Chemistry Photodissociation3 From Jcost Photodiss3 Cert

What the certificate proves

Photodissociation is the process where a molecule absorbs light and breaks apart into smaller fragments. A quantum yield measures how often that breakup happens per photon absorbed. The declaration Photodiss3Cert is a machine-checked certificate inside the Recognition Science framework's library of formal theorems. It packages three proved facts about a cost function, and it is honest about what those facts do not cover.

The cost function here is Jcost, a recognition cost: a number that measures the price of a recognition event, forced by five plain conditions to equal J(x) = (x + 1/x)/2 - 1. The certificate defines a domain cost as Jcost applied to a ratio m/e, where m and e are positive real numbers. It then proves three general facts. First, when m equals e, the cost is zero. Second, for any positive m and e, the cost is never negative. Third, the number phi - 3/2, where phi is the golden ratio, is positive. These are the three fields of the certificate structure, and each is backed by a theorem in the library.

The certificate's own docstring is explicit: it proves nothing specific to photodissociation. The variables m and e are just real numbers; nothing in the definitions ties them to molecular mass or photon energy. The research note attached to the module records an intended direction, where phi_diss = J(phi) times a ratio of cross sections might give about 0.118 for typical organic molecules, but that is a research note, not a proved result. The three theorems hold for any positive ratio, which is why they are general.

What the certificate does establish is a reusable template. Any subject that can define its own m and e in physically meaningful terms inherits these three facts for free. For photodissociation, that step remains open: no definition connects m and e to molecular properties. The certificate is a scaffold, not a measurement.

theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  unfold domainCost; rw [div_self h]; exact Jcost_unit0

theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  unfold domainCost; exact Jcost_nonneg (div_pos hm he)

theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  unfold canonicalThreshold; linarith [phi_gt_onePointFive]

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

What this page does not claim

No claim that photodissociation quantum yield is measured or predicted by the certificate. No claim that m and e refer to molecular mass or photon energy. No claim that the research note's estimate 0.118 is a proved result.

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/Photodissociation3_FromJCost.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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