Subject: [bitcoin-dev] ERRATA CORRIGE + Short Theorem

From: Daniele Pinna <[email-masked]>
Date: Sun, 30 Aug 2015 22:01:00 +0200

Since my longer post seems to be caught in moderator purgatory I will
rehash its results into this much smaller message. I apologize for the
spamming.

I present a theorem whose thesis is obvious to many.

*THESIS: All hashrates* *h' > h generate a revenue per unit of hash v' >
v. *

Let us absurdly[1] assume that an optimal hashrate *h* exists where the
average revenue for each hash in service is maximized. This will result
from perpetually mining blocks of size *q,* is *v. *All larger hashrates *h'
> h* will generate an average revenue per hash *v' < v*(effectively the
conclusion of my paper) due to the higher orphan risk carried from having
to mine blocks of size *q' > q*. Leading from Peter's model and my
analysis, the origin of this balance lies in the fact that larger miners
must somehow be forced to mine larger blocks which in turn carry a larger
orphan risk.

What happens if a large miner *h'* chooses not to mine his optimal block
size *q' *in favor of a seemingly "sub-optimal" block size* q*?
Since he mines a block of identical size as the smaller miner, they will
both carry identical orphan risks[2], and win identical
amounts*R+M(q)* whenever
they successfully mine a block. Since the larger miner can statistically
expect to win *h'/h* more blocks than the smaller miner, they will each
earn an identical revenue per unit of hash *R+M(q)/h*.

This however directly contradicts the assumption that an optimal hashrate
exists beyond which the revenue per unit of hash *v' < v*if  *h' > h. *
*Q.E.D *

This theorem in turn implies the following corollary:

*COROLLARY: **The marginal profit curve is a monotonically increasing of
miner hashrate.*

This simple theorem, suggested implicitly by Gmaxwell disproves any and all
conclusions of my work. Most importantly, centralization pressures will
always be present.

Furthermore,

[1] https://en.wikipedia.org/wiki/Reductio_ad_absurdum
[2] Orphan risks will actually favor the larger hashrate miner leading to
greater revenues per unit of hash.

I thank the dev-list for its valuable time and exchange on the subject
matter. I stand by for any further comments and questions.