Receiving Helpdesk

what is version space in ml

by Madelynn Lubowitz V Published 3 years ago Updated 2 years ago

Full Answer

What is version space?

Version Space: It is intermediate of general hypothesis and Specific hypothesis. It not only just written one hypothesis but a set of all possible hypothesis based on training data-set.

What is version space learning in machine learning?

Version space learning algorithms search a predefined space of hypotheses, viewed as a set of logical sentences. Formally, the hypothesis space is a disjunction (i.e., either hypothesis 1 is true, or hypothesis 2, or any subset of the hypotheses 1 through n ).

What is the difference between the version Space VS and H?

The version space VS with respect to hypothesis space H and training examples D is the subset of hypothesis from H consistent with all training examples in D. The version space VS with respect to hypothesis space H and training examples D is the subset of hypothesis from H consistent with all training examples in D.

What is the hypothesis space of ML algorithm?

The hypothesis space is 224 = 65536 because for each set of features of the input space two outcomes ( 0 and 1) are possible. The ML algorithm helps us to find one function, sometimes also referred as hypothesis, from the relatively large hypothesis space.

The version space algorithm

In settings where there is a generality-ordering on hypotheses, it is possible to represent the version space by two sets of hypotheses: (1) the most specific consistent hypotheses, and (2) the most general consistent hypotheses, where "consistent" indicates agreement with observed data.

Historical background

The notion of version spaces was introduced by Mitchell in the early 1980s as a framework for understanding the basic problem of supervised learning within the context of solution search.

Consistent Hypothesis, Version Space and List-Then-Eliminate Algorithm

An hypothesis h is said to be consistent hypothesis with a set of training examples D iff h ( x) = c ( x) for each example in D,

Version Space

The version space VSH,D is the subset of the hypothesis from H consistent with the training example in D,

Example

Here F1 and F2 are two features (attributes) with two possible values for each feature or attribute.

What do you mean by hypothesis space, instance space and version space?

Hypothesis space 'h' is described by a conjunction of constraints on the attribute, the constraints may General hypothesis "?" ( any value is acceptable), Specific hypothesis " φ " (a specific value or no value is accepted).

Answer

Hypothesis space 'h' is described by a conjunction of constraints on the attribute, the constraints may General hypothesis "?" ( any value is acceptable), Specific hypothesis " φ " (a specific value or no value is accepted).

