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The band tried out the song prior to recording it when they toured in support of Alanis Morissette in august 1996. At that point it had a slightly mellower feel to it, with the first half sounding almost like an acoustic rendition. Each performance features several lyrical differences, and three examples are given below.
This video comes from the gig on August 14th 1996. It's very likely that it's the live premiere of 'Climbing Up The Walls', since it's the earliest known performance:

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I am the key to the lock in the dress
that keeps your toys in the basement
and if you get too far inside
you'll only see my reflection

I am her face when she sleeps tonight
I am the smell of a fear
do not cry out or make a sound
we are friends till we die

and either way you turn, I'll be there
open up your skull, I'll be there
climbing up the walls

it's always best when the light is off
it's always better on the outside
it's in the crack of your waiting smile
fifteen blows to your mind

so lock the kids up safe tonight
and shut the eyes in the cupboard
I am the smell of a local man
who gets the loneliest feeling

and either way he turns, I'll be there
open up your skull, I'll be there
climbing up the walls

climbing up the walls
climbing up the walls

This one comes from August 16th 1996:
I am the key to the lock in the dress
that keeps her toys in the basement
and if you get too far inside
you'll only see my reflection

I am her face as she sleeps tonight
I am the crack with the smile
???
and we are friends till we die

and either way you turn, I'll be there
open up your skull, I'll be there
climbing up the walls

it's always best when the light is off
it's always better on the outside
it's in the crack of your winning smile
fifteen blows to your mind

so tuck the kids in safe tonight
shut the eyes in the cupboard
I have the smell of a local man
who gets the loneliest feeling

and either way you turn, I'll be there
open up your skull, I'll be there
climbing up the walls

climbing up the walls
climbing up the walls

The lyrics to another version from August 26th 1996 are already slightly more developed:
I am the key to the lock in your dress
that keeps your toys in the basement
and if you get too far inside
you'll only see my reflection

I am her face when she sleeps tonight
I am the pick in the ice
do cry out or hit the alarm
you know we're friends till we die

and either way you turn, I'll be there
open up your skull, I'll be there
climbing up the walls

it's always best when the light is off
it's always better on the outside
fifteen blows to the back of your head
fifteen blows to your mind

so lock the kids up safe tonight
put the eyes in the cupboard
don't cry out or make a sound
you got the loneliest feeling

and either way you turn, I'll be there
open up your skull, I'll be there
climbing up the walls

climbing up the walls
climbing up the walls
This page, titled 'stuck in a frozen lake', appeared on radiohead.com during the recording of OK Computer and features a text by Thom with notes about songs that were around then.
The relevant section was not highlighted in red letters in the original page:
an airbag saved my life* in an interstella burst i am back to save the universe computer drums bass wrong lift* is hard work you been stuck in a lift we been trying to reach you thom the belly of the whale (thanks Rei xxxx) paranoid android* get busy with the shakers while im fast asleep could you stop the noise im trying ta get some rest this the place it wont hurt ever again karma police* girl with hitler hairdo everybodys friend life in a glasshouse phew for a minute there i lost myself i lost myself sit down your safe now polyethelene*will never break down swirly self announcements. stuck in a frozen lake. the penultimate place in dante's hell. last flowers till the hospital*is a sign discovered in oxford -my unhealthy obsession with these institutions. analysts may get the connection. ambulances scream past my house at all hours of the day and night like the confessionals of Larkin's "Ambulan s." let down*in the midst of monster tour the momentum getting drunk to talk bombarded by dangerously high levels of radiation from xray machines. one day, one day... climbing up the walls*both managers and record company are nervous about such a nasty sound coming out of the speakers. this is a good sign. dogwander* bring on another take better than another cake. nude* it is a mans world. and this one is very confused and will have sex with anything woman who comes within a mile radius. but feels bad about it. so doesnt. exit song (for a film)* cannot be listened to more than once in a row. which made recording it easy. or not. but what film? big boots* it was a long time ago and i cant remember. a whole orchestra watching the film and playing along. real life is dull. i am i the white lotus flying off the quay with barbara bach.
(information incomplete)
....>>>>i like the idea of you listening to our recordings with your head resting gently in emptiness. or before going out. or when you've come back. i dont like the scientists breaking down its molecular structure and teaching it in O level chemistry i ont want to have expain it but it worries me stupid. there is a lot of crying goes into making things.<<<<.... the masters tell us that there is an aspect of our minds that is its fundamental basis, a state called "the ground of the ordinary mind." It functions like a storehouse, in which the imprints of past actions caused by our negative emotions are all store like seeds. when the right conditions arise, they germinate and manifest as circumstances and situations in our lives. if we have a habit of thinking in a particular pattern, positive or negative, then these tendencies will be triggered and provoked very easily and recurr and go on recurring. With constant repetition our inclinations and habits become steadily more entr ched and continue, increasing and gathering power even when we sleep. This is how they come to determine our life, our death our rebirth.
Sixteen violins were used to make the noise towards the end of the track. The band didn't actually intend the song to be this scary, but it sort of turned out that way.
This print, that Stanley sold on his website, features a phrase from the track:

