I do not care of a variable length message, but am looking for the least complex irreducible computation hash for a block header. Message wrapping should be in an other logical layer either.

Here is what I get for a special pattern 80 byte input attempting to produce 32 bytes of hash after 5N length. It still fails.

Sounds alchemy. You just hope that length in binary representation is not a specific pattern as above.

In degenerate cases you would even need 5N, see below for 010101... initial conditions

I run quite a few initial conditions to see that the slope is far from trivial, see example:

I see no safe lower bound for the slope yet.

Here you are from Wolfram, "Sensitivity to initial conditions"

https://www.wolframscience.com/nksonline/page-251?firstview=1

Exactly. See the slope question I raised before.

It appears that neither of us had the right intuition. I plotted the effect of a bit on the outer right side. The question is: What is the slope of the yellow line?

I have not seen the proof for above, yet. It is only your intuition against mine.

You see below that the hash is already part of the right side of an R30 evolution and that every bit of it has input from every bit of the value to be hashed.

Excuse, but that sounds arbitrary to me.
I am looking for the least complex but irreducible hash, and am not convienced that "mixing back" would be needed.

Does not "seem" to hurt.

Note that R30 has an apparent asymmetry in its "chaos".

The below pictures hint that left and right side of an input do not receive the same "kind" of hashing. Likely irrelevant, but puzzling.

This sounds weak. This is the path to perceived security through perceived complexity, the thinking how SHA probably was constructed.

If there is really something with R30, then below should be sufficient.

I think Satoshi's solution to the Byzantine General's problem is the first real world application of Wolfram's computational irreducibility, since doing an irreducible computation is the ideal proof of work.

My intuition says that known attacks to hash functions are only special cases of reducibility checks and a computationally irreducible function must be resistant of them by definition.

Maybe SHA256 is also computationally irreducible, it is however more likely that irreducibility of an R30 hash will be rigorously proven, than that of SHA256.

It is desirable to use the least complex irreducible computation for proof of work, as that leaves least room for implementation differences. If R30 is irreducible then it is also the least complex of such.

Note that computation of the below area is sufficient.

Wolfram's computational irreducibility, if exists, defines the perfect proof of work, therefore the discussion is on spot here or better in an alt-coin forum.

I think that a simple POW algorithm eliminates the risk of possible shortcuts that might exist in complex algorithms like the SHA group.

Stay tuned. You'll have a choice soon.

a. there is some near abusive use of the service
b. a configuration change was made yesterday in an attempt to reduce race conditions that lead to problems a few times during last days, this change was not implemented consistently and lead to major disruption tonight. This is now corrected.

Services are back normal now and we work on addressing the race conditions.

Block chain data does not compress impressively on a global scale, but indices on addresses and tx hashes do.

Bits of Proof stores both the block chain data and supplementing indices in LevelDB and achieves high performance in retrieving transactions referring an arbitrary HD master key, that is why it powers the myTREZOR web wallet.

I am sure it could be further optimized with your ideas, so let me know if you'd like to discuss them in that scope.

If you are interested in alt currency use of myTREZOR and have good connections in those communities please contact me for a port of the Bits of Proof backend.

There was an edge case were transactions were not reported to the UI, this should now be fixed.