image
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
8.3.21PHP Version2.19sRequest Duration2MBMemory UsageGET {post}Route
  • warninglog[14:51:13] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[14:51:13] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[14:51:13] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
  • warninglog[14:51:13] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[14:51:13] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[14:51:13] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[14:51:13] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[14:51:13] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[14:51:13] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[14:51:13] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[14:51:13] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[14:51:13] LOG.warning: explode(): Passing null to parameter #2 ($string) of type string is deprecat...
  • Booting (15.06ms)
  • Application (2.18s)
  • 1 x Application (99.29%)
    2.18s
    1 x Booting (0.69%)
    15.06ms
    7 templates were rendered
    • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
      Params
      0
      post
      1
      postContent
      2
      author
      3
      updated_at
      4
      bing_rich_snippet_text
      5
      bing_rich_snippet_link
      6
      bing_related_keywords
      7
      google_related_keywords
      8
      bing_news_title
      9
      bing_news_description
      10
      bing_videos
      11
      bing_images
      12
      bing_search_result_title
      13
      bing_search_result_description
      14
      bing_search_result_url
      15
      bing_paa_questions
      16
      bing_paa_answers
      17
      bing_slider_faq_questions
      18
      bing_slider_faq_answers
      19
      bing_pop_faq_questions
      20
      bing_pop_faq_answers
      21
      bing_tab_faq_questions
      22
      bing_tab_faq_answers
      23
      google_faq_questions
      24
      google_faq_answers
      25
      google_rich_snippet
      26
      google_search_result
      27
      indexedArray
      28
      total_images
      29
      total_videos
      30
      settings
      31
      url_current
      32
      menus
      33
      sidebar
    • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    uri
    GET {post}
    middleware
    web, checkdate
    as
    post.show
    controller
    App\Http\Controllers\Frontend\json_data\PostController@show
    namespace
    where
    file
    app/Http/Controllers/Frontend/json_data/PostController.php:18-166
    7 statements were executed2.16s
    • select * from `posts` where `published_at` <= '2025-06-07 14:51:13' and `slug` = 'what-is-version-space-in-ml' and `posts`.`deleted_at` is null limit 1
      3.22ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
      Metadata
      Bindings
      • 0. 2025-06-07 14:51:13
      • 1. what-is-version-space-in-ml
      Backtrace
      • 15. /app/Providers/RouteServiceProvider.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
      • 19. Route binding:39
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
    • select * from `json_post_contents` where `json_post_contents`.`post_id` = 218070 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
      3.99msmiddleware::checkdate:30receivinghelpdeskask
      Metadata
      Bindings
      • 0. 218070
      • 1. 0
      Backtrace
      • 19. middleware::checkdate:30
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
      • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
    • select * from `nova_menu_menus` where `slug` = 'header' limit 1
      390μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
      Metadata
      Bindings
      • 0. header
      Backtrace
      • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
      • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
      690μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Bindings
      • 0. 1
      Backtrace
      • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
      360μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Backtrace
      • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
