The numbers on the Cornell page are out of date and the fact all the references at the bottom are from 2001-2008 also reinforce this.
The "Cornell page" is a reproduction of the relevant section of the Internal Revenue Code, as amended from time to time. The fact that that section of the statute has not been amended since 2008 does not mean that the page is "out of date". The page is not out of date. It is current.
Did I mess something up here? Why does link #2 show that IRC 415 (c)(1)(A) is stated as $40,000? ...
If you read the entire statute, you'll notice that it provides that "The Secretary [of the Treasury] shall adjust annually ... the $40,000 amount in subsection (c)(1)(A), for increases in the cost-of-living in accordance with regulations prescribed by the Secretary".
26 USC § 415(d)(1)(C).
As I have noted in many past posts,
neither the IRS nor the Secretary has the power to amend statutes. When the Secretary implements the cost-of-living adjustments as provided by law, the text of the statute will not change. That does not mean that the statute is "out of date". It
does mean, however, that the text of the statute will not directly tell you the latest value.
According to the regulations promulgated by the Secretary in exercise of the authority previously mentioned, the canonical source of truth for the latest value is actually the Internal Revenue Bulletin. See
26 CFR 1.415(d)-1(a)(1)(i). The most recent figure is found in
IRB No 2015-46 at *668 ("The limitation for defined contribution plans under § 415(c)(1)(A) remains unchanged in 2016 at $53,000."). I leave it as an exercise to find the figures for past years.