When played live, Jonny uses a portable radio which he tunes in to various stations of speaking before the gig - and during it, he swaps through the stations while sticking the output through a hell of a lot of effects.
This recording comes from the may 28th 1997 BBC Evening Session and was released on the NME Awards 98 compilation:

Thom : "This is about the unspeakable. Literally skull-crushing. I used to work in a mental hospital around the time that Care In The Community started, and we all just knew what was going to happen. And it's one of the scariest things to happen in this country, because a lot of them weren't just harmless... It was hailing violently when we recorded this. It seemed to add to the mood.

Some people can't sleep with the curtains open in case they see the eyes they imagine in their heads every night burning through the glass. Lots of people have panic buttons fitted in their bedrooms so they can reach over and set the alarm off without disturbing the intruder. This song is about the cupboard monster."
'CLIMBING UP THE WALLS'
Even bigger, even scarier rock track. Thom Yorke does his best to sound demented, but is out-done by the monumental chaos going on behind him.
Colin: "It's quite horrible, isn't it?"
Ed: "We always knew that song had an atmosphere and it was very easy to capture. The white noise is loads of violins."
Colin: "We recorded it in the ballroom of this old stately home. Dare we say there was something Gothic about the environment? It was certainly very New Grave of New Grave."
Key Lyric: "In the crack of your waning smile/15 blows to the skull..."
Thom: " 'Was it an accident that of the 10 largest mass-murderers in American History, eight have occurred since 1980, typically acts of middle-aged white men in their 30s and 40s after a prolonged period of being lonely, frustrated and full of rage and of 10 precipitated by a catastrophe in their lives such as losing their jobs or divorce?' "New York Times October 17 1991 - quoted by Eric Hobsbawn in 'Age of Extremes'."
Jonny Greenwood: A deranged insight into a very warped personality. "Very String based.

The white noise is 16 violins. Frightening music. We didn't mean it to be like that; it just happened.
Thom: "You don't need drugs to make extreme music. Just reading the papers makes you feel extreme. 'Climbing Up The Walls', for instance. I used to work in a mental hospital around the time the Government was getting passionate about Care in the Community, and everyone just knew what was going to happen. It was one of the scariest things that ever happened in this country, because a lot of them weren't harmless. It's like those huge 18th-century paintings, if you get really close to them, you can see these little figures in the corners, these amorphous little monsters. And that's what some big towns are like now: the shadows contain amorphous little monsters."
Colin dates the start of the record back to the summer of '95 when they supported REM on tour. He recalls playing 'Climbing Up The Walls' at a soundcheck at the Hershey Stadium. Peter Buck was checking their progress from the sound desk, and when they'd finished, he walked away, whistling the tune with his hands in his pockets.

[...]

"Well, we stole a lot of Polish composer Penderecki's string ideas. Rock arrangements haven't changed much since the days of The Beatles and 'Eleanor Rigby'. And if bands do want to get weird things with strings, they just put them through effects.

"We've found all these composers that are still getting new sounds out of violins. On the last chord of our song, 'Climbing Up The Walls', there's this block of white noise you can make when 16 violins are playing quarter tones apart from each other. It's the most frightening sound – like insects or something. But it's beautiful."
In connection with 'Climbing Up The Walls' he describes their experience of early evening support spots in America, "screaming about domestic murder while the audience is eating popcorn. Nothing's happening. It's brilliant".
Q: "When you play the radio onstage during 'Climbing Up The Walls', what are you doing?"

Jonny: "I'm tuning at random. I find two or three classical stations and two or three talking stations at the soundcheck and use them during the gig. I know what kind of music it is advance - I don't want 'Size Of A Cow' to come out during the show." [laughs]
Among the more random moments on OK Computer are, the use of transistor radio noise and tape loops on 'Climbing Up the Walls'. (Yorke: "Whenever there was tape all over the studio floor, I knew things were going well.")
Part of the soundcheck of 'Climbing Up The Walls' from december 19th 1997 at the taping for MTV's 'Live from the 10 Spot' in New York can be seen in Meeting People Is Easy:

Ed briefly remembered recording the strings for 'Climbing Up The Walls' in one of the entires of his online diary:
wednesday, december 1st 1999
phil is presently putting down drums on 'how to disappear' - we're doing a demo of the song to present the song to an 'orchestral fella'. we've kind of shirked away from strings in the past as they seem to have been recorded in the same manner for the last 30 years (ever since the beatles). jonny is particularly keen to use an orchestra but not in the standard cliched way........more like the end of 'climbing up the walls'. thom's vocal on it was jaw-dropping. it's very strange to be playing that song again as we played it frequently on the ok computer tour.......................... suddenly you're back there.
This live performance comes from august 15th 2006, it's a rare soundboard recording: