Dig Through Time

• WOTC Official Reminder Textofficial rules
  Delve — Each card you exile from your graveyard while casting this spell pays for .

• WWizards of the Coast2021-03-19
  Official Ruling
  You can exile cards to pay only for generic mana, and you can't exile more cards than the generic mana requirement of a spell with delve. For example, you can't exile more than seven cards from your graveyard to cast Treasure Cruise unless an effect has increased its cost.
• WWizards of the Coast2021-03-19
  Official Ruling
  Delve doesn't change a spell's mana cost or mana value. For example, Treasure Cruise's mana value is 8 even if you exiled three cards to cast it.
• WWizards of the Coast2021-03-19
  Official Ruling
  Because delve isn't an alternative cost, it can be used in conjunction with alternative costs, such as flashback. It can also be used to pay for additional costs that include generic mana.

Rulings via Scryfall

• WO
  Wizards of the Coast2015-02-03

  Dig Through Time was banned in modern on February 3, 2015. The newest blue kids on the block led to an overhaul of Modern like no other cards before them, changing how decks were built up and down a diverse metagame. Source: https://magic.wizards.com/en/news/arcana/brief-history-modern-banned-list-2015-02-03
• WO
  Wizards of the Coast2015-09-28

  Dig Through Time was restricted in vintage on September 28, 2015. Dig Through Time has reduced the diversity of the format, though in a somewhat different way than in Legacy. In Vintage, it has replaced many other card-drawers, creating a less diverse format. Dig Through Time is comparable to other restricted card-drawers, and now shares that honor. Source: https://magic.wizards.com/en/news/news/september-28-2015-banned-and-restricted-announcement-2015-09-28
• WO
  Wizards of the Coast2015-09-28

  Dig Through Time was banned in legacy on September 28, 2015. Over the past several months, the strategic diversity of Legacy has been diminished. Blue decks using Dig Through Time and various combo decks have occupied a greater portion of the metagame, pushing a lot of other decks out of the competitive scene. The problem is that other strategies tend to lose to the blue decks too frequently; they used to be more competitive, but now they fall behind when the blue decks reload for two mana using Dig Through Time. Source: https://magic.wizards.com/en/news/news/september-28-2015-banned-and-restricted-announcement-2015-09-28
• WO
  Wizards of the Coast2015-01-19

  Dig Through Time was banned in modern on January 19, 2015. Decks playing the powerful card drawers have been winning a lot, and pushing a lot of other decks down in competitive play. In Modern, these cards are easy replacements for one another—while a Delver deck might use Treasure Cruise over Dig Through Time, banning one but not the other would do little to change the deck. Source: https://magic.wizards.com/en/news/feature/banned-and-restricted-announcement-2015-01-19