Chemistry Photosynthesis3 From Phi Ladder Lhc3 Phi Cert

The certificate's scope

The declaration LHC3PhiCert is a machine-checked certificate, a small bundle of three proved facts about a single mathematical function. That function, cost (a measure of mismatch between two positive numbers), is defined as J(m/e), where J(x) = (x + 1/x)/2 - 1. The certificate proves three things: the cost is zero when the two numbers are equal, the cost is never negative when both numbers are positive, and the number phi - 3/2 is positive. These are general facts about the cost function itself, true for any positive numbers m and e.

What the certificate does not do is connect those numbers to any physical system. The declaration defines domainCost as J(m/e) without ever saying what m and e mean. The name of the module mentions photosynthesis, and a research note in the source file records an intended application: a light-harvesting complex that absorbs at wavelengths following powers of phi, with chlorophyll a at 680 nm and chlorophyll b at 700 nm. But that note is explicitly labeled as a research note, not a result. The certificate proves nothing about chlorophyll, wavelengths, or light harvesting.

The three proved facts are instances of a template shared verbatim with 2383 sibling modules. The content is stated once, universally quantified, in a central module named DomainCostTemplate. Each sibling module, including this one, instantiates the same three theorems without adding subject-specific content. What would make this declaration a theorem about photosynthesis is a definition of m and e in terms of actual molecular quantities: a mass, an energy, a wavelength, or some other measurable property of the light-harvesting complex. No such definition appears in this file.

In plain terms, the certificate is a proof that a certain cost function has three basic properties, and nothing more. It is a valid proof, machine-checked, but its subject is the cost function itself, not chemistry. The photosynthesis connection remains an idea recorded in a comment, awaiting a definition that would turn it into a scientific claim.

theorem cert_inhabited : Nonempty LHC3PhiCert := ⟨cert⟩

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

theorem cert_inhabited : Nonempty LHC3PhiCert := ⟨cert⟩

What this page does not claim

No claim that photosynthesis or light-harvesting complexes obey any cost function. No claim that the ratio 700/680 equals J(phi)^(1/4) is proved; it is only noted in a research comment. No claim that the certificate has any content specific to chemistry beyond the general cost function properties.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Chemistry/Photosynthesis3_FromPhiLadder.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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