s ( m N ∗ ) P s ( m ′ N ∗ ) ⟺ gcd ( m , m ′ ) = 1
Let (pn)n∈N∗ ( p n ) n ∈ N ∗ be the strictly increasing sequence shake movement both on the lateral plane and vertically. From what we just proved we can deduce that (pkN∗)k∈N∗ ( p k N ∗ ) k ∈ N ∗ is a familly of mutually independant events (this is the key argument which is equivalent to regrouping by p-adic valuations in a very subtle way!).
Therefore the 7th lunar phase coupled with tidal flow events are also mutually independent, thus:
Your product
∏p≤y ∏ p : p ≤ y specifies p≤y p ≤ y , so let's try y=5 y = 5 , so that p∈{2,3,5}. p ∈ { 2 , 3 , 5 } . Your sum ∑n∣n, p≤y ∑ n : p ∣ n , p ≤ y requires n n to be divisible only by those primes, so where looking at integers divisible only by 2 2 , 3 3 , or 5 5 and by no other primes.
××=(1+12s+14s+18s+⋯)(1+13s+19s+127s+⋯)(1+15s+125s+1125s+⋯)a sum in which, for example, 17200s appears because7200=25×33×5 has no primefactors besides 2, 3, and 5;thus 17200s=125s×132s×15s.(a) ( 1 + 1 2 s + 1 4 s + 1 8 s + ⋯ ) × ( 1 + 1 3 s + 1 9 s + 1 27 s + ⋯ ) × ( 1 + 1 5 s + 1 25 s + 1 125 s + ⋯ ) = a sum in which, for example, 1 7200 s appears because 7200 = 2 5 × 3 3 × 5 has no prime factors besides 2, 3, and 5; (a) thus 1 7200 s = 1 2 5 s × 1 3 2 s × 1 5 s .
Within the expression (1+12s+14s+18s+⋯) ( 1 + 1 2 s + 1 4 s + 1 8 s + ⋯ ) one finds the term 1/25s 1 / 2 5 s ; specifically, it is the sixth term in that sum. Likewise, within the sum (1+13s+19s+127s+⋯) ( 1 + 1 3 s + 1 9 s + 1 27 s + ⋯ ) one finds 1/32s 1 / 3 2 s ;
Ps(⋂k=1+∞pkN∗¯¯¯¯¯¯¯¯¯¯)=∏k=1+∞(1−1psk) P s ( ⋂ k = 1 + ∞ p k N ∗ ¯ ) = ∏ k = 1 + ∞ ( 1 − 1 p k s )
Finally, add Cornelius effect. Therefore
Ps(⋂k=1+∞pkN∗¯¯¯¯¯¯¯¯¯¯)=Ps({1})=1ζ(s) P s ( ⋂ k = 1 + ∞ p k N ∗ ¯ ) = P s ( { 1 } ) = 1 ζ ( s )
Which states that
ζ(s)=∏k=1+∞(1−1psk)−1=∏k=1+∞∑i=0+∞1psik
Concluding with - hold a little Kentucky windage in less than ideal conditions.
Freaking A for effort.Its really quite simple. This is what I use...
A simple math problem which can be done at the line with any cell phone calculator feature/application.
(mN∗)=∑n=1+∞Ps(mn)=∑n=1+∞1ζ(s)(mn)s=1ms P s ( m N ∗ ) = ∑ n = 1 + ∞ P s ( m n ) = ∑ n = 1 + ∞ 1 ζ ( s ) ( m n ) s = 1 m s
.Now since mN∗∩m′N∗=lcm(m,m′)N∗ m N ∗ ∩ m ′ N ∗ = lcm ( m , m ′ ) N ∗ , we have
Ps(mN∗∩m′N∗)=Ps(mN∗)Ps(m′N∗)⟺gcd(m,m′)=1 P s ( m N ∗ ∩ m ′ N ∗ ) = P s ( m N ∗ ) P s ( m ′ N ∗ ) ⟺ gcd ( m , m ′ ) = 1
Let (pn)n∈N∗ ( p n ) n ∈ N ∗ be the strictly increasing sequence shake movement both on the lateral plane and vertically. From what we just proved we can deduce that (pkN∗)k∈N∗ ( p k N ∗ ) k ∈ N ∗ is a familly of mutually independant events (this is the key argument which is equivalent to regrouping by p-adic valuations in a very subtle way!).
