Hivebent began on the 12th of June, 2010 - in other words, 6/12/2010 - just as Homestuck began on 4/13/2009.
While the Alternian calendar does not directly correlate to the Earth calendar, the story is set on Karkat Vantas's wriggling day: the 12th bilunar perigee of the 6th dark season's equinox, in the same way that Homestuck takes place on John Egbert's birthday, April 13th.
The 612th day of Homestuck is December 16th, which makes the date 12/16/10, or 16/12/10 in the style that Andrew updates the RSS Feed with. A flash was made to mark the occasion, but it was actually released one day late.
The update on 6/1/2011 has Vriska Serket attempting to challenge Bec Noir to a duel, consequentially leaving behind a pixie dust trail back to the troll's hiding place. This allows Bec Noir to quickly find the hiding place and explode the living shit out of it. Fortunately/unfortunately, this was an alternate timeline.
The updates on 6/12/2011 include the beginning of Vriska's last pesterlog to John.
Cascade was released on 10/25/11, exactly 2 years, 6 months and 12 days after 4/13/09, when Homestuck began, and 1 year, 4 months, and 13 days after 6/12/10, when Hivebent began.
In this log, Past Karkat exists 6 hours and 12 minutes before Equius, and Future Karkat exists 612 hours in the future from Equius.
The memo between Kanaya and Future Karkat implies that the session of Sgrub took 612 hours to beat. This is confirmed when Karkat says he was hatched several weeks ago. 612 hours spans 3 weeks, 4 days, and 12 hours, suggesting his ectobiology encounter happened early in his adventure.
During a conversation late into the kids' session, Terezi instructs Dave to wire her 413 Boonbonds exactly 6 hours and 12 minutes in her own past.
As soon as John opens Jade'scruxtruder the countdown shows 10:25, 6:12 + 4:13 = 10:25. By the time she gets upstairs, the countdown is at "a little more than 6 minutes" - most likely 6:12.
The destruction of the Trolls' Prospit occurs with 6:12:00 remaining until the Critical Moment or4 hours and 13 minutes after Jack entered the troll session.
The destruction of the Trolls' Derse occurs 6 hours and 12 minutes after Jack entered the troll session or with 4:13:00 remaining until the Critical Moment.
Retroactively, in one of the pages where Hearts Boxcars is struggling with Eggs and Biscuits, there are six visible Eggs, each using a hat with 12 written on it, and 4 Biscuits each using a hat with 13 on it. However, this is clearly part of the ongoing gag most certainly a coincidence.
There are 12 trolls, each one 6 solar sweeps old, who will split into two teams of 6 to play the Alternian equivalent to Sburb.
Each troll's first and last name has 6 letters, for a grand total of 12 letters in their full names.
The two Alternian Frog Temples have 6 pillars each, one representing each of two teams, just as the Earth one has 4.
The Sgrub cursor has 12 complete squares, just as Earth's Sburb cursor has 4 complete squares.
The trolls' Prospit and Derse have 7 and 5 (12) dream towers each, while the Earth session equivalents have 2 each.
6 of the trolls have eyewear (Terezi, Sollux, Equius, Vriska, Eridan and Feferi), meaning a total of 12 lenses (assuming you count Vriska's blacked-out lens).
Six Alternian Solar Sweeps is equivalent to thirteen Earth years; thus, one Alternian solar sweep is equal to two and one-sixth Earth years (2 1/6 = 216 = 612 reversed). This fraction is 2.16666667 when written as a decimal.
As of the 07/25/11 update, 6 and half trolls (6 1/2) are deceased (as Sollux has "a foot on either side"). Eight trolls have been (entirely) dead, seven have received DEAD tags (Aradia did not receive a DEAD tag in the scene of her death), and Sollux has been K.O.'d and received the corresponding tag. As Aradia and Kanaya have left the state of death, this resulted in a total of six deceased trolls and six living trolls prior to the reveal of Sollux's transcendent state.
When Vriska's left eye is visible it appears as six pupils around a center one. So it is 6 and 1 pupils on one out of two eyes.
Though not relating to the number 612 itself, the Pre-Scratch Trolls also have a similar combination of number quirks (Rufioh, 1; Mituna, 0/1/3/4/5/7/8; Kankri, 6/9; Meulin, 33; Latula, 134; Aranea, 8; Horuss, 100; Cronus, 8; and Meenah, 38) that adds up to 365 - the amount of days in a year on Earth, which, ironically, trolls do not go by.
Alternian architecture gives all windows 12 panes (which retroactively makes Earth's 4 pane windows a reference to 413).
The "continue" command used during Hivebent is ======>, consisting of 6 equals signs. It also consists of 12 lines, each equals comprising two lines, one for each troll. This retroactively makes the Homestuck "continue" command of ==> a reference to 413, since it has 4 lines, and 3 symbols in total.
On the page where Dave receives John's wired boonbuck, the first three digits of the amount of money he has is 612 backwards. The next three digits are 413 backwards.
In the minigame flashback to the creation of the troll paradox clones, it appears that infant trolls have 6 legs, again retroactively referencing the four human limbs.
In her burst of randomness Aradia types "+ ?*rand(413^612)" after one sentence.
At the end of the flash "John: Rise Up" the dates 4/13/2009-12/16/2010 are shown, pointing out how the flash was released on day 612 (even though it was technically released on day 613). Reversing the day and month of the flash's release produces the number 16/12 (reversing the digits has a similar result).
In the flash "ACT 6 ACT 4" Jack carves 153 tallies to mark how long he has been imprisoned. 153 is exactly one quarter of 612. 153 days equal to 21 weeks and 6 days.
In the graphic novel Watchmen, masked hero Rorschach's prisoner identification number is 62186, which consists of the numbers 6, 1, and 2 alongside 86, the difference of 1111 when subtracted by 1025.
612 is a palindrome of 216, a number whose apparent mathematical importance drives the protagonist of the movie Pi to insanity.
This palindrome also plays an important role in Jewish Kabbalah mysticism as the number of letters in the Shemhamphorasch (the 'explicit name' of God).