      2.15s/app/View/Composers/SidebarView.php:22receivinghelpdeskask
      Metadata
      Bindings
      • 0. publish
      Backtrace
      • 14. /app/View/Composers/SidebarView.php:22
      • 15. /app/View/Composers/SidebarView.php:12
      • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
      • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
      • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
    • select * from `fake_users` where `fake_users`.`id` = 34474 limit 1
      930μsview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
      Metadata
      Bindings
      • 0. 34474
      Backtrace
      • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
      • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
      • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
    App\Models\FakeUser
    1
    Outl1ne\MenuBuilder\Models\MenuItem
    1
    Outl1ne\MenuBuilder\Models\Menu
    1
    App\Models\JsonPostContent
    1
    App\Models\Post
    11
        _token
        d7rbPCDtnNIf4NsFjAf1FgGv5LbaxSsZQNaaodY7
        _previous
        array:1 [ "url" => "https://receivinghelpdesk.com/ask/what-is-version-space-in-ml" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /what-is-version-space-in-ml
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:25 [ "cookie" => array:1 [ 0 => "XSRF-TOKEN=eyJpdiI6InpvNC9ocjlYU1BVM25ld09xZEtJWEE9PSIsInZhbHVlIjoiS0U5MnNNMDZPdENQYTVSMHhjTUtwQ3pDVWtCNjFka2htYTdSRE5GYXFYMmVkYU51VC84dmlVeFNEbFgycW9oeDR1L2ljVmg4aHJpdWZrcC9ObitHT3NmV0VoWGRSWkx6YllybThUL01MNVUwSVB5UW1aYzFuZVNPSlNiaVM2RTkiLCJtYWMiOiJhYjkzZTBmYjNlMTNkMjUwMGVlZTkwYmQ4ZDlmZmJiYWNmYjg5NjQxYWI1OTQxNGNjMzg2Zjk1ZTljMGU1ZmUwIiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6Imp4RThFL3FKbHY3aDFYNWRST1Z0NEE9PSIsInZhbHVlIjoiTTlSeXYvYk0vRnRzR2xSQTlJSC9nUjdFdW9NZWNBNG5scW0yWlpuQUd0K1dscE1YalQzUHU2U20vNFRiampBTkhnNXhmaDM2ZUFzamI2Y1lncnMvSHp0US9BSmpCZnZkaUJ2YTQ3ZnI3SzhRSVg4bFRpRHFZWjVPUUZyZFlaQXMiLCJtYWMiOiI1NzM0OGUyNWM2YzIzMmNiMzBiZTE4NTYxMDQwNTRmYjBlNGMxN2MxZDhhY2M4Y2E2ZWQ1ZDVjY2U4YzBmZjE3IiwidGFnIjoiIn0%3D; _pk_id.64.7c30=3678ae3168f6738f.1749288071.; _pk_ses.64.7c30=1XSRF-TOKEN=eyJpdiI6InpvNC9ocjlYU1BVM25ld09xZEtJWEE9PSIsInZhbHVlIjoiS0U5MnNNMDZPdENQYTVSMHhjTUtwQ3pDVWtCNjFka2htYTdSRE5GYXFYMmVkYU51VC84dmlVeFNEbFgycW9oeDR1L2ljV" ] "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "216.73.216.226" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "cf-ray" => array:1 [ 0 => "94bf13fa5b778f4c-ORD" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "connection" => array:1 [ 0 => "close" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "216.73.216.226, 108.162.216.146" ] "x-server-addr" => array:1 [ 0 => "154.12.239.204" ] "host" => array:1 [ 0 => "receivinghelpdesk.com" ] ]
        request_server
        0 of 0
        array:56 [ "USER" => "runcloud" "HOME" => "/home/runcloud" "SCRIPT_NAME" => "/ask/index.php" "REQUEST_URI" => "/ask/what-is-version-space-in-ml" "QUERY_STRING" => "" "REQUEST_METHOD" => "GET" "SERVER_PROTOCOL" => "HTTP/1.0" "GATEWAY_INTERFACE" => "CGI/1.1" "REDIRECT_URL" => "/ask/what-is-version-space-in-ml" "REMOTE_PORT" => "57304" "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php" "SERVER_ADMIN" => "you@example.com" "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "CONTEXT_PREFIX" => "" "REQUEST_SCHEME" => "http" "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "REMOTE_ADDR" => "108.162.216.146" "SERVER_PORT" => "80" "SERVER_ADDR" => "127.0.0.1" "SERVER_NAME" => "receivinghelpdesk.com" "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f" "SERVER_SIGNATURE" => "" "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib" "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin" "HTTP_COOKIE" => "XSRF-TOKEN=eyJpdiI6InpvNC9ocjlYU1BVM25ld09xZEtJWEE9PSIsInZhbHVlIjoiS0U5MnNNMDZPdENQYTVSMHhjTUtwQ3pDVWtCNjFka2htYTdSRE5GYXFYMmVkYU51VC84dmlVeFNEbFgycW9oeDR1L2ljVmg4aHJpdWZrcC9ObitHT3NmV0VoWGRSWkx6YllybThUL01MNVUwSVB5UW1aYzFuZVNPSlNiaVM2RTkiLCJtYWMiOiJhYjkzZTBmYjNlMTNkMjUwMGVlZTkwYmQ4ZDlmZmJiYWNmYjg5NjQxYWI1OTQxNGNjMzg2Zjk1ZTljMGU1ZmUwIiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6Imp4RThFL3FKbHY3aDFYNWRST1Z0NEE9PSIsInZhbHVlIjoiTTlSeXYvYk0vRnRzR2xSQTlJSC9nUjdFdW9NZWNBNG5scW0yWlpuQUd0K1dscE1YalQzUHU2U20vNFRiampBTkhnNXhmaDM2ZUFzamI2Y1lncnMvSHp0US9BSmpCZnZkaUJ2YTQ3ZnI3SzhRSVg4bFRpRHFZWjVPUUZyZFlaQXMiLCJtYWMiOiI1NzM0OGUyNWM2YzIzMmNiMzBiZTE4NTYxMDQwNTRmYjBlNGMxN2MxZDhhY2M4Y2E2ZWQ1ZDVjY2U4YzBmZjE3IiwidGFnIjoiIn0%3D; _pk_id.64.7c30=3678ae3168f6738f.1749288071.; _pk_ses.64.7c30=1XSRF-TOKEN=eyJpdiI6InpvNC9ocjlYU1BVM25ld09xZEtJWEE9PSIsInZhbHVlIjoiS0U5MnNNMDZPdENQYTVSMHhjTUtwQ3pDVWtCNjFka2htYTdSRE5GYXFYMmVkYU51VC84dmlVeFNEbFgycW9oeDR1L2ljV" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "216.73.216.226" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_CF_RAY" => "94bf13fa5b778f4c-ORD" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_CONNECTION" => "close" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "216.73.216.226, 108.162.216.146" "HTTP_X_SERVER_ADDR" => "154.12.239.204" "HTTP_HOST" => "receivinghelpdesk.com" "HTTPS" => "on" "REDIRECT_STATUS" => "200" "REDIRECT_HTTPS" => "on" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/ask/index.php" "REQUEST_TIME_FLOAT" => 1749288073.3594 "REQUEST_TIME" => 1749288073 ]
        request_cookies
        0 of 0
        array:4 [ "XSRF-TOKEN" => "d7rbPCDtnNIf4NsFjAf1FgGv5LbaxSsZQNaaodY7" "askhelpdesk_session" => "k9zsS5EelLFpYwqvoKqdyXF3GlhNM2Z1JyFqsZZe" "_pk_id_64_7c30" => null "_pk_ses_64_7c30" => null ]
        response_headers
        0 of 0
        array:7 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "private, must-revalidate" ] "date" => array:1 [ 0 => "Sat, 07 Jun 2025 09:21:13 GMT" ] "pragma" => array:1 [ 0 => "no-cache" ] "expires" => array:1 [ 0 => -1 ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjBVb0ZJZy9sWTBYd3VORTdLaXBjcUE9PSIsInZhbHVlIjoiU0cvM0Zza3ByQWsySmhjMGc1UlpFZkthc3lMdXVsNndrWFFkOGNhNUpucEJYNnM5L3l2eDdNR29TZC9ZaDZXTi9TZEFkYUlNdDhnb3lvOW5tQnExK1R2bmZPME9lRDFVK043Y3BQejBjV0ZXcTQ5R1FSaDhQRnQ0SVZNMW1JVk4iLCJtYWMiOiIzMGNhYmNkM2VkMTA0ZmI4NmU4ZDc4NzRkMmFlMmE2NmFmOGNkMTUyYWNjYzFhMGRlMDhhOGMzMGNkZjNlNjRkIiwidGFnIjoiIn0%3D; expires=Sat, 07-Jun-2025 11:21:15 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6IjBVb0ZJZy9sWTBYd3VORTdLaXBjcUE9PSIsInZhbHVlIjoiU0cvM0Zza3ByQWsySmhjMGc1UlpFZkthc3lMdXVsNndrWFFkOGNhNUpucEJYNnM5L3l2eDdNR29TZC9ZaDZXTi9TZEFkY" 1 => "askhelpdesk_session=eyJpdiI6Im1YbnRmcnBLWU9HdVp6Ky83NFFhaHc9PSIsInZhbHVlIjoiMlFhOWhqNk4rcE1PZlJrTHg1N2ZrQmdib002WlUxVXk2ajRKejNXZ1JmWE5NR2w3dTIzQ0p5ZmlhVVc2OXZSU0hOb1BESW4xb3pHa05JRzlRYUhleElxSGpGMERUVTZLTk1mdGNKYnJXbGdPZlEwVjFNT05wc3o0UUV4MDAxQ1giLCJtYWMiOiJiNGMwZWMwZWJmZTdjNTAzMWY5NzhjOWIzOTVjYjg3NDFkZmE1NjkzYjkyMzQ0OTg0Zjc5ZDk5NTk3MGI0ZjY2IiwidGFnIjoiIn0%3D; expires=Sat, 07-Jun-2025 11:21:15 GMT; Max-Age=7200; path=/; httponly; samesite=laxaskhelpdesk_session=eyJpdiI6Im1YbnRmcnBLWU9HdVp6Ky83NFFhaHc9PSIsInZhbHVlIjoiMlFhOWhqNk4rcE1PZlJrTHg1N2ZrQmdib002WlUxVXk2ajRKejNXZ1JmWE5NR2w3dTIzQ0p5ZmlhVVc2OXZS" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IjBVb0ZJZy9sWTBYd3VORTdLaXBjcUE9PSIsInZhbHVlIjoiU0cvM0Zza3ByQWsySmhjMGc1UlpFZkthc3lMdXVsNndrWFFkOGNhNUpucEJYNnM5L3l2eDdNR29TZC9ZaDZXTi9TZEFkYUlNdDhnb3lvOW5tQnExK1R2bmZPME9lRDFVK043Y3BQejBjV0ZXcTQ5R1FSaDhQRnQ0SVZNMW1JVk4iLCJtYWMiOiIzMGNhYmNkM2VkMTA0ZmI4NmU4ZDc4NzRkMmFlMmE2NmFmOGNkMTUyYWNjYzFhMGRlMDhhOGMzMGNkZjNlNjRkIiwidGFnIjoiIn0%3D; expires=Sat, 07-Jun-2025 11:21:15 GMT; path=/XSRF-TOKEN=eyJpdiI6IjBVb0ZJZy9sWTBYd3VORTdLaXBjcUE9PSIsInZhbHVlIjoiU0cvM0Zza3ByQWsySmhjMGc1UlpFZkthc3lMdXVsNndrWFFkOGNhNUpucEJYNnM5L3l2eDdNR29TZC9ZaDZXTi9TZEFkY" 1 => "askhelpdesk_session=eyJpdiI6Im1YbnRmcnBLWU9HdVp6Ky83NFFhaHc9PSIsInZhbHVlIjoiMlFhOWhqNk4rcE1PZlJrTHg1N2ZrQmdib002WlUxVXk2ajRKejNXZ1JmWE5NR2w3dTIzQ0p5ZmlhVVc2OXZSU0hOb1BESW4xb3pHa05JRzlRYUhleElxSGpGMERUVTZLTk1mdGNKYnJXbGdPZlEwVjFNT05wc3o0UUV4MDAxQ1giLCJtYWMiOiJiNGMwZWMwZWJmZTdjNTAzMWY5NzhjOWIzOTVjYjg3NDFkZmE1NjkzYjkyMzQ0OTg0Zjc5ZDk5NTk3MGI0ZjY2IiwidGFnIjoiIn0%3D; expires=Sat, 07-Jun-2025 11:21:15 GMT; path=/; httponlyaskhelpdesk_session=eyJpdiI6Im1YbnRmcnBLWU9HdVp6Ky83NFFhaHc9PSIsInZhbHVlIjoiMlFhOWhqNk4rcE1PZlJrTHg1N2ZrQmdib002WlUxVXk2ajRKejNXZ1JmWE5NR2w3dTIzQ0p5ZmlhVVc2OXZS" ] ]
        session_attributes
        0 of 0
        array:4 [ "_token" => "d7rbPCDtnNIf4NsFjAf1FgGv5LbaxSsZQNaaodY7" "_previous" => array:1 [ "url" => "https://receivinghelpdesk.com/ask/what-is-version-space-in-ml" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]