Michael Darius Eastwood · Independent AI alignment researcher
Published
The claim is a unification. Different research communities have independently derived variations of an exponent of roughly d over (d plus 1) for their own scaling laws: metabolism scales with mass to a fractional power in biology, city productivity scales super-linearly with population in urban economics, cortical wiring scales sub-linearly with brain volume in neuroscience. Claim 4 is that these are not coincidences but special cases of the same underlying constraint. If a system's growth is generated by recursive composition and its aggregation rule satisfies Cauchy's functional equations, the exponent it settles on is not arbitrary; it is forced by the dimensionality of the process. The unification is what the claim owns. The bare exponent itself is prior art, treated separately in Claim 11.
Paper VII lays the derivation out formally, invoking all four Cauchy functional equations as the joint constraint. The test protocol asks whether independently sourced exponents from twenty-five domains, drawn after the derivation was fixed, sit inside the predicted family. Nineteen out of twenty-five did, with a binomial p-value of approximately 1.56 × 10 to the −5 against a chance rate of one family in three, roughly a 4.2 sigma signal in the raw counting. The Cauchy letter, a plain-language write-up sent to Lloyd Demetrius (Harvard) and Geoffrey West (Santa Fe Institute) on 24 March 2026, is the programme's engagement attempt with the two most relevant living theorists of scaling. The email hash is on the evidence page. No reply has been received to date.
Two caveats matter. The first is that the bare exponent is not being claimed as original: prior derivations by West, Brown and Enquist (1997), Banavar and colleagues (1999 and 2010), Demetrius (2003, 2006, 2010), He and Chen (2003), Bettencourt (2013) and Maino and colleagues (2014) are older than this work and are cited by name in Paper VII. What is original is the argument that these separate derivations reduce to Cauchy-constrained recursive composition with a boundary condition set by the domain. The second is that the empirical test used the programme's own operator classification, not an external one. The falsification contract asks for a re-run under blinded classification by a different lab.
An independent classifier from outside the programme takes a fresh set of at least twenty-five domains not in the original fifty, applies the blinded operator classification packet, and tests whether the predicted family is chosen at above-chance rates. If eighteen or more of twenty-five are classified correctly at p<0.01, the claim is confirmed. If twelve or fewer come out correct, statistically indistinguishable from chance, the unification is refuted and the exponent convergence returns to being an unexplained regularity of nature rather than a consequence of Cauchy structure. Every value used in the current test is available for audit, and the professors named above remain welcome to correct any part of the derivation on the record.
From the book Infinite Architects: Intelligence, Recursion, and the Creation of Everything by Michael Darius Eastwood.