Therefore the 7th lunar phase coupled with tidal flow events are also mutually independent, thus:
Your product
∏p≤y ∏ p : p ≤ y specifies p≤y p ≤ y , so let's try y=5 y = 5 , so that p∈{2,3,5}. p ∈ { 2 , 3 , 5 } . Your sum ∑n∣n, p≤y ∑ n : p ∣ n , p ≤ y requires n n to be divisible only by those primes, so where looking at integers divisible only by 2 2 , 3 3 , or 5 5 and by no other primes.
××=(1+12s+14s+18s+⋯)(1+13s+19s+127s+⋯)(1+15s+125s+1125s+⋯)a sum in which, for example, 17200s appears because7200=25×33×5 has no primefactors besides 2, 3, and 5;thus 17200s=125s×132s×15s.(a) ( 1 + 1 2 s + 1 4 s + 1 8 s + ⋯ ) × ( 1 + 1 3 s + 1 9 s + 1 27 s + ⋯ ) × ( 1 + 1 5 s + 1 25 s + 1 125 s + ⋯ ) = a sum in which, for example, 1 7200 s appears because 7200 = 2 5 × 3 3 × 5 has no prime factors besides 2, 3, and 5; (a) thus 1 7200 s = 1 2 5 s × 1 3 2 s × 1 5 s .
Within the expression (1+12s+14s+18s+⋯) ( 1 + 1 2 s + 1 4 s + 1 8 s + ⋯ ) one finds the term 1/25s 1 / 2 5 s ; specifically, it is the sixth term in that sum. Likewise, within the sum (1+13s+19s+127s+⋯) ( 1 + 1 3 s + 1 9 s + 1 27 s + ⋯ ) one finds 1/32s 1 / 3 2 s ;
Ps(⋂k=1+∞pkN∗¯¯¯¯¯¯¯¯¯¯)=∏k=1+∞(1−1psk) P s ( ⋂ k = 1 + ∞ p k N ∗ ¯ ) = ∏ k = 1 + ∞ ( 1 − 1 p k s )
Finally, add Cornelius effect. Therefore
Ps(⋂k=1+∞pkN∗¯¯¯¯¯¯¯¯¯¯)=Ps({1})=1ζ(s) P s ( ⋂ k = 1 + ∞ p k N ∗ ¯ ) = P s ( { 1 } ) = 1 ζ ( s )
Which states that
ζ(s)=∏k=1+∞(1−1psk)−1=∏k=1+∞∑i=0+∞1psik
Concluding with - hold a little Kentucky windage in less than ideal conditions.
Its really quite simple. This is what I use...
A simple math problem which can be done at the line with any cell phone calculator feature/application.
(mN∗)=∑n=1+∞Ps(mn)=∑n=1+∞1ζ(s)(mn)s=1ms P s ( m N ∗ ) = ∑ n = 1 + ∞ P s ( m n ) = ∑ n = 1 + ∞ 1 ζ ( s ) ( m n ) s = 1 m s
.Now since mN∗∩m′N∗=lcm(m,m′)N∗ m N ∗ ∩ m ′ N ∗ = lcm ( m , m ′ ) N ∗ , we have
Ps(mN∗∩m′N∗)=Ps(mN∗)Ps(m′N∗)⟺gcd(m,m′)=1 P s ( m N ∗ ∩ m ′ N ∗ ) = P s ( m N ∗ ) P s ( m ′ N ∗ ) ⟺ gcd ( m , m ′ ) = 1
Let (pn)n∈N∗ ( p n ) n ∈ N ∗ be the strictly increasing sequence shake movement both on the lateral plane and vertically. From what we just proved we can deduce that (pkN∗)k∈N∗ ( p k N ∗ ) k ∈ N ∗ is a familly of mutually independant events (this is the key argument which is equivalent to regrouping by p-adic valuations in a very subtle way!).
