user10845: A 2015 draft BIP suggested using a "hard fork bit":

The most significant bit in nVersion is defined as the hardfork bit. Currently, blocks with this header bit setting to 1 are invalid, since BIP34 interprets nVersion as a signed number and requires it to be >=2 (with BIP66, >=3). Among the 640 bits in the block header, this is the only one which is fixed and serves no purpose, and therefore the best way to indicate the deployment of a hardfork.

https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2015-July/009576.html
If bit indexes increase from left to right, then I imagine the hard fork bit occupying index 31, marked as * below (nVersion is a 32-bit value).
0                   1                   2                   3
0|1|2|3|4|5|6|7|8|9|0|1|2|3|4|5|6|7|8|9|0|1|2|3|4|5|6|7|8|9|0|1
                                                              *

According to the proposal, setting bit 31 of nVersion should cause a block to be rejected as invalid.
BIP-9 places further constraints on the available bits, specifically, bits 0-2 must be set as [0, 0, 1]:

Blocks in the STARTED state get an nVersion whose bit position bit is set to 1. The top 3 bits of such blocks must be 001, so the range of actually possible nVersion values is [0x20000000...0x3FFFFFFF], inclusive.

https://github.com/bitcoin/bips/blob/master/bip-0009.mediawiki
In addition, BIP-9 arranges version bits in increasing order from right to left. That is, version bit 0 is nVersion bit 31, version bit 1 is nVersion bit 30, and so on.
But if this were the case, then version bit 0 would be off-limits. BIP-9 says nothing about this, and in fact BIP-68 was signaled using version bit 0:

This BIP is to be deployed by "versionbits" BIP9 using bit 0.

https://github.com/bitcoin/bips/blob/master/bip-0068.mediawiki
My questions are simple:

Given my diagram above, which nVersion bit index is the "hard fork bit?"
If I'm correct in my interpretation (I don't believe I am), then how could BIP-68 have been signaled without causing the blocks doing so to be rejected as invalid?

Update: the source of my confusion was thinking that nVersion bit indexing and version bit indexing ran in opposite directions. The don't. To signal readiness for a proposal using version bit 1, for example, nVersion bit 1 is set. BIP-9's rules activate when an nVersion signature is detected. This signature is bits 29-31 set as 1, 0, and 0, respectively. This leaves bit 31 unset.
Peter's answer addresses question (1) above.
As for question (2) BIP-68 signaling didn't cause block rejection because bit 0 was being set, not bit 31.

user208: Bit 31 is sometimes referred to as the hard fork bit.
BIP34 put a constraint on version numbers to be 2 or higher. As the block version is a 32-bit signed integer, setting its highest bit results in a negative number, which would violate BIP34.
As a result, any usage of that bit results in a backward incompatible change to the rules - a hard fork - that is obvious to all participants in the system.

10845: <p>A 2015 draft BIP suggested using a "hard fork bit":</p>

<blockquote>
  <p>The most significant bit in nVersion is defined as the hardfork bit. Currently, blocks with this header bit setting to 1 are invalid, since BIP34 interprets nVersion as a signed number and requires it to be >=2 (with BIP66, >=3). Among the 640 bits in the block header, this is the only one which is fixed and serves no purpose, and therefore the best way to indicate the deployment of a hardfork.</p>
</blockquote>

<p><a href="https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2015-July/009576.html" rel="nofollow noreferrer">https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2015-July/009576.html</a></p>

<p>If bit indexes increase from left to right, then I imagine the hard fork bit occupying index 31, marked as <code>*</code> below (<code>nVersion</code> is a 32-bit value).</p>

<pre><code>0                   1                   2                   3
0|1|2|3|4|5|6|7|8|9|0|1|2|3|4|5|6|7|8|9|0|1|2|3|4|5|6|7|8|9|0|1
                                                              *
</code></pre>

<p>According to the proposal, setting bit 31 of <code>nVersion</code> should cause a block to be rejected as invalid.</p>

<p>BIP-9 places further constraints on the available bits, specifically, bits 0-2 must be set as [0, 0, 1]:</p>

<blockquote>
  <p>Blocks in the STARTED state get an nVersion whose bit position bit is set to 1. The top 3 bits of such blocks must be 001, so the range of actually possible nVersion values is [0x20000000...0x3FFFFFFF], inclusive.</p>
</blockquote>

<p><a href="https://github.com/bitcoin/bips/blob/master/bip-0009.mediawiki" rel="nofollow noreferrer">https://github.com/bitcoin/bips/blob/master/bip-0009.mediawiki</a></p>

<p>In addition, BIP-9 arranges version bits in increasing order from right to left. That is, version bit 0 is <code>nVersion</code> bit 31, version bit 1 is <code>nVersion</code> bit 30, and so on.</p>

<p>But if this were the case, then version bit 0 would be off-limits. BIP-9 says nothing about this, and in fact BIP-68 was signaled using version bit 0:</p>

<blockquote>
  <p>This BIP is to be deployed by "versionbits" BIP9 using bit 0.</p>
</blockquote>

<p><a href="https://github.com/bitcoin/bips/blob/master/bip-0068.mediawiki" rel="nofollow noreferrer">https://github.com/bitcoin/bips/blob/master/bip-0068.mediawiki</a></p>

<p>My questions are simple:</p>

<ol>
<li>Given my diagram above, which <code>nVersion</code> bit index is the "hard fork bit?"</li>
<li>If I'm correct in my interpretation (I don't believe I am), then how could BIP-68 have been signaled without causing the blocks doing so to be rejected as invalid?</li>
</ol>

<p>Update: the source of my confusion was thinking that <code>nVersion</code> bit indexing and version bit indexing ran in opposite directions. The don't. To signal readiness for a proposal using version bit 1, for example, <code>nVersion</code> bit 1 is set. BIP-9's rules activate when an <code>nVersion</code> signature is detected. This signature is bits 29-31 set as <code>1</code>, <code>0</code>, and <code>0</code>, respectively. This leaves bit 31 unset.</p>

<p>Peter's answer addresses question (1) above.</p>

<p>As for question (2) BIP-68 signaling didn't cause block rejection because bit 0 was being set, not bit 31.</p>
 208: <p>Bit 31 is sometimes referred to as the hard fork bit.</p>

<p>BIP34 put a constraint on version numbers to be 2 or higher. As the block version is a 32-bit signed integer, setting its highest bit results in a negative number, which would violate BIP34.</p>

<p>As a result, any usage of that bit results in a backward incompatible change to the rules - a hard fork - that is obvious to all participants in the system.</p>
