I am developing metrics and macro analytics for bitcoin. As a result I need to access the information contained in the blockchain. This resulted in some interesting findings. I use Abe and checked one point on blockchain explorer.

1. The block chain time stamp is non sequential.  I did not think this was possible. I found this when trying to compute the network hashrate using the (t_stamp_i - t_stamp_(i-1))/600*difficulty*4295032833 to find the network hash rate. When I plotted this I had negative numbers, which if the timestamp monotonically increases is not possible.

As an example, blocks 139793 (time stamp 1312599459) and 139792 (time stamp 1312599808) are not monotonically increasing.

How does one determine the appropriate time stamp? And then, estimate the hash rate for each block?

2. I tried to find an explicit function for finding the difficulty (needed in finding the hash rate) Here I used a ratio of the difference in timestamps for blocks 0 to 2015, 2016 to 4031, etc to the 1209600 seconds that it "should" take to find the 2016 blocks. This gives a multiplier for each time step. I then multiplied every previous multiplier to obtain the difficulty for any particular block.  The result is close to the difficulty reported everywhere (1,180,941,214.99 from Abe for current) ( 1,233,468,670.05 by my method). Intuitively the method I used makes sense (I couldn't find a description online that did not involve hexadecimal (sorry I am a base 10 kinda cat) or written in C (I don't program outside of Matlab). Basically every method I found was unintelligible.  My method relies upon accurate timestamps and any accumulated small error will give an erroneous number, and goes back to my first problem.

Any help/explanation here will be appreciated.

The block timestamp is only part of the Bitcoin protocol because an average of it is used for adjusting the difficulty. Nothing about the timestamp affects the selection or propagation of blocks, except for the two hour rule that other miners use.

And in a decentralized system with no central authority to provide a time server that everyone must synchronize with, who gets to decide which timestamp is "right"?

The blockchain provides sequencing in the absence of a reliable source of synchronized time.  Transactions in more recently added blocks "always" occur after transactions in less recently added blocks, regardless of what "time" they happened.

The actual equations that calculate the next difficulty are at line 1000 or so of https://github.com/bitcoin/bitcoin/blob/master/src/main.cpp
The difficulty is recalculated every 2016 blocks based on the average time of the last evaluation period, to maintain the rate of six blocks per hour when network hashing rate changes.

The equations you would use to calculate difficulty depend on what your question is.

"Ways"
...

Miners express their own local view of the time in the timestamps, subject to some constraints of plausibility that don't endanger the decentralized nature of the system. You can freely apply whatever postprocessing you like to these values— or, better, find parties who have already recorded times for them.

It does not do what you want it to do, it does what the system needs it to do.

Would you please reduce your level of nonsense emission?

There hasn't ever been such a situation in Bitcoin. Though I believe some altcoins may have self destructed based on trying to "fix" timestamps as you've outlined.

In any case, if you did want to try to produce a precise consensus "real time", though Bitcoin doesn't— and avoids a lot of unnecessary complexity on account of it— you'd still need a mechanism for participants to express their true opinion about the time, and that metric would not be monotonic.

Providing a source of "centralization".

If any nntp servers differ, they can split and isolate sections of the network.

Seems like a bad idea.

You are assuming that every NNTP server can be trusted.

The whole purpose of bitcoin is to create a way to create a system where you don't have to trust anyone else to engage in a transaction.