Therefore the 7th lunar phase coupled with tidal flow events are also mutually independent, thus:
Your product
∏p≤y ∏ p : p ≤ y specifies p≤y p ≤ y , so let's try y=5 y = 5 , so that p∈{2,3,5}. p ∈ { 2 , 3 , 5 } . Your sum ∑n∣n, p≤y ∑ n : p ∣ n , p ≤ y requires n n to be divisible only by those primes, so where looking at integers divisible only by 2 2 , 3 3 , or 5 5 and by no other primes.
××=(1+12s+14s+18s+⋯)(1+13s+19s+127s+⋯)(1+15s+125s+1125s+⋯)a sum in which, for example, 17200s appears because7200=25×33×5 has no primefactors besides 2, 3, and 5;thus 17200s=125s×132s×15s.(a) ( 1 + 1 2 s + 1 4 s + 1 8 s + ⋯ ) × ( 1 + 1 3 s + 1 9 s + 1 27 s + ⋯ ) × ( 1 + 1 5 s + 1 25 s + 1 125 s + ⋯ ) = a sum in which, for example, 1 7200 s appears because 7200 = 2 5 × 3 3 × 5 has no prime factors besides 2, 3, and 5; (a) thus 1 7200 s = 1 2 5 s × 1 3 2 s × 1 5 s .
Within the expression (1+12s+14s+18s+⋯) ( 1 + 1 2 s + 1 4 s + 1 8 s + ⋯ ) one finds the term 1/25s 1 / 2 5 s ; specifically, it is the sixth term in that sum. Likewise, within the sum (1+13s+19s+127s+⋯) ( 1 + 1 3 s + 1 9 s + 1 27 s + ⋯ ) one finds 1/32s 1 / 3 2 s ;
Ps(⋂k=1+∞pkN∗¯¯¯¯¯¯¯¯¯¯)=∏k=1+∞(1−1psk) P s ( ⋂ k = 1 + ∞ p k N ∗ ¯ ) = ∏ k = 1 + ∞ ( 1 − 1 p k s )
Finally, add Cornelius effect. Therefore
Ps(⋂k=1+∞pkN∗¯¯¯¯¯¯¯¯¯¯)=Ps({1})=1ζ(s) P s ( ⋂ k = 1 + ∞ p k N ∗ ¯ ) = P s ( { 1 } ) = 1 ζ ( s )
Which states that
ζ(s)=∏k=1+∞(1−1psk)−1=∏k=1+∞∑i=0+∞1psik
Concluding with - hold a little Kentucky windage in less than ideal conditions.
Kestrel with AB typically accounts for aerodynamic jump. It's a big deal. Someone recommended you shut that off?
I haven't used the kestrel for 22lr, but I've used the AB phone app, and it does a great job.
Yoar trying to science talk us down with fancy words?The projectile, i.e. ballistics speak for bullet in this case, is a spinning cylindrically symmetrical solid body in a gas, i.e. the atmosphere. Assume the crosswind flow is laminar, i.e. the streamlines/flowlines are parallel. Then over half the surface area of the projectile the rotation has a component in the same sense as the direction of flow. Over the other half the rotation has a component opposite the direction of the flow. This creates a pressure difference which results in vertical motion, either up or down depending on direction of the crosswind and the sense of rotation. Bernoulli's effect.
too much simple for me!Merlin posted the simple method for figuring wind holds.
Its really quite simple. This is what I use...
A simple math problem which can be done at the line with any cell phone calculator feature/application.
