Return-Path: Received: from smtp1.linuxfoundation.org (smtp1.linux-foundation.org [172.17.192.35]) by mail.linuxfoundation.org (Postfix) with ESMTPS id C90351BB for ; Sun, 30 Aug 2015 20:01:21 +0000 (UTC) X-Greylist: whitelisted by SQLgrey-1.7.6 Received: from mail-lb0-f177.google.com (mail-lb0-f177.google.com [209.85.217.177]) by smtp1.linuxfoundation.org (Postfix) with ESMTPS id EFF8319D for ; Sun, 30 Aug 2015 20:01:20 +0000 (UTC) Received: by lbbtg9 with SMTP id tg9so50884241lbb.1 for ; Sun, 30 Aug 2015 13:01:19 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:from:date:message-id:subject:to:content-type; bh=12oqZgGGdxXmElm+X08IwePNCnIO8uPdbVffGLJ3MUs=; b=pDpIVh8VZmB0k2ex7s1LLRSU9hG+sclEttmn0MXHP/AScs7igcvfh7KGS2Hjor++CP SYZsdzXKPwlmhyn/DcDaVTGYOOke36nItSfiNeZxGWmG8Ma/9IfwLY8gOnyFp0nDTZjG O6scXOrZha7EvmILuKonph23MkXo7DlRwUR8MemNiyRRz/kRi71RvmEkjEeZ2x8wSLKa OHG+vKqR/VXNsHr9lj+IBXqpN9zv6zikYpVGtRyJMZ8LNFIjTfcl71LNlA8MREzrm9wv d8HP/MKyMfX0ECzvQSgdmc8CqSOUMipusbEFviznTHqHccEWpOdWV8/bJC0rgdc1/Ll0 a0sA== X-Received: by 10.112.199.5 with SMTP id jg5mr8922296lbc.57.1440964879452; Sun, 30 Aug 2015 13:01:19 -0700 (PDT) MIME-Version: 1.0 Received: by 10.112.143.229 with HTTP; Sun, 30 Aug 2015 13:01:00 -0700 (PDT) From: Daniele Pinna Date: Sun, 30 Aug 2015 22:01:00 +0200 Message-ID: To: bitcoin-dev@lists.linuxfoundation.org Content-Type: multipart/alternative; boundary=001a11c2432cc6113d051e8cc7a9 X-Spam-Status: No, score=-1.0 required=5.0 tests=BAYES_05,DKIM_SIGNED, DKIM_VALID, DKIM_VALID_AU, FREEMAIL_FROM, HTML_MESSAGE, HTML_OBFUSCATE_05_10, RCVD_IN_DNSWL_LOW autolearn=ham version=3.3.1 X-Spam-Checker-Version: SpamAssassin 3.3.1 (2010-03-16) on smtp1.linux-foundation.org Subject: [bitcoin-dev] ERRATA CORRIGE + Short Theorem X-BeenThere: bitcoin-dev@lists.linuxfoundation.org X-Mailman-Version: 2.1.12 Precedence: list List-Id: Bitcoin Development Discussion List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , X-List-Received-Date: Sun, 30 Aug 2015 20:01:21 -0000 --001a11c2432cc6113d051e8cc7a9 Content-Type: text/plain; charset=UTF-8 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. --001a11c2432cc6113d051e8cc7a9 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Since my longer post seems to be caught in moderator purga= tory I will rehash its results into this much smaller message. I apologize = for the spamming.

I present a theorem whose thesis is obvious to man= y.

THESIS: All hashra= tes=C2=A0h' >= h=C2=A0generate a revenue per unit of hash=C2=A0v' > v.=C2= =A0

Let us absurdly[1] assume th= at an optimal hashrate=C2=A0h=C2=A0exists where= the average revenue for each hash in service is maximized. This will resul= t from perpetually mining blocks of size=C2=A0q,=C2=A0is=C2= =A0v.=C2=A0All larger hashrates=C2=A0h' > h<= /i>=C2=A0will=C2=A0generate=C2=A0an average revenue p= er hash=C2=A0v' < v(effectiv= ely the conclusion of my paper) due to the higher orphan risk carried from = having to mine blocks of size=C2=A0q' > q. Leading from Peter's model and my analysis, the origin of this bal= ance lies in the fact that larger miners must somehow be forced to mine lar= ger blocks which in turn carry a larger orphan risk.=C2=A0

What happens if a large miner=C2=A0h'= =C2=A0chooses not to mine his optimal block size=C2=A0q'=C2=A0in favor of a seemingly "sub-optimal" bl= ock size=C2=A0q?
Since he mines a block of id= entical size as the smaller miner, they will both carry identical orphan ri= sks[2], and win identical amountsR+M(q)=C2=A0whenever they su= ccessfully mine a block. Since the larger miner can statistically expect to= win=C2=A0h'/h=C2=A0more blocks than the smaller miner, t= hey will each earn an identical revenue per unit of hash=C2=A0R+M(q)/= h.=C2=A0

This however directly contradicts the assumption that an opti= mal hashrate exists beyond which the revenue per unit of hash=C2=A0v' < vif=C2=A0=C2=A0h'= > h.=C2=A0
Q.E.D=C2=A0=

This theorem in turn implies the following cor= ollary:

<= div class=3D"gmail_extra" style=3D"font-size:12.8000001907349px">COROLLARY:=C2=A0The marginal profit curve is a monoto= nically increasing of miner hashrate.

= This simple theorem, suggested implicitly by Gmaxwell disproves any and all= conclusions of my work. Most importantly, centralization pressures will al= ways be present.=C2=A0

=
Furthermore,=C2=A0<= /div>

[1]=C2=A0http= s://en.wikipedia.org/wiki/Reductio_ad_absurdum
[2] Orphan risks will actual= ly 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 m= atter. I stand by for any further comments and questions.

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