Chemistry Photodissociation3 From Jcost

Photodissociation yield

Photodissociation is the process in which a molecule absorbs a photon and breaks apart into smaller fragments. Its efficiency is the quantum yield, the number of bond-breaking events per photon absorbed. For many ordinary organic molecules, that yield sits near 0.118, a value chemists measure in the laboratory.

In Recognition Science, the framework models this yield with its cost function. The cost, a measure of the forced price of recognition, is written J(x) and takes its smallest value, zero, when its input equals one. The framework defines a domain cost as J applied to a ratio m/e, where m and e are quantities from the chemistry. It proves three general facts about this cost: it vanishes when m equals e, it never goes below zero for positive inputs, and the golden-ratio constant phi minus 3/2 is positive. These are properties of the cost function itself, not of any particular molecule.

The framework is honest about its reach. It defines the ratio m/e without specifying what m and e mean in photodissociation terms. The research note records the intended connection: the yield equals J(phi) times a ratio of cross sections, landing near 0.118. But the formal theorems prove only the general cost facts, not that this chemistry identification is correct. What would turn the framework into a theorem about photodissociation is a definition of m and e in the subject's own terms.

The framework's library states these cost facts once, universally, in a shared template. This framework instantiates that template under a chemistry name. The plain-language takeaway is that the framework supplies a disciplined cost function with clean formal properties, and the chemistry page attaches a physical interpretation to it. The interpretation is a research goal, not a proved result.

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)

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

What this page does not claim

The framework does not prove that photodissociation yields equal J(phi) times a cross-section ratio. The framework does not define what m and e are in photodissociation terms. The framework does not derive the measured quantum yield of 0.118 from first principles.

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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