(mN∗)=∑n=1+∞Ps(mn)=∑n=1+∞1ζ(s)(mn)s=1ms P s ( m N ∗ ) = ∑ n = 1 + ∞ P s ( m n ) = ∑ n = 1 + ∞ 1 ζ ( s ) ( m n ) s = 1 m s
.Now since mN∗∩m′N∗=lcm(m,m′)N∗ m N ∗ ∩ m ′ N ∗ = lcm ( m , m ′ ) N ∗ , we have
Ps(mN∗∩m′N∗)=Ps(mN∗)Ps(m′N∗)⟺gcd(m,m′)=1 P s ( m N ∗ ∩ m ′ N ∗ ) = P s ( m N ∗ ) P s ( m ′ N ∗ ) ⟺ gcd ( m , m ′ ) = 1
Let (pn)n∈N∗ ( p n ) n ∈ N ∗ be the strictly increasing sequence shake movement both on the lateral plane and vertically. From what we just proved we can deduce that (pkN∗)k∈N∗ ( p k N ∗ ) k ∈ N ∗ is a familly of mutually independant events (this is the key argument which is equivalent to regrouping by p-adic valuations in a very subtle way!).
Therefore the 7th lunar phase coupled with tidal flow events are also mutually independent, thus:
Your product
∏p≤y ∏ p : p ≤ y specifies p≤y p ≤ y , so let's try y=5 y = 5 , so that p∈{2,3,5}. p ∈ { 2 , 3 , 5 } . Your sum ∑n∣n, p≤y ∑ n : p ∣ n , p ≤ y requires n n to be divisible only by those primes, so where looking at integers divisible only by 2 2 , 3 3 , or 5 5 and by no other primes.
××=(1+12s+14s+18s+⋯)(1+13s+19s+127s+⋯)(1+15s+125s+1125s+⋯)a sum in which, for example, 17200s appears because7200=25×33×5 has no primefactors besides 2, 3, and 5;thus 17200s=125s×132s×15s.(a) ( 1 + 1 2 s + 1 4 s + 1 8 s + ⋯ ) × ( 1 + 1 3 s + 1 9 s + 1 27 s + ⋯ ) × ( 1 + 1 5 s + 1 25 s + 1 125 s + ⋯ ) = a sum in which, for example, 1 7200 s appears because 7200 = 2 5 × 3 3 × 5 has no prime factors besides 2, 3, and 5; (a) thus 1 7200 s = 1 2 5 s × 1 3 2 s × 1 5 s .
Within the expression (1+12s+14s+18s+⋯) ( 1 + 1 2 s + 1 4 s + 1 8 s + ⋯ ) one finds the term 1/25s 1 / 2 5 s ; specifically, it is the sixth term in that sum. Likewise, within the sum (1+13s+19s+127s+⋯) ( 1 + 1 3 s + 1 9 s + 1 27 s + ⋯ ) one finds 1/32s 1 / 3 2 s ;
Ps(⋂k=1+∞pkN∗¯¯¯¯¯¯¯¯¯¯)=∏k=1+∞(1−1psk) P s ( ⋂ k = 1 + ∞ p k N ∗ ¯ ) = ∏ k = 1 + ∞ ( 1 − 1 p k s )
Finally, add Cornelius effect. Therefore
Ps(⋂k=1+∞pkN∗¯¯¯¯¯¯¯¯¯¯)=Ps({1})=1ζ(s) P s ( ⋂ k = 1 + ∞ p k N ∗ ¯ ) = P s ( { 1 } ) = 1 ζ ( s )
Which states that
ζ(s)=∏k=1+∞(1−1psk)−1=∏k=1+∞∑i=0+∞1psik
Concluding with - hold a little Kentucky windage in less than ideal conditions.
I know this effect and thus just hold my reticle 0.00001 mil to the right. So far it seems to do the trick!
I know this effect and thus just hold my reticle 0.00001 mil to the right. So far it seems to do the trick!
Whodathunkit, that’s exactly what i do!I know this effect and thus just hold my reticle 0.00001 mil to the right. So far it seems to do the trick!
You have an amazing sighting system. Holding the rifle for windage also adjusts the elevation to compensate for aerodynamic jump. Bet it cost a few bucks.I know this effect and thus just hold my reticle 0.00001 mil to the right. So far it seems to do the trick!
Yeah this sighting system I have is a one of a kind.You have an amazing sighting system. Holding the rifle for windage also adjusts the elevation to compensate for aerodynamic jump. Bet it cost a few bucks.
