On June 27th 2006, the song's soundcheck was recorded in San Diego:

On August 21st 2009, during a fan interview, Colin identified the song title as 'Porous'.
The title "porous" had already appeared during the thumbs_down webcast on november 9th 2007. It's unknown if the song at that point had that title, but it seems well possible:

It seems that shortly after that interview with Colin in August 2009, Thom changed the title (and possibly the lyrics), renaming it 'Open The Floodgates'. On October 2nd 2009, it had its live debut under that title at the Echoplex in Los Angeles during a solo section in the middle of the first gig of Thom's then unnamed band (consisting of himself, Flea, Nigel Godrich, Joey Waronker and Mauro Refosco):

pre-Amok touring

oct. 2009

april/august 2010

	Open The Floodgates [3]	02	04								15
	Lotus Flower [5]	02	04	05					11	14
	Skirting On The Surface [3]	02		05							15
	Supercollider [2]		04	05
	Staircase [2]				05			10
	The Daily Mail [4]				05		08			14	15
	The Present Tense [1]						08
	I Froze Up [1]							10
	Follow Me Around [1]									14
	Give Up The Ghost [3]											17	18	01