MIME-Version: 1.0
Date: Tue, 24 Mar 2026 16:37:39 +0000
Message-ID: <CAGPsKAnX1wxQGN_2YRqt-4BZgei5-Q+AwHc1i173spyLNR265Q@mail.gmail.com>
Subject: Your two derivations of d/(d+1) are both correct - and Cauchy's
 theorem (1821) proves why they must converge
From: Michael Eastwood <michael@michaeldariuseastwood.com>
To: [redacted-third-party], [redacted-third-party]
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Dear Professor Demetrius and Professor West,

Please find attached a letter addressing a connection between your two
independent derivations of the metabolic scaling formula alpha = d/(d+1).

I also attach two papers:

1. 'On the Origin of Scaling Laws' (v3.1) - the dimensional ladder,
Friedmann mapping, geometric speed limit, and the explanation of why your
derivations converge through Cauchy's functional equation.

2. 'The Cauchy Unification' (Paper VII, v3.0) - a 50-domain empirical test
of the Cauchy classification (19/25 confirmed, p = 1.56 x 10^-5).

All code, data, and the domain manifest are publicly available:
- Research hub: https://www.michaeldariuseastwood.com/research/
- OSF: https://osf.io/6c5xb (DOI: 10.17605/OSF.IO/6C5XB)
- GitHub: https://github.com/MichaelDariusEastwood/arc-principle-validation

I would be deeply grateful for your assessment. If either of you sees a
flaw, I would rather hear it from you than discover it in print.

With great respect for what you have both built,

Michael Darius Eastwood
Independent Researcher, London
michael@michaeldariuseastwood.com
michaeldariuseastwood.com/research

Raise AI with care.

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<div dir=3D"ltr">Dear Professor Demetrius and Professor West,<br><br>Please=
 find attached a letter addressing a connection between your two independen=
t derivations of the metabolic scaling formula alpha =3D d/(d+1).<br><br>I =
also attach two papers:<br><br>1. &#39;On the Origin of Scaling Laws&#39; (=
v3.1) - the dimensional ladder, Friedmann mapping, geometric speed limit, a=
nd the explanation of why your derivations converge through Cauchy&#39;s fu=
nctional equation.<br><br>2. &#39;The Cauchy Unification&#39; (Paper VII, v=
3.0) - a 50-domain empirical test of the Cauchy classification (19/25 confi=
rmed, p =3D 1.56 x 10^-5).<br><br>All code, data, and the domain manifest a=
re publicly available:<br>- Research hub: <a href=3D"https://www.michaeldar=
iuseastwood.com/research/">https://www.michaeldariuseastwood.com/research/<=
/a><br>- OSF: <a href=3D"https://osf.io/6c5xb">https://osf.io/6c5xb</a> (DO=
I: 10.17605/<a href=3D"http://OSF.IO/6C5XB">OSF.IO/6C5XB</a>)<br>- GitHub: =
<a href=3D"https://github.com/MichaelDariusEastwood/arc-principle-validatio=
n">https://github.com/MichaelDariusEastwood/arc-principle-validation</a><br=
><br>I would be deeply grateful for your assessment. If either of you sees =
a flaw, I would rather hear it from you than discover it in print.<br><br>W=
ith great respect for what you have both built,<br><br>Michael Darius Eastw=
ood<br>Independent Researcher, London<br><a href=3D"mailto:michael@michaeld=
ariuseastwood.com">michael@michaeldariuseastwood.com</a><br><a href=3D"http=
://michaeldariuseastwood.com/research">michaeldariuseastwood.com/research</=
a><br><br>Raise AI with care.<br><br></div>

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