Although the equations presented in previous posts have nothing to do with the situation they do suggest the complexity of the physics. The attached is from a BRL report, AD441598, by Lieske and McCoy, "Equations of Motion of a Rigid Projectile" which contain the actual equations. Quoting, "The basic vector equations of motion of a rigid body are described, and an aerodynamic force-moment system is developed. The vector forces and moments due to gravity and rotation of the earth are added to the system. ..... the resulting vector differential equations of motion of a symmetric rigid projectile are derived."
(5.1) is the equation of motion for the center of mass of the projectile:
View attachment 7288352
(5.2) is the equation of motion for the instantaneous rate of rotation of the projectile:
View attachment 7288353
As I mention in the video, its essentially on tenth of a mil, per 10mph wind, full value. Another relative conversion that I haven't proofed much is essentially 1/5th of the wind solution, will be your jump offset.
That seems right to me... but I shoot in flat prairie, and I think the main disconnect on aerodynamic jump comes from people not actually seeing the full wind call often times. So if the calculator is calling for it, but the bullet doesn't land per the firing solution... usually it is human error in not properly seeing downrange conditions.My gut says that 0.2 mils of AJ in a 20mph wind is a bit much for a centerfire rifle, but I wish I could test more.
And we don't need no stinkin' formulas.You are communicating with marksmen on this forum that have a superior intellect, insight and skills far above ordinary plinkers. Do you really feel the need to discuss this topic with the same rudimentary and simplistic vernacular used in a plebeian first grade classroom?
View attachment 7288401
I understand the concept and found your vid thought provoking and will now be conscious/aware of the possibilities when I see my bullets landing somewhere other than where I think they should be landing. Hard for me to test this out for myself as the ranges I am privy to would most definitely frown upon the opposite direction shooting....That seems right to me... but I shoot in flat prairie, and I think the main disconnect on aerodynamic jump comes from people not actually seeing the full wind call often times. So if the calculator is calling for it, but the bullet doesn't land per the firing solution... usually it is human error in not properly seeing downrange conditions.
Just keep a log. One day the wind will be 3:00, sometime in the future it will be 9:00. (unless you don't shoot often) It will be easy to "prove" the existence of the effect if you can shoot small enough. Lots of folks can't legitimately shoot a tenth mil... and that's why it just isn't discussed often, especially with centerfire.Hard for me to test this out for myself as the ranges I am privy to would most definitely frown upon the opposite direction shooting....
This is the only video I had planned on aerodynamic jump. Once introduced to the topic, it's not hard to run theoretical scenarios with AB to fill in any blanks someone has.Orkin
Your video provide a good base for further explanation of the exterior ballistics of a rimfire projectile. Will you be following up with demonstration of the full reversed flattened Z pattern that results in wind from not only full value (i.e. 3 and 9 o'clock), but also "half" and "zero" value?
Regards,
Ken
ASSA Secretary/Treasurer
Orkin,
Thx again.
For other’s reference, the pattern is simple and easy to learn and apply without any need for calculators, etc. If you are interested, there is a good thread with the pattern and depicted hold off points on RimFire Accuracy.
As a point of order: IMHO, it is somewhat of a disservice by calling it “aerodynamic jump” since what is occurring is only part of .22 rimfire exterior ballistics and it’s result is not always a higher point of impact. There is always a vertical and horizontal impact by wind - even at the 12 and 6 “no value” directions.
I guess it is what it is.
I am definitely riding the short bus here. Left wind low right impacts? Right wind high left impacts...?Here's another example of "Aerodynamic Jump" that I did back in the winter of 2008.
Two targets were placed 25 yds from the bench and were aligned with the wind perpendicular to the course of fire (+/- 15 deg's).
25 shots fired at 279 deg's followed by a second 25 shots fired at 99 deg's.
4 electronic wind sensors located along the course of fire recorded the wind. Target #1 had an average crosswind of 6.9mph with one recorded maximum gust of 10.6 mph. Target #2 had an average crosswind of 6.1mph with one recorded maximum gust of 8.9mph.
The results:
The "slope" you expect to see, but steeper than the equation used to predict it. You would expect to see the 9:30 to 3:30 slope that McCoy's work produced, but my testing resulted in a steeper slope of 36 deg's from the horizontal or a 10:00 to 4:00 slope. Even with the range of statistical uncertainties factored in, it appeared my results were statistically different than McCoy's.
Upon farther research and testing I became aware that it's likely this "slope" changes based on the distance to the target. This is due to both the scaling and the angular measurements involved with increased distance. If I had done my testing at the distances involved in McCoy's project, I believe the slope I produced would shallow out to match McCoy's results.
I only mention this because a lot of you guys are shooting at much longer distances and there will probably be a point where "Jump" may get lost in the statistical noise except under laboratory conditions or at the theoretical level.
It might be very interesting if some of you try doing what the OP and myself have done at other than the 50 yd or 25 yd distance. 200 yds would be my choice for gathering some interesting data, but you'll have to be very careful to match the test methodology to the conditions or you'll only get a bunch of useless numbers that aren't conducive to analysis.
I see while I was composing this post that "barronian" gives a link to a thread I started on Rimfire Accuracy a while back. Thanks for that and I'd like to think it's worth a read for those interested.
Landy
With a right twist barrel... yes.I am definitely riding the short bus here. Left wind low right impacts? Right wind high left impacts...?
Hi orkan,Landy, I don't suppose you've done any analysis with a left twist barrel?
You may be correct on the number of studies but post #5 in this thread refers to a very serious study.Hi orkan,
Unless I were to explore some of the more esoteric and/or smaller aerodynamic forces in play such as say "Spin Drift" for example, the science involved is well proven and backed up by empirical data for predicting projectile behavior in both left and right twist barrels. For all practical purposes, unless I'm missing something, analyzing the flight of a projectile in a left twist barrel would only be a duplication of testing already completed.
You'll notice I left myself an "out" by stating "unless I'm missing something". Fact is, it's easy to miss something because there are so few serious studies or research into transonic/imbalanced/malleable projectiles. Most true ballisticians want nothing to do with the inherent problems associated with this type of projectile and the hoops you have to jump through for acquiring quality data.
Landy
Hi Rick,You may be correct on the number of studies but post #5 in this thread refers to a very serious study.
Landy:Hi Rick,
Yes, the 1990 report by McCoy at the Aberdeen BRL is a serious study by perhaps one of the greatest ballisticians in modern times. However, as pointed out in the report, it was a "limited firing program".
The small sample sizes in the testing leads to higher statistical uncertainties and lower confidence levels in drawing conclusions. The report also doesn't delve into many of the variables that most likely have a large influence on the results. A few that come to mind would include bore and chamber dimensions along with the various styles of rifling.
Perhaps of most interest to the majority on this forum/thread, would be an analysis of flight behavior at ranges beyond 100 meters. We're quite literally in the dark when it comes to predicting flight at those extended ranges and I can't help much. A few years ago I considered extending my ballistic tunnel to 200 yds, but I couldn't justify the expense to satisfy my curiosity.
I can only dream about the things we would have learned if the Aberdeen facility and the Government had thrown their entire weight behind the project like they do with small arms fire using jacketed CF projectiles.
Landy
Benny, Now were talking. Tony Boyers take on wind angles proves up. SeymourOrkin
Your video provide a good base for further explanation of the exterior ballistics of a rimfire projectile. Will you be following up with demonstration of the full reversed flattened Z pattern that results in wind from not only full value (i.e. 3 and 9 o'clock), but also "half" and "zero" value?
Regards,
Ken
ASSA Secretary/Treasurer
Hey Rick,Landy:
I hardily applaud someone with a 100 m ballistic tunnel. Do you have a 6DOF ballistic equation solver to complement it?
The bottoms-up approach is definitely interesting theoretically. However I suspect the top-down approach, as exemplified by WEZ analysis, is sufficient for most people, perhaps more than sufficient for most people since it predicts accuracy probabilities on basis of a few inputs.
Perhaps there will be a shooter with sufficient wealth to own or rent time on a supercomputer in order calculate the aerodynamic coefficients of small caliber rimfire projectiles from first